Chem, Lap 9: Gas Laws
Formula review for quiz #1:
-Boyle's Law = volume vs pressure (PV=PV) -Gay Lussac's Law = temperature vs pressure (P/T = P/T) -Charles' Law = temperature vs volume (V/T=V/T)
density
-density = mass / volume -Ideal gas law: PV = nRT -plug in a substitute for moles: PV = (grams/molar mass) RT -simplify: PV = gRT / molar mass -rearrange to get grams over volume: g/V = (P)(molar mass) / RT -substitute g/V for density: density = P(molar mass) / RT
Avogadro's Law
-describes the relationship between Volume and moles at a constant temperature and pressure -If the volume increases, then the number of moles increases (to ensure that the pressure stays constant) -if the volume decreases, then the number of moles decreases -direct relationship (graph will be a straight line) -V/n = V/n
What is the relationship between Kelvin temperature and Kinetic energy?
-direct relationship -as temperature increases, Kinetic energy increases -as temperature decreases, Kinetic energy decreases -graph will be a straight line
What is the relationship between density and temperature?
-At constant pressure and amount of moles, as temperature (In Kelvin!!!) increases, density decreases, and as temperature decreases, density increases -indirect relationship -This is because as temperature increases, volume must increase in order to keep the pressure the same. If volume increases and the number of moles of gas are kept the same, then the density decreases -This ONLY applies at a constant pressure and moles!!!!
What is the relationship between density and pressure?
-At constant temperature and amount of moles, As density increases, pressure increases (direct relationship) -In order to increase the density, either the mass must increase, or the volume must decrease, both of which cause pressure to increase (however, this relationship is at a constant amount of moles, so only the volume can be changed, not the mass) -Likewise, pressure is increased by decreasing the volume on a constant amount of gas, which increases the density of this gas
What is a direct relationship?
- As one variable increases, the other increases BY THE SAME FACTOR - As one variable decreases, the other decreases BY THE SAME FACTOR -ex: temperature in Kelvin doubles, then pressure will also double
What is the relationship between temperature and pressure of gas?
- temperature of a gas increases > particles move faster > particles have greater kinetic energy > more kinetic energy means that particles will collide more often are with more force > pressure increases (and can even lead to an explosion in extreme circumstances) -therefore, as temperature increases, pressure increases. As temperature decreases, pressure decreases -temperature and pressure have a direct relationship (this only applies to KELVIN, NOT to celsius
temperature
-A measure of the average energy of motion of the particles of a substance -lots of energy = hot -low energy = cold -measured in Kelvin
Kinetic Molecular Theory (KMT)
-A model used to explain the behavior of gases in terms of the motion of their particles -provides the basis for the gas laws -makes three major assumptions about the particles in a gas: 1. Gas particles move in a straight line until they collide with other particles or the walls of their container 2. The motion of the particles is constant and random 3. There are no attractive or repulsive force among the particles
polar molecule
-A molecule that has electrically charged areas due to unequally sharing electrons -molecules will typically be polar if the molecule is formed from very different elements, such as H and Fl, rather than from similar (or the same) elements such as H and H
Standard Temperature and Pressure (STP)
-A temperature of 0ºC or 273 K -a pressure of 1.00 atm (or any of the equivalents)
formula review for quiz #2:
-Boyle's Law = volume vs pressure (PV=PV) -Gay Lussac's Law = temperature vs pressure (P/T = P/T) -Charles' Law = temperature vs volume (V/T=V/T) -combined gas law = volume vs pressure vs temperature (PV/T = PV/T