[CHEMISTRY]: Chapter 2: Gases-- Kinetic Molecular Theory (KMT)
Mnemonic for diatomic molecules...
"I Have No Bright Or Clever Friends" : hydrogen, nitrogen, fluorine, oxygen, chlorine, iodine, and bromine
What are the main points to kinetic molecular theory (KMT)?
1. All matter consists of particles: either atoms or molecules 2. All particles are in constant motion 3. Their collisions are perfectly elastic; meaning they bounce back 4. For ideal gases only: the forces between particles are negligible, meaning small enough to be ignored. 5. The kinetic energy of a gaseous particle is directly proportional to the temperature of a gas
Why does an increase in temperature also increase pressure?
By heating a gas, you add kinetic energy to the particles; as a result, the particles collide with greater force upon other objects, so those objects experience greater pressure.
What is the pressure and temperature for SATP?
101.3 Kpa, 298K, according to the textbook
How do we convert from one pressure unit to another?
101.3 kPa = 1 atm
What is the equivalent of all units of pressure?
101.3 kPa = 700 mm Hg = 1 atm...
How is the relationship between volume and temperature in Charles' Law represented?
V ∝ T or T ∝ V
Avogadro's Law: Represent the directly proportional part.
V ∝ n
Molar volume: Under certain conditions (meaning STP, SATP), the volume of any gas could be simply calculated through what?
a molar volume ratio.
Test Q: A balloon vendor wishes to fill the greatest number of balloons from his helium tank. Each balloon is to have a volume of 2 liters. What would be the best atmospheric conditions to inflate the maximum number of conditions?
- A high temperature results in a greater volume (inflation) since temperature is directly proportional to volume (numerator is directly proportional to denominator...)... This is also Charles' Law... - A low pressure results in an increased volume, since pressure is inversely proportional to volume (numerator is inversely proportional to other numerator)... this is also Boyle's Law...
Explain the following phenomenon using the particle model of matter: A hydroplane can easily fly through a cloud and can also land on the surface of a lake.
- All matter is composed of particles (ions, atoms or molecules) that are infinitely small with more or less space between them depending on their phase. - Particles of matter attract or repel each other, and the force that attracts or repels them from each other varies depending on the distance that separates them
Explain the following phenomenon using the particle model of matter: Fishing on a lake in the winter requires a little more effort since the ice must be broken.
- All matter is composed of particles (ions, atoms or molecules) that are infinitely small with more or less space between them depending on their phase. - Particles of matter attract or repel each other, and the force that attracts or repels them from each other varies depending on the distance that separates them (since the ice is in its solid phase)
What are examples of diffusion?
- Distribution of perfume where it is sprayed in one part of a room, yet soon you can smell it everywhere. - Movement of a drop of food coloring in a glass of water, where eventually the entire glass will be colored. - Making tea, where molecules from the tea cross the tea bag and spread out into the cup of water. - Shaking salt into water. The salt dissolves and the ions move until they are evenly distributed. - Lighting a cigarette, where the smoke spreads to all parts of a room. - Placing a drop of food coloring onto a square of gelatin, so that eventually the color will spread to a lighter color throughout the block. - Carbon dioxide bubbles diffuse from an open soda, leaving it flat. - If you place a wilted celery stick in water, water will diffuse into the plant, making it firm again.
How is the translational motion of particles different from the other two forms of motion?
- With translation, there's more freedom of movement - In translation, a molecule simply moves in a straight line from one collision to the next, whereas in rotation, a molecule can rotate on the x, y, and z axis. In vibration, there are three modes in which an object can vibrate in: symmetrical and asymmetrical stretching as well as bending.
What allows solids to have their own shape and to occupy a defined volume?
- due to the forces that exist between them. - the position of particles results from an equilibrium between these forces - particles cannot slide against each other and change the shape of the solid, since the forces that bind them are very difficult to modify.
Describe the graph for Avogadro's Law. What is on the axes? Where does the line start? What is the title? Which quadrant is it and why?
- x axis: # of moles (mol) - y-axis: Volume (L) - Line starts at (0,0) See notes for how the line looks for this law as well as all other laws... - Title: V vs. n (y vs. x) - Only first quadrant because you can't have negative values.
Also put units for factor of change
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Always make sense of your answers for the simple gas laws (so for example if it makes sense that one is greater than the other).
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Always put down your units throughout the formula and in the answer for the simple gas laws.
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Always put your units down for a formula/Law
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Charles' Law and Gay-Lussac's Law: Always convert your temperature to kelvin by adding 273 to your degrees Celsius value.
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For Graham's Law: v₁/v₂ = √M₂/M₁ , divide first, then square root.
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Must know about STP and SATP, what they stand for and what's their kelvin and temperature.
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The maximum variation means the difference: Final - Initial.
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Use "ANS" on calculator if the value is something like 33.33333333.... especially for factor of change so that it is accurate.
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At STP, 2 mol has a volume of what?
1 mol = 22.4 L, so 2 mol x 22.4 = 44.8 L (it is a ratio)
Molar mass is the mass of what?
1 mole
Molar volume is the volume of what?
1 mole
Dalton's Law: A mixture of He, Ne and Ar gases have a total pressure of 105.0 kPa. If there is 15% Ar, 60% He and 25% Ne, what is the partial pressure of each gas?
1. Argon will take up 15% of the total pressure (105.0 kPa), Helium will take up 60% of the total pressure, and Neon will take up 25% of the total pressure... so, convert your percentages to decimals and multiply it with 105.0 KPa...: P(Ar) = 0.15 x 105.0 kPa = 15.75 kPa P(He) = 0.60 x 105.0 kPa = 63 kPa P(Ne) = 0.25 x 105.0 kPa = 26.25 kPa *What's in brackets should be written as a subscript... If you add them all together: 15.75 kPa + 63 kPa + 26.25 KPa, then it should equal the total, = 105.0 kPa.
In what three ways do particles vibrate?
1. Bending 2. Asymmetric stretching; uneven stretching in/out 3. Symmetric stretching; even stretching in/out See my textbook homework drawing!
A 25.0 mL sample of oxygen is collected at a temperature of 90 K and a pressure of 100 kPa. What volume will the oxygen have when its temperature reaches 75 kPa? By what factor did the pressure change? What's the factor of change for the volume?
1. Collect your data: V = 25.0 mL T = 90 K P = 100 kPa T = 75 kPa V = ? Since it is asking for volume, and the only gas law that has both volume and pressure is Boyle's Law: P₁V₁ = P₂V₂. It is not Gay-Lussac's law because it doesn't have volume in it and that's what the question is asking for. 2. Use the formula. Always put down your units! Isolate. P₁V₁ = P₂V₂ ^Initial = ^ Final (easiest way to think of it) 100 kPa x 25 mL = 75 kPa x V₂ V₂ = 33.333333... mL Here you see that as pressure decreases, the volume will increase. The numbers show this. 3. Factor of change = Final value / Initial value (for the pressure) 75 kPa . 100 kPa = 0.75 BUT it is preferred that you put into fraction form so you could see that volume and pressure are inversely proportional: 3/4 4. Factor of change = Final value / Initial value (for the volume) 33.3333 mL/24.0 mL = 1.33333.... or 4/3. Notice how the fractions are flipped? That's because the factors (pressure and volume) are inversely proportional.
Test Q: A weather balloon is filled with 200 L of helium at a temperature of 23°C and a pressure of 98.3 kPa. After the balloon rises 12 km into the stratosphere, the temperature decreases to -60°C and the pressure decreases to 0.112 kPa. What will be the new volume of the weather balloon?
1. Compile your data V1 = 200 L T1 = 23 + 273 = 296 k P1 = 98.3 kPa T2 = -60 + 273 = 213 k P2 = 0.112 kPa V2 = ? The formula used is not something we've learned! We can't solve it using Charles' Law because pressure is NOT a constant in this problem! This was a trick question!
Textbook example pg. 79: A sample of helium (He) gas is collected at ambient temperature in a 2.5 L elastic rubber ball at normal atmospheric pressure. The ball is then immersed in a container of water, also at room temperature, such that the external pressure exerted on its walls increases to 110.6 kPa. What is the final volume of the ball?
1. Compile your data: "ambient" temperature-- it is SATP because SATP stands for Standard AMBIENT TEMPERATURE and pressure T₁/₂ = will stay constant at 298 k, because room temperature is also 298 k V₁ = 2.5 L P₁ = at normal atmospheric pressure, that is 1 atm = 101.3 kPa P₂ = 110.6 kPa V₂ = ? 2. Use Boyle's Law: P₁V₁ = P₂V₂ 101.3 kPa x 2.5 L = 110.6 kPa x V₂ V₂ = 2.3 L is the final volume of the ball
The pressure of a gas at 100 kPa rises from 20 degrees Celsius to 85 degrees Celsius. What is its new pressure?
1. Compile your data: P₁ = 100 kPa T₁ = 20 degrees Celsius + 273 k = 293 k T₂ = 85 degrees Celsius + 273 k = 358 k 2. Since we're missing P₂, we use Gay-Lussac's Law: P₁ / T₁ = P₂ / T₂ 100 kPa/ T₁ = P₂ / 293 k = P₂ / 358 k P₂ = 122 kPa
Textbook pg. 98 #21. A ball is filled with a given of hydrogen (H₂) at 22°C. The volume of the ball is 18.4 L at this point. The ball is then submerged in water and its volume increases by one quarter. What is the temperature of the water?
1. Compile your data: T1 = 22 degrees + 273 K = 295 k V1 = 18.4 L V2 = increases by one quarter... 18.4 x 1/4 = 4.6, 18.4 + 4.6 = 23 L T2 = ? 2. Use Charles' Law: V₁/T₁ = V₂/T₂ 18.4 L / 295 k = 23 L / T2 T₂ = 368.75 k
A gas at 200 K occupies 1.45 L. What volume does it occupy at 250 k? What do you notice about the new volume?
1. Compile your data: T₁ = 200 K V₁ = 1.45 L T₂ = 250 k V₂ = ? 2. Use the formula, Charles' Law, and isolate: V₁/T₁ = V₂/T₂ Initial = Final 1.45 L / 200 K = V₂ / 250 K V₂ = 1.8125 L Notice how V₂ is bigger because temperature is greater and they're proportional, so the new volume will also be greater.
What are the different behaviors of gases?
1. Compressibility 2. Expansion 3. Diffusion, Effusion (Graham's Law)
Test Q: Last winter, the internal pressure for the tires on a car was set at 175 kPa when the temperature was -30°C. According to the manufacturer's recommendations, the internal pressure for these tires should not exceed 250 kPa. The following summer, the wheels on this car were misaligned. Given this defect and the relatively high temperature of the asphalt on the roads in the summer, the temperature of the tires could have risen above 85°C. If the temperature of the tires reaches 85°C, will the internal pressure correspond to the manufacturer's recommendation? Explain your answer.
1. Convert right away to kelvin -30 + 273 = 23 k 85 + 273 = 358 k 2. Compile your data: P1 = 175 kPa T1 = 23 k P2 = ? It is not 250 kPa because we need to check if the internal pressure exceeds 250 kPa and will thus correspond to the manufacturer's recommendation. T2 = 358 k 3. Use Gay-Lussac's Law: P₁ / T₁ = P₂ / T₂ 175 kPa / 23 k = P2 / 358 k P2 = 257.83 kPa 4. Answer: Since the internal pressure exceeds 250 kPa, no, it will not.
Textbook example pg. 83: A 28.7 mL sample of oxygen gas is collected in a glass syringe at SATP. The syringe is placed in an oven at 65°C until the gas attains the temperature of the oven. What volume will the oxygen occupy if the atmospheric pressure in the oven is the same as outside the oven? If the syringe can contain a volume of 50 mL, will the mobile piston be able to retain the gas inside?
1. Convert right away to kelvin: 65°C + 273 k = 338 k At SATP... that's 298 k 2. Compile your data: V₁ = 28.7 mL T₁ = 298 k V₂ = is what we need to find because we need to find out if the mobile piston will be able to retain the gas inside T₂ = 338 k Since they say the atmospheric pressure will be constant, we do not use Boyle's Law, nor Gay-Lussac's Law. 2. Use Charles' Law: V₁/T₁ = V₂/T₂ 28.7 mL /298 k = V₂/338 k V₂ = 32.6 mL Answer: yes, since V₂ is lower than 50 mL, the mobile piston will be able to retain the gas inside.
Molar Volume: What volume is occupied by 40 g of methane gas, CH₄, at STP?
1. Find the number of moles of methane gas: n = m/M = 40 g/16 g/mol (always indicate your units throughout your formula and in final answer...) = 2.5 mol CH₄ 2. Since it says STP, simply do the molar volume ratio: 22.4 L/1 mol = x L/2.5 mol = 56 L
Stoichiometry: Potassium, K, oxidizes to form potassium oxide, K₂O. If 19.5 g of potassium are oxidized, what mass of potassium is formed? 4K + O₂ → 2K₂O
1. Find the number of moles of potassium: n = m/M = 19.5 / 39 = 0.5 mol K 2. Use molar ratio: From balanced equation Your calculations 4 mol K / 2 mol K₂O = 0.5 mol K / x mol K₂O x = 0.25 mol K₂O 3. Solve the problem: m = n x M = 0.25 mol x 94 g/mol = 23.5 g of K₂O
Stoichiometry and Gas Laws: Potassium, K, oxidizes to form potassium oxide, K₂O. If 19.5 g of potassium are oxidized at STP, what volume of oxygen gas, O₂, is consumed? 4K + O₂ → 2K₂O
1. Find the number of moles of potassium: n = m/M = 19.5 g / 39 g/mol = 0.5 mol of K. 2. Use molar ratio: 4 mol K/1 mol 0₂ = 0.5 mol K / x mol O₂ = 0.125 mol of O₂ 3. Solve the problem. We will use n = PV/RT because we're given STP. Plug in your info: V = 0.125 mol x 8.31 kPaL/molK x 273 K / 101.3 kPa V = 2.8 L Or, since you're given STP, and as a recap from molar volume: STP --> 22.4 L/mol, we can do a MOLAR VOLUME RATIO...: 22.4 L / 1 mol = x / 0.125 mol = 2.8 L
Test Q: A 7.6 L tank, fitted with a manometer, contains an unknown gas. We vary the temperature and then determine the pressure of the gas. The graph shows the result (basically it is a line passing through zero: we have the following points: (250, 400), (275, 450), (300, 500), (325, 550), where on the x-axis it shows temperature (in Kelvin), and on the y-axis it shows pressure (in kPa) If the tank is stored at a temperature of 27°C and it contains 26 g of gas, identify the gas from among the following. H₂, NH₃, N₂, CO₂, SO₂, Cl₂
1. Identify your variables: Initial... V= 7.6 L From a point of the graph, we can obtain: T (K) = 300 K P = 500 kPa We will NOT use the general gas law because we don't have enough information, not even if were to cancel out. So therefore we must use the ideal gas law: PV = nRT P = 500 kPa V = 7.6 L n = ? R = 8.31 kPaL/molK T = 300 K Isolate for n: n = PV/RT n = 500 kPa x 7.6 L / 8.31 kPaL/molK x 300 K n = 1.52 mol of an unknown gas Then we can solve for the molar mass to help identify our gas...: M = n/M M = 1.52 mol / 26 g M = 17.1 g/mol You'd calculate all the molar masses of the gases given, and see that M = 17.1 g/mol matches up with NH³ N x molar mass of N found on PT 3 x molar mass of H found on PT = 17.1 g/mol Ask Dad why the 27°C is irrelevant.
An unknown gas takes 192 seconds to effuse through a porous barrier, while the same volume of nitrogen (N₂) effuses across the same barrier in 84 seconds. The conditions of temperature and pressure are identical for the two gases. What is the molar mass of the unknown gas?
1. Notice how temperature and pressure are constants, so we use Graham's Law because T and P are excluded from the formula and we're also dealing with time. v₁/v₂ = √M₂/M₁ 2. The 192 seconds and 84 seconds is NOT a rate, it is a time. In order to convert it to m/s, we put it as: x / 192 and x/84. The "x" will represent the # of meters in those 192 and 84 seconds. 3. v₁/v₂ = √M₂/M₁ x/192 / x/84 = √28 g/mol/M₁ You may enter it in your calculator as... 1/192 ÷ (1/84) (7/16)² = 28 g/mol/M2 Or Convert it to decimal so that it is easier to square root... 0.4375² = 28 g/mol/M2 0.19 = 28 g/mol/M2 Cross multiply... = 146.29 g/mol of the unknown gas Ask Dad how we would get the # of meters (if it is possible)?
Test Q: A cylinder of oxygen (O₂), is left in a hot car. The cylinder has a volume of 10 L and contains 5 moles of oxygen. If the cylinder can withstand a pressure of 20.7 atm, what is the highest Celsius temperature to which the cylinder can be safely exposed?
1. Write down your info: V = 10 L n = 5 moles P = 20.7 atm 2. Since the problem doesn't mention a change in variables, we can use the ideal gas law since the ideal gas law is used when there's no initial/final conditions...: PV = nRT 20.7 atm x 10 L = 5 mol x 0.082 atmL/molK x T T = 504.8 K - 273 K = about 232 degrees Celsius
A container possesses 3L internal volume. This volume is divided equally in two by a gas-tight seal. On one half of the seal, neon gas resides at 5 atm. The other half of the container is kept under vacuum. Suddenly and with great fanfare, the internal seal is broken. What is the final pressure within the container?
2.5 atm. Under the initial conditions, gas at 5 atm resides in a 1.5L volume. When the seal is removed, the entire 3L of the container becomes available to the gas, which expands to occupy the new volume. Predictably, its pressure decreases. To calculate the new pressure, P2, plug in the known values and solve: P2 = (5 atm × 1.5L) / 3L = 2.5 atm The final volume is 3 L because at first, the initial temperature is 1.5 L since the volume is split in half. But once the seal breaks, the final volume is 3 L. The pressure at 1.5 L is 5 atm, as they say, and vacuum means that the pressure is 0 atm... So, V1 = 1.5 L, P1 = 5 atm and V2 = 3 L. Plug this into the P1V1 = P2V2 (Boyle's Law) formula.
Molar volume: At STP, 1 mol of any gas has a volume of what?
22.4 L... (MEMORIZE...)
What is the molar volume at SATP?
24.5 L/mol (MUST MEMORIZE...)
What is STP's pressure and temperature?
273 k and and 101.3 kPa
What is room temperature in kelvin?
298 k...
What is the absolute temperature of 5?
5 k, kelvin
What is velocity?
A RATE of speed. Example: m/s, not just meters (or seconds)
The properties of a gas can be altered by changing what conditions? The relationship between the variables are described in what?
A. Pressure, P B. Volume, V (upper-case V) C. Temperature, T (upper-case T) D. Quantity of gas (# of moles, n) The relationship between the variables are described in the simple gas laws.
What is the lowest temperature possible?
Absolute 0 (i.e. 0 kelvin); Absolute zero is the point at which the fundamental particles of nature have minimal vibrational motion
Gay-Lussac's Law: What is the relationship?
Absolute temperature is directly proportional to pressure.
What are three important points from the particle model of matter?
According to this model: - All matter is composed of particles (ions, atoms or molecules) that are infinitely small with more or less space between them depending on their phase. - Particles of matter attract or repel each other, and the force that attracts or repels them from each other varies depending on the distance that separates them - Particles of matter are always moving
What is ∝ ?
Alpha symbol- is "directly proportional to". For inversely proportional, it's, for example: P ∝ 1/V
What's the difference between atoms and molecules?
An atom is just that, a single atom, made from protons, neutrons and electrons. A molecule is a group of atoms bonded together via ionic, metallic or covalent bonding.
What is an ideal gas?
An ideal gas is a theoretical gas composed of many randomly moving point particles that do not interact except when they collide elastically.
What is an ideal gas? What behaviors must they exhibit?
An ideal gas is any gas that exhibits the following behaviors: 1. All collisions between atoms or molecules are perfectly elastic, meaning that they bounce back/rebounds. They also retain their kinetic energy. 2. There are no intermolecular attractive forces.
Describe Gay-Lussac's Law.
An increase in temperature results in an increase in a molecule's kinetic energy and velocity. If molecules are moving faster, then the force of their impact upon colliding with another molecule will increase as well. As temperature increases, the number of collisions increase, and so pressure increase (pressure is the amount of force exerted on a given area). A decrease in temperature results in a decrease in a molecule's kinetic energy and velocity. If the molecules are moving slower, then the force of their impact upon colliding with another molecule will decrease. As temperature decreases, the number of collisions decrease, and so pressure decreases.
What are ions?
Atoms that gain or lose electrons in an attempt to complete their outer shell.
What is the effect of pressure on states?
As temperature and pressure change, an element can be pushed over the boundary from one phase to another. Typically, low temperatures and high pressures promote solid forms, and high temperatures and low pressures promote gaseous forms. Liquids occupy the middle ground. High pressure causes heat to be released. If you compress a gas, it gets hot and tries to lose heat for pressure to go down. If you have a hot cylinder, the heat is going to escape from it because the gas is going to cool down. If you compress the gas, after loosing the heat, it could turn into a liquid or solid. It looses the heat to the environment. Tends to become a liquid or solid. Now you made it so dense that the molecules don't have much room and they will behave like molecules like a liquid or solid. That's how you get liquid nitrogen from nitrogen gas. That's also how you get dry ice from carbon dioxide from compressing carbon dioxide. Similarly, if you cool it down without compressing it it will turn into a liquid or solid. When you compress, the temperature could still be the same as the room but it has lost heat.
Explain Boyle's Law.
As the volume of a gas decreases, gas particles move closer to one another. The number of collisions will increase and this increases the pressure. Also, as the volume of a gas increases, gas particles are further apart. The number of collisions decreases and so does the pressure.
At the same temperature, how would the pressure of an ideal gas differ from that of a gas with mutually attractive particles? How would it differ from that of a gas with mutually repulsive particles?
At a given temperature, an ideal gas would exert greater pressure than a gas with mutually attractive particles and lower pressure than a gas with mutually repulsive particles. On average, mutual attraction allows particles to occupy a smaller volume at a given kinetic energy (since they're going to want to stick together), while mutual repulsion causes particles to attempt to occupy a larger volume (since they're going to be farther apart)
Why can you smell perfume?
Because of effusion, if the door were closed and there was a slit at the bottom, let's say. It's also diffusion and because gases can translate. Gases are also very far apart so they can mix with other gases (diffusion). Gases are very small too, which allows them to effuse.
As temperature increases, volume increases. How does this explain SATP?
Compared to STP, where the volume is equal to 22.4 L/mol, at SATP, the temperature increases. Therefore since temperature and volume are proportional, the volume will increase since in SATP, the temperature is increased to 298 k (compared to 273 k).
Test Q: Neon gas is pumped inside glass tubing to make a "neon sign" for a video arcade. The glass tubing has a volume of 2.40x10² mL and the gas exerts a pressure of 3.60x10² kPa. The same mass of neon gas, at the same temperature, is used to make another sign with a volume of 6.30 x 10² mL. How much pressure would be exerted by the neon gas?
Compile your data: V1 = 2.40 x 10² mL P1 = 3.60 x 10² kPa Molar mass is constant, and so is temperature. V2 = 6.30 x 10² mL Use Boyle's Law: P₁V₁ = P₂V₂ 3.60 x 10² kPa x 2.40 x 10² mL = P2 x 6.30 x 10² mL P2 = 137.14 kPa
In Boyle's Law, what must be constant?
Constant means roughly the same (doesn't change). Temperature and the number of moles must be constant for Boyle's Law.
What's the difference between Dalton's Law and Dalton's Law of partial pressure?
Dalton's Law: P(total) = P(a) + P(b) + P(c)... PT = total pressure of the mixture PA, PB, PC: partial pressure for each individual gas in the mixture. The letters following P must be subscripts and are usually replaced by elements/compounds... , which states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of each of the component gases Dalton's Law of partial pressure: PT / nT = PA/nA = PB/nB = ... , which states that the partial pressure of a gas is proportional to the number of moles of that gas in the gaseous mixture.
How do we convert from Celsius to Kelvin?
Degrees in Celsius + 273 = Kelvin temperature (MUST KNOW...)
All matter is composed of particles (ions, atoms or molecules) that are infinitely small with more or less space between them depending on their phase. How does the phase change with the distance between the particles?
The closer the particles are to one another, the more solid it is.
What does diffusion and effusion have anything to do with Graham's Law?
Different gases diffuse at different rates, depending on their molar masses (see Chapter 7 for details on molar masses: I'm guessing in the chemistry workbook for dummies). The rates at which two gases diffuse can be compared using Graham's Law. Graham's Law also applies to effusion, the process in which gas molecules flow through a small hole in a container. Whether gases diffuse or effuse, they do so at a rate inversely proportional to the square root of their molar mass. In other words, more massive gas molecules diffuse and effuse more slowly than less massive gas molecules.
What is diffusion? (Workbook definition)
Diffusion is the movement of a substance from an area of higher concentration to an area of lower concentration. Diffusion occurs spontaneously, on its own. Diffusion leads to mixing, eventually producing a homogenous mixture in which the concentration of any gaseous component is equal throughout an entire volume. Of course, that state of complete diffusion is an equilibrium state; achieving equilibrium can take time.
In a mixture of gases, 35% of it is composed of methane gas. If the partial pressure of methane is 55 kPa, what is the total pressure?
Do proportions: 35% / 100% = 55 kPa / x x = 157.14 kPa...
Trick for molar formulas.
Do the triangle thing, it becomes: "mothers not Mothers"
When temperature goes on the x-axis, is it in Celsius or kelvin?
Either. If it is in degrees Celsius, then the x-intercept is -273. Ask Dad how the "k" would change when getting two points? Would we convert the slope to kelvin or the values of the two points? Answer: Yes, wouldn't matter whether you convert the x and y values or just the slope to kelvin because you're still adding 273.
What is the formula for kinetic energy?
Ek = 1/2mv² Ek is the kinetic energy, measured in Joules m is the Molar Mass of the element or compound v is the velocity; will never be asked to solve for velocity
Formula for factor of change
Final Value / Initial Value = Factor of Change
Which of the following statements is false according to the kinetic theory of gases? Gas particles have a kinetic energy that is proportional to their temperature. Gas particles are minuscule compared to the size of the container that they are in. Gas particles are spread out so that they are far away from each other. Gas particles always move in an upward direction
Gas particles have a kinetic energy that is proportional to their temperature: true Gas particles are minuscule compared to the size of the container that they are in: true; particles are infinitely small Gas particles are spread out so that they are far away from each other: true Gas particles always move in an upward direction: False; they can also move in a downward direction so long as they move in a translational, rotational and vibrational motion
Explain gas particles with kinetic energy.
Gas particles have a lot of kinetic energy, and constantly zip about, colliding with one another or with other objects. This is a complicated picture, but scientists simplified things by assuming that all the motions of the particles were random, that the only motion was translation (moving from place to place, as opposed to twisting, vibrating, and spinning), and that when particles collided, the collisions were elastic (perfectly bouncy, with no loss of energy).
Which of the following will increase the number of collisions between gas molecules in a container? Increasing the size of the container. Letting some of the gas out of the container. Heating the gas. Bringing the container up a mountain where there is less atmospheric pressure.
Heating the gas. It is not the last choice because: if the container is closed, the atmospheric pressure doesn't affect the number of collisions. So in this case, it is closed because the answer doesn't include that. But, if the container were opened, then there is less pressure at altitude, so there will be fewer collisions.
Trick to knowing capital/lower-case letter V, v?
Look at the second letter of the word...: VElocity, therefore lower-case (e occurs first before o in the alphabet), and VOlume, therefore capital V.
Is kelvin a capital letter or lower-case letter?
It's a capital letter: "K"...
Which of the following occurs when a gas is heated? Its molecules gain more kinetic energy. It condenses to a liquid. It causes all of the bonds to get broken. It turns into plasma.
Its molecules gain more kinetic energy. Plasma by the way is The state of matter that does not have a definite shape or volume and is made up of electrically neutral particles...
What are the different formulas for moles?
MEMORIZE... 1. n = m/M 2. n = PV/RT 3. n = C x V
To what temperature must a gas in a rigid container be heated in order to double the pressure it exerts at 20°C?
Make up your own numbers for this. So for example, we have: P₁ = 9 kPa P₂ will be doubled, so 9 x 2 = 18 kPa T1 = 20 degrees Celsius + 273 K = 293 K, it is the initial temperature because they want to know the final temperature after you heat it up T2 = ? Use Gay-Lussac's Law to solve, should get 586 K
Gases can be diatomic. What does that mean? Give examples.
two atoms; I₂, H₂, N₂... two of the same atom
An amateur entomologist captures a particularly excellent ladybug specimen in a plastic jar. The internal volume of the jar is 0.5L, and the air within the jar is initially at 1 atm. The bug-lover is so excited by the catch that he squeezes the jar fervently in his sweaty palm, compressing it such that the final pressure within the jar is 1.25 atm. What is the final volume of the ladybug's prison?
Not going to solve, but just know that you keep your pressure values the same at 1 atm, no need to convert to kPa... but you can, using proportions, convert to kPa...
A teacher combines hydrogen gas at 125 kPa and neon gas at 235 kPa and carbon dioxide at 325 kPa. What is the total pressure of the mixture?
Just add all your values: 125 kPa + 235 kPa + 325 kPa = 685 kPa...
Charles' Law: The temperature of a gas is measured in what?
Kelvin
In kinetic molecular theory, what is the temperature measured in? What is this called?
Kelvin degrees; absolute temperature
What are the units for pressure?
Kilopascal, kPa (the k and a are lower case, with P being upper-case), and the atmosphere, atm. The units could be either of them as long as they're consistent.
Ice floats in water. Based on the usual assumptions of kinetic theory, why is this weird?
Kinetic theory describes matter as moving from solid to liquid phase (melting) as you add energy to the sample. The added energy causes the particles to undergo greater motion, and to collide with other particles more energetically. Usually, this means that a liquid is less dense than a solid sample of the same material, because the greater motion of the liquid particles prevents close packing. Solid water (ice), on the other hand, is less dense than liquid water because of the unique geometry of water crystals. Because solid water is less dense than liquid water, ice floats in water.
Inversely proportional graph
Know how the graph looks! And know where P and V goes on the axes. The dependent variable is normally on the x-axis, while the independent variable is on the y-axis. Usually the x-axis is the independent variable and the y-axis is the dependent variable. That means that pressure is a function of x, since P is on the y-axis and V is on the x-axis. They are related to each other, it's not that one depends on the other.
Rank the four gases from slowest to fastest: CH₄, CO₂, Ar, Cl₂
Lightweight molecules will move faster than heavier molecules. Therefore, find the molar mass of each molecule: CH₄: M = 16 g/mol CO₂: M = 44 g/mol Ar: M = 40 g/mol Cl₂: M = 70 g/mol From slowest to fastest, the order is: Cl₂, CO₂, Ar, CH₄
Textbook pg. 97 #16. A syringe with a maximum volume of 60.0 cm³ takes in a 14.5 cm³ sample of oxygen (O₂) gas at 24.3 °C. What maximum variation in temperature does the oxygen undergo before the piston is completely pushed out of the syringe?
Maximum variation means the difference in temperature... 1. Compile your data: V1 = 14.5 cm³ V2 = 60.0 cm³, since it is the maximum volume T1 = 24.3°C, must convert to kelvin...: 24.3 + 273K = 297.3 k 2. Use Charles' Law: V₁/T₁ = V₂/T₂ 14.5 cm³ / 297.3 k = 60.0 cm³/T₂ Cross multiply T₂ = 1230.21 k Maximum variation: 1230.21 k - 297.3 k = 932.91 k
How can gases be?
Monatomic, diatomic, or in compound
Do particles lose kinetic energy by colliding with each other? Explain why or why not.
No because the collisions are perfectly elastic, meaning that they bounce back
Are the forces negligible for water? Explain.
No; for water, the forces between particles are NOT negligible. Water doesn't play by the rules and in fact there are many unique things about water.
CONTINUE WITH THE ABOVE EXAMPLE
Ok
Know STP, SATP (the temperature, what it stands for, and pressure...)
Ok
See Dad's math on chemistry Q's in binder about the inversely proportional part.
Ok
Simple gas laws won't be given for exams...
Ok
Describe the math behind Charles' Law.
On a graph, it's a directly proportional graph, meaning it's a positive-sloped line passing through (0,0). V (volume) is on the y-axis and T (temperature) is in kelvin and is on the x-axis. Ask Dad why. And the title of the graph is V vs. T (Ask Dad why). There is no y-intercept in this graph. Must be in the first quadrant because it would be impossible to have negative values. The slope is always constant (the same) for that line. Let's say we take two points: (T₁,V₁) and (T₂, V₂) and also (0,0) Calculate the slope for both: a = V2 - 0 / T2 - 0 = k or a = V1 - 0 / T1 - 0) = k So generally V / T = k *the "k" is the same number for both!
When temperature is kept constant (notice how T, temperature, is excluded from the Boyle's Law formula), the pressure and volume of a gas are inversely proportional to one another. What equation represents this? Explain.
P ∝ 1 / V This is because the V is on the x-axis and the P is on the y-axis. Basically, P = 1/V.
What is the formula for Dalton's Law? What do the components represent?
P(total) = P(a) + P(b) + P(c)... PT = total pressure of the mixture PA, PB, PC: partial pressure for each individual gas in the mixture. The letters following P must be subscripts and are usually replaced by elements/compounds...
What is Dalton's Law of partial pressure? What do its components represent?
PT / nT = PA/nA = PB/nB = ... *The subscripts following P and n should be written as subscripts... Where: PT = total pressure PA and PB = partial pressures of gases A and B within the mixture nT = total # of moles in gas mixture nA and nB = # of moles of each gas in the mixture
By analyzing the general gas law, we can notice that what?
PV ∝ nT or in other words, numerator ∝ denominator
What is the formula for the ideal gas law?
PV=nRT
Explain the following phenomenon using the particle model of matter: Milk spreads throughout a cup of coffee.
Particles are always moving
Explain the following phenomenon using the particle model of matter: Water vapor can mix with air to make it humid.
Particles are always moving and particles of matter attract or repel each other, and the force that attracts or repels them from each other varies because in this situation there's a change of phase
What size are particles? Explain.
Particles are infinitely small; not measurable by any instrument, but they're still present.
Explain the following phenomenon using the particle model of matter: The smell of skunk spray seeps into a house even when the windows are closed.
Particles of matter are always moving and are infinitely small because they can move through small spaces.
Avogadro's Law: What are the constants? What do "constants" mean?
Pressure and temperature, meaning that they're the same value.
What relationship does Boyle's Law deal with?
Pressure and volume
Gay-Lussac's Law
P₁ / T₁ = P₂ / T₂ *Temperature must be in Kelvin
What is the formula for the General Gas Law?
P₁V₁/(n₁T₁) = P₂V₂/(n₂T₂) MUST PUT BRACKETS ON DENOMINATOR!... Also, when things are constant, just elimate them from the formula....
What are the units for Boyle's Law?
Recall that Boyle's Law is: P₁V₁ = P₂V₂. The units don't matter. Pressure must be in either kPa or atm. Volume can be in any unit. Just be consistent with the units.
At a given temperature, the rate of diffusion of oxygen gas is 0.82 m/s. Find the rate of diffusion of neon gas at this temperature.
Recall that Graham's Law states that when temperature and pressure are constant (notice how these variables are not in the formula), the rate at which a gas moves (DIFFUSION or effusion) is inversely proportional to the square root of the molar masses. 1. Use the formula: v₁/v₂ = √M₂/M₁ 2. Find the molar masses: Oxygen gas: 32 g/mol Neon: 20 g/mol 3. Plug in your values to the formula. Doesn't matter whether you say Neon is 1 or 2 (same thing for the velocity's)... Just make sure it corresponds to V's subscript. Same thing for oxygen gas. ALWAYS PUT DOWN YOUR UNITS. v₁/v₂ = √M₂/M₁ 0.082 m/s/v₂ = √20g/mol/32g/mol DIVIDE FIRST, THEN SQUARE ROOT: V₂ = 0.10 m/s for neon Neon is lighter, so it's moving faster than oxygen gas. If you look at both velocity values, it makes sense.
Charles' Law: When temperature is in Celsius, what is the x-intercept?
Recall that for this law, the temperature (in kelvin) goes on x-axis. The x-intercept will be -273 because you must add 273 to Celsius to convert any temperature to kelvin.
What is the molar volume at STP? At SATP? MUST MEMORIZE...
STP: 22.4 L/mol SATP: 24.5 L/mol
At STP, a gas occupies 0.5 L in a rigid ball. What pressure will the nanometer display if the ball is submerged in a container filled with water at 20°C?
STP: P₁ = 101.3 kPa, T₁ = 273 k T₂ = 20°C + 273 k = 293 k P₂ = ? Use Gay-Lussac's Law to solve
What are the constants in Gay-Lussac's law?
Since Gay-Lussac's law is the relationship between temperature and pressure, the constants will be the volume and the number of moles. So whatever is excluded from the formula.
Dalton's Law: P(total) = P(a) + P(b) + P(c)... what happens to the P(total) if the number of moles is halved?
Since P is directly proportional to the number of moles, then the P will be halved, too (ask Dad if correct).
How does the disorder of a gas compare to that of a liquid or solid? Explain.
Since gas particles move freely, the gas phase is extremely disorderly compared to the liquid phase (which is less so) and the solid phase (where there is very little disorder).
Test Q: What happens to the pressure of a gas when its volume is doubled and the temperature is changed from 100°C to 50°C?
Since pressure and volume are inversely proportional to one another, if the volume is doubled, the pressure will be halved (or, in other words, decreased by a factor of 1/2). The temperature part is something we haven't learned yet, but keep it here for later...
What is the change in the pressure if the temperature in Kelvin is tripled? Assume that the number of moles and volume are constant.
Since temperature and pressure are directly proportional, then the pressure will triple as well. It is 3 times its original value.
Mystery Gas A effuses 4.0 times faster than oxygen. What is it the likely identity of the Mystery Gas?
Since we're talking about effusion, we will use Graham's Law since effusion ties into Graham's Law. It is as follows: v₁/v₂ = √M₂/M₁ Let's start with what we know, that being the molar mass of oxygen gas: it is a gas because gases can effuse (and diffuse). It is a physical property of a gas. Liquids can also diffuse and effuse. 16 g/mol Like the previous example, we'll only apply the second part of the formula with the factor change... A lightweight gas will move faster, that's why you divide 32 by 16. If it said that it moved 4 times slower, then you would do 32 x 16 = 512 g/mol, because a heavier molecule will effuse slower. 4 = √32/M₁ Square the four to get rid of the square root 16 = 32/ M1 M1 = 2 g/mol, which is hydrogen gas... It is always a gas because we're dealing with effusion/diffusion. So for chapter 2, everything is in gas so long as it's part of the mneumonic: "I Have No Bright Or Clever Friends" : hydrogen, nitrogen, fluorine, oxygen, chlorine, iodine, and bromine
How much faster does hydrogen gas effuse than neon gas?
Since we're talking about effusion, we will use Graham's Law since effusion ties into Graham's Law. It is as follows: v₁/v₂ = √M₂/M₁ Let's start with what we know, that being the molar masses: H₂ = 1 x 2 = 2 g/mol Ne (there is no "Ne₂"): 20 g/mol We also know that Graham's Law deals with an inversely proportional relationship, so apply the second part of the formula; DO NOT FORGET TO SQUARE ROOT... AND MAKE SURE THE GREATER VALUE GOES ON TOP OF THE SMALLER VALUE... √(20/2) = 3.2 So, dihydrogen effuses 3.2 times faster than neon.
Boyle's Law: What is the general equation for the graph representing P vs. V? Explain.
Since xy = a (OR y = a/x, simply cross multiply), and since P is on the y-axis and V is on the x-axis, you have P x V = k. This means that for every point on the graph, when you multiply P and V, you'll always get the same answer of the k value. Remember that "k" means temperature that is measured in kelvin. And remember that in Boyle's Law, the temperature is constant-- that's why it's always the same answer of the k value. For example, you have the following points: A (V1, P1) --> V1 x P1 = k B (V2, P2) --> V2 x P2 = k EXACT SAME "k" VALUE!
Categorize the phases of matter according to the degree of disorder of the particles that compose the matter. Start with the phase with the least disorder.
Solid, liquid, gas In a solid, the particles are uniformly placed. In a gas, they're a bit all over the place and very far from one another. In a liquid, it's a little bit of both.
Particles of matter attract or repel each other, and the force that attracts or repels them from each other varies depending on the distance that separates them. In which state will the force of attraction be stronger? Weaker?
Solids will have the strongest force of attraction. Liquids will have a strong force of attraction. Gases will have a negligible force of attraction.
Since V ∝ n, that means that...
V/n = k. So if you take two points and you get the slope, that's y/x, so V/n = k, the slope, which is always the same value (and it is temperature in Kelvin).
What does SATP stand for?
Standard Ambient Temperature and Pressure
What does STP stand for?
Standard Temperature Pressure
What does STP stand for? Must know this...
Standard Temperature and Pressure
Represent Gay-Lussac's Law mathematically.
T ∝ P. Ask Dad if it can be P ∝ T. Answer: It can. *T must be in Kelvin P is on the y-axis and T is on the x-axis (Ask Dad why). Again, it's a straight line that passes through (0,0). X and y are not necessarily the same value because the scale on the axes can be different. If one doubles, the other doubles as well. If we take two points: (0,0) with (T1, P1) or (T2, P2) a = P2 - 0 / T2 - 0 = k a = P1 - 0 / T1 - 0 = k *Pick your points in order (x1, y1, x2, y2) *k is the same value. The equation for the graph can be represented with: P / T = a (like in the formula, but in the formula "a" is not there, but they are equal to each other because of the same k value):
Test Q: At 20°C, a syringe contains a given volume of oxygen gas, O₂, at a pressure of 100 kPa. When the temperature is raised to 40°C while the pressure is kept constant, the volume of gas stabilizes at 20 mL. What is the initial volume of gas in the syringe?
T1 = 20 + 273 = 293 k P1 = 100 kPa, which stays constant, so this means that P2 will ALSO be 100kpa. Since pressure is a constant, the formula used will NOT include pressure. T2 = 40 + 273 = 313 k V2 = 20 mL Use Charles' Law: V₁/T₁ = V₂/T₂ V₁/293 k = 20 mL/313 k V1 = 18.72 mL
If the gas being studied is an ideal gas, then the constant is equal to what?
TWO CONSTANTS: R = 8.31 kPaL/molK = 0.082 atmL/molK
An unknown gas is collected in a 250 mL container which is then sealed. Using electronic instruments, the gas inside the container is found to exert a pressure of 135.5 kPa at 15°C. What pressure would the gas exert if the temperature in kelvin (K) is doubled?
The constant is volume: 250 mL because they do not describe a change in volume. P₁ = 135.5 kPa T₁ = 15°C + 273 k = 288 K T₂, temperature is doubled: 288 K x 2 = 576 K P₂ = ? Use Gay-Lussac's law to solve for P₂.
What relationship does Charles' Law explore? Explain.
The directly proportional relationship between volume and absolute temperature. As one increases, the other increases as well, and vice-versa.
If: A (V1, P1) --> V1 x P1 = k B (V2, P2) --> V2 x P2 = k EXACT SAME "k" VALUE! Then what is Boyle's Law?
V1 x P1 = V2 x P2 OR you could write it as: P₁V₁ = P₂V₂. It's just in alphabetical order this way. Since the k value will be the same, you could just equate the two together (P1, V1, P2, V2)
A cup of water is put into a freezer and cools to the solid phase within an hour. The water remains at that temperature for six months. After six months, the cup is retrieved from the freezer. The cup is empty. What happened?
The frozen water sublimed, moving directly from a solid to a gaseous state. This process occurs slowly at the temperatures and pressures found within normal household freezers, but does occur.
What are ideal gases?
The gas particles were assumed to neither attract nor repel one another. Gases that actually behave in this simplified way are called ideal
Lab demo: The heat from the hot plate transformed its heat energy to the water inside the can, warming the water which turned into air (water vapor) and causing the air to be less dense. How did this affect what happened to the can?
The heat caused the metal of the can to be softer and more malleable since the metal was conducting heat.
Lab demo: What effect did the heat from the hot plate have on the contents of the can?
The heat from the hot plate transformed its heat energy to the water inside the can, warming the water which turned into air (water vapor) and causing the air to be less dense. Less dense = warmer
Test Q: A balloon is filled with an ideal gas and the initial pressure is recorded. Then, the absolute temperature is tripled, the volume is tripled, and the number of moles is tripled. What best describes the final pressure of the gas?
The ideal gas law is: PV = nRT If we isolate P, we get: nRT/V = P Ask Dad why the final pressure is 3 times higher. So I guess these are all directly proportional to P? What about volume? Isn't the volume supposed to make the pressure decrease?
Lab demo: Describe the contents of the can after the heating process.
The inside of the can had warm air (not just H₂O, other gases as well), water vapor and hot water.
Dalton's Law: Describe the relationship.
The partial pressure of a gas is proportional to the number of moles of that gas in the gaseous mixture.
What is the kinetic energy like in a liquid and gas?
The particles within a liquid are much closer together than those in a gas. As a result, applying pressure to a liquid does very little to change the volume. The particles still have an appreciable amount of kinetic energy associated with them, so they may undergo various kinds of twisting, stretching, and vibrating motions. In addition, the particles can slide past one another (translate) fairly easily, so liquids are fluid, though less fluid than gases. Fluid matter assumes the shape of anything that contains it. The state of matter with the least amount of kinetic energy is the solid. In a solid, the particles are packed together quite tightly and undergo almost no translation. Therefore, solids are not fluid. Matter in the solid state may still vibrate in place or undergo other low-energy types of motion, however, depending on its temperature (in other words, on its kinetic energy).
What is cm³?
a unit for volume
Workbook explanation of Boyle's Law
The relationship makes good sense in light of kinetic molecular theory. At a given temperature and number of particles, more collisions will occur at smaller volumes. These increased collisions produce greater pressure. And vice versa.
What type(s) of motion do liquid molecules undergo?
vibration and rotation. Rotation can occur on any axis; x, y, z
Plasma
The state of matter that does not have a definite shape or volume and is made up of electrically neutral particles
How does the temperature and pressure affect the states?
The temperatures and pressures at which different types of matter switch between states depend on the unique properties of the atoms or molecules within that matter. Typically, particles that are very attracted to one another and have easily stackable shapes tend toward condensed states. Particles with no mutual attraction (or that have mutual repulsion) and with not so easily stackable shapes tend toward the gaseous state. Think of a football game between fiercely rival schools. When fans of either school sit in their own section of the stands, the crowd is orderly, sitting nicely in rows. Put rival fans into the same section of the stands, however, and they'll repel each other with great energy
The rate of effusion of an unknown gas is estimated at 43.0 mL/min. Under the same conditions, the rate of effusion of pure carbon dioxide is 32.0 mL/min. What is the molar mass of the unknown gas? Before you calculate anything, which gas is going to be faster and what does this imply?
The unknown gas is moving faster,therefore the molar mass is going to be lighter because of the inversely proportional relationship between velocity and molar mass. Since we're talking about rates, let's use the Graham's Law: v₁/v₂ = √M₂/M₁ Find the molar masses first 43.0 / 32.0 = √44 g/mol /M₁ 1.34375² = 44/M1 (divide the left side, then square the left side to get rid of the square root) 1.806 = 46/M1 M1 = 25.47 g/mol
How is the ideal gas law different from the other gas laws?
There are no initial/final conditions. Whatever the problem describes, it is happening at one time.
Avogadro's Law: Two cylinders are used to store different gas samples. If each cylinder is at 273 K and 100 kPa, which cylinder is larger? Cylinder A contains 16 grams of oxygen gas, O₂. Cylinder B contains 16 g of neon gas, Ne.
This is a theory question. Notice how temperature and pressure are constants here, therefore it is Avogadro's Law because these variables are excluded in the formula. We know that volume is directly proportional to the number of moles. So all you need to do is find the molar mass of each, find the number of moles, and the one with the greater number of moles is the one with the greater volume since volume and the number of moles are directly proportional. Explain this on a test... (that they are proportional). Molar of oxygen gas: 32 g/mol, n = 0.5 mol M of Neon: 20 g/mol, n = 0.8 mol Neon gas has the greater volume.
Describe the graph for the general gas law. What can we deduce from this graph?
Title: PV vs nT x-axis: nT (molK) (n x T) y-axis: PV (kPaL) Line: straight and goes through (0,0) Since PV vs nT provides us with a direct variation function, then the slope, PV/nT is a constant, k: PV/nT = k (it's like doing y2-y1/x2-x1 = a)
General Gas Law: A 100 g sample of carbon dioxide, CO₂, is placed into a 1.5 L balloon at 20°C and 100 kPa. The balloon is then brought outside at a temperature of 27°C and a pressure of 1.1 atm. If 10 g of the carbon dioxide has escaped from the balloon, what is its new volume?
Trick: List all your values as such: P1: 100 kPa V1: 1.5 L n1: m/M = 2.27 mol T1: 20 + 273 = 293 K P2: 101.3 kPa x 1.1 atm = 111.3 kPa V2: Unknown n2: n/m = 2.05 mol T2: 27 + 273 = 300 K 1. Find the number of moles for carbon dioxide using n = m/M. 2. "10 g escaped" : 100 g - 10 g = 90 g, so calculate the number of moles (n2) using 90 g. 3. Plug values into formula and isolate V2. Fairly obvious on how to solve.
True or false: All particles are in constant motion.
True
Prove that the pressure doubles when the volume is halved.
Use this equation: P = 1/V, P = 1 / 1/2, P = 2
Prove that the pressure is halved when the volume is doubled.
Use this equation: P = 1/V, P = 1/2
What does upper-case V represent? Lower-case v? Lower-case t? Upper-case T?
Volume, V. Velocity, v. Time, t (not in one of the simple gas laws). Temperature, T (in one of the simple gas laws)
Jacques Charles's ghost attempts to inflate his sagging celestial hot air balloon with short bursts from a burner. The initial volume of the balloon is 300L (ghosts don't require large balloons). Trying to impress the passing spirit of a recently departed séductrice, Jacques lets fly a long burst from the burner. The long burn increases the temperature of the air within in the balloon from 40.0°C to 50.0°C. How much does the balloon inflate?
V₁ = 300 L T₁ = 40 + 273 = 313 k T₂ = 50 + 273 = 323 k Charles' Law: V₁/T₁ = V₂/T₂ 300 L / 313 k = V₂ / 323 k V₂ = 309.58 L
What is the formula for Charles' Law? What are the constants?
V₁/T₁ = V₂/T₂. The constants are pressure and # of moles.
What is the formula for Avogadro's Law? What are the units?
V₁/n₁=V₂/n₂ n is in moles, mol. V can be anything, but it has to be consistent. So it can be in L, ml, and cm³.
What kind of relationship in Boyle's Law? What must be kept constant?
When temperature is kept constant (notice how T, temperature, is excluded from the Boyle's Law formula), the pressure and volume of a gas are inversely proportional to one another.
Lab demo: What happened to the soda can at the end of the demonstration? Why did it implode?
When the soda can was placed in the water bath, no air is able to go in or out of the can. As the can experiences a drop in temperature because of the water which is colder than the can that has just been heated up, the pressure inside the can also goes down as a result, therefore the pressure of the water in the water bath is great enough to crush the can. Pressure and temperature are directly proportional (Gay-Lussac's Law). Pressure is defined as the amount of force exerted on a given area. The pressure DIFFERENCE (which is going to be very big because of hot vs. cold) between the inside of the can and the outside of the can is what caused it to implode. Also, when the can is placed in the water bath, the steam inside the can condenses and takes less room, which makes the pressure in the can drop. There's less steam/gas inside the can, so there's less pressure inside the can because the steam has been condensed, but the volume of the can is still the same.
Describe the relationship between volume and temperature in Charles' Law.
When the temperature of a gas is increased, the energy of the particles will increase. This increase in energy results in an increase in the particle's speed, resulting in more collisions with greater force (also resulting in an increase in pressure).(The gas particles will move farther out and push wall even more and occupies more space). When the molecules move at a greater speed, they move further from one another and take up more space; thus results in an increase in volume because the particles will want to take up more space. Volume affects how close they are to one another. The reverse is true.
What type(s) of motion do gases undergo?
vibration, translation, and rotation
Graham's Law
v₁/v₂ = √M₂/M₁ (square root applies to both M₂ and M₁) v: velocity; usually m/s, though the units are not important BUT must be consistent M: molar mass
Will carbon dioxide and helium have the same kinetic energy? What has to be the same in order for them to have the same kinetic energy?
While they both have a different molar mass, velocity is what makes them the same. The velocity won't be the same number either, but it according to how heavy/lightweight the molecules are, will move at their own velocity but will ultimately equal to the same average kinetic energy. They bounce off of each other and they transfer Ek to each other. Energy never gets lost, only converted or transferred (like in this case).
The distance between gas particles is very large. What does this allow?
a given quantity of a gas can be compressed into a smaller volume (compressibility)
What is stoichiometry?
a method of problem-solving that makes use of the law of conservation of matter
Dalton's Law: The partial pressure of CO₂ in a mixture of gases is 0.9 atm. The total pressure of the mixture is 1.2 atm. a) What % of the mixture is carbon dioxide? b) There are a total of 5 moles of gas in the mixture. What mass of carbon dioxide is present?
a) Do a ratio: 100% / x = 1.2 atm . 0.9 atm (since 100% of the pressure is 1.2 atm) x = 75% b) PT / nT = PCO₂ /nCO₂ *The letters and CO₂ following P should be subscripts... 1.2 atm / 5 mol = 0.9 atm / nCO₂ nCO₂ = 3.75 mol OR you could do: 0.75 x 5 mol = 3.75 mol m = n x M m = 3.75 mol x 44 g/mol m = 165 g
Since gases translate, they can collide with other particles or the walls of their container. These collions do what?
apply force
How is pressure defined?
as the amount of force exerted on a given area.
Lightweight molecules move faster or slower than heavier molecules?
faster
At a given temperature, the molecules of ALL gases have the same what?
average kinetic energy. So it doesn't matter which gas/element/compound it is, it will always be the same
What is a gas' volume determined?
by their container, not by the size of individual molecules
Since gases translate, what can they do?
collide with other particles or the walls of their container.
What does the property of expansion allow a gas to do? Explain.
fill up any space since they can move randomly in any direction
What is kinetic energy?
energy of motion
At 25°C, a gas has a pressure of 700 mm Hg. If the container is heated to 50°C, what is the final pressure exerted by the gas?
mm Hg is just another unit for pressure... T₁ = 25°C + 273 k = 298 k P₁ = 700 mm Hg T₂ = 50°C + 273 k = 323 k P₂ = ? Use Gay-Lussac's Law to solve
We measure the quantity of gas particles in what?
moles, n.
How do gas molecules move?
from one point to another
Units for density
g/mL or g/cm³
For ideal gases only: the forces between particles are negligible, meaning small enough to be ignored. This is virtually (practically) the case for which gases?
gases like helium, nitrogen and oxygen, but is not as valid for gases like water vapor, whose particles are attracted to one another.
Which of the following phases of matter have translational motion?
gases mainly (even though liquids have it too)
What is translation motion?
goes up and down
What makes gas particles move faster? Explain.
heat; absorbed energy converted into kinetic energy
The three modes for vibrational motion...
https://www.youtube.com/watch?v=xITzGUjongU
As seen in kinetic molecular theory, gases have the ability to move in what way? Give an example.
in all ways: vibration, rotation and translation. They can move randomly in any direction. For example, they can move to a high pressure environment to a low pressure environment.
What are manometers?
instruments used to measure pressure
What is kPaL?
it is a multiple of P x V
What is diffusion?
it is when gases mix and blend in with other gases in a container; diffusion is a slow process (at least if we don't aid it into diffusion, for example, heating it), and it can take a while for the gas to blend in uniformly.
The kinetic energy of a gaseous particle doubles. What will happen to the temperature of the gas?
it will double as well because kinetic energy and temperature are directly proportional to each other
To make use of the general gas law, temperature value must be in what?
kelvin, k
As learned in kinetic molecular theory, the distance between gas particles is very large or small?
large, since the particles can move more freely
Since gases move (translate), they will also do what?
mix in and blend with other gases in a container (diffusion)
Gases can be in compound. What does that mean? Give examples.
more than one TYPE of element/atom: H₂O, CO₂
What is the formula for number of moles?
n = m/M (where n is measured in moles, mol. Mass, m, is in grams, g. Molar mass, M, is in g/mol).
For ideal gases only, the forces between particles are _____________.
negligible, meaning that they are small enough to be ignored.
Continue from the test #5
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If the problem doesn't mention a change in variable, just assume that it is constant...
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You can round your molar mass to the nearest whole number...
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You will be given Graham's Law on exams, as well as R = 8.31 kPaL/molK = 0.082 atmL/molK...
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Gases can be monatomic. What does that mean? Give examples.
one atom; He, Ar, Ne
Workbook: What does kinetic energy result in?
particles of matter within a gas (atoms or molecules) undergo a serious amount of motion as a result of the kinetic energy within them.
All matter consists of what? Explain.
particles; either atoms or molecules
How are a particles' collisions?
perfectly elastic; they bounce back. It's not like they slow down as they collide. They will move at the same speed even when they collide with one another.
When the conditions of pressure, volume and temperature are changed, what about matter will change?
physical properties of matter
The greater the number of collisions, the greater the what?
pressure
When temperature and pressure are constant, the volume that a gas occupies is proportional to what? What law is this?
proportional to the number of particles present. This is Avogadro's Law.
How can the behavior of a gas under new conditions be described?
qualitatively, quantitatively or through simple gas laws.
What does Dalton's Law state?
that the total pressure of a mixture of gases is equal to the sum of the partial pressures of each of the component gases
What does Graham's Law state?
that when temperature and pressure are constant (notice how these variables are not in the formula), the rate at which a gas moves (diffusion or effusion) is inversely proportional to the square root of the molar masses. In other words, if you have a heavier molecule (greater molar mass), it'll have a slower velocity (smaller velocity). If you have a lighter molecule (smaller molar mass), it'll have a faster velocity (greater velocity).
Workbook: More about absolute zero.
the Kelvin scale sets its zero at a very extreme condition, called absolute zero. There is indeed something very absolute about this zero, because it's the temperature at which all particles freeze, ceasing all movement. Absolute zero is the lowest possible temperature, representing the complete absence of heat. It's as low as you can possibly go.
Why can we state that solids and liquids are virtually incompressible, while gases are compressible?
the forces of attraction between particles in solids and liquids make them virtually (practically) incompressible, so you can't squeeze them together and in gas particles, the forces of attraction are negligible (small enough to be ignored).
When more than two factors (P, V, T, and n) are changed, we make use of what?
the general gas law.
Stoichiometry: What is used in stoichiometric calculations?
the molar ratio in a balanced equation
What will happen to the pressure in a container as temperature decreases?
the number of collisions decrease since the kinetic energy of the molecules is slower, therefore the pressure will decrease, too
What will happen to the pressure in a container as temperature increases?
the number of collisions increase since the kinetic energy of the molecules is faster, therefore the pressure will increase, too
Dalton's Law: The pressure of each gas in a mixture is called what?
the partial pressure of that gas
What is the kinetic energy of a gaseous particle directly proportional to?
the temperature of a gas
Graham's Law: What will happen to the velocity if the molar mass of a molecule is doubled?
the velocity will be halved since it is an inversely proportional relationship. Velocity is inversely proportional to the SQUARE ROOT OF "M"; not that it is inversely proportional to "M".
How will the square root affect the formula if asked about the inversely proportion part about Graham's Law?
the velocity will be halved since it is an inversely proportional relationship. Velocity is inversely proportional to the SQUARE ROOT OF "M"; not that it is inversely proportional to "M". See Dad's math in chemistry binder which explores that relationship.
What allows liquids to assume the shape of whatever container they are poured in?
their familiar freedom
What type of motion do particles in a solid undergo? Is this the only type of motion experienced by this state of matter?
they vibrate, and yes; it is the only type of motion for solids
How do you solve stoichiometric problems that involve gases?
we can use the stoichiometric techniques together with the gas laws.
When can we make use of the simply gas laws? What are those factors?
when ONLY two of the factors that influence the behavior of a gas are changed while the others are constant. These factors include P, V, T and n.
When does effusion occur?
when a gas passes through a very small opening
What's an example of effusion?
when balloons deflate because of tiny openings in balloon.
Charles' Law: If the volume is doubled, what will happen to the temperature in Kelvin?
will also double (IN KELVIN...)
What is the general equation for the inverse function?
y = a / x OR xy = a (same thing). It's like saying y = 1 / x, but you could scale x or y by a factor of "a"; meaning that if you had y = 2/x for example, the inverse function line would be stretched upwards compared to y = 1/x. If you had y=1/2x, then the line would curve lower. There is no "b" because there is no y-intercept.
Symbol for density
ρ
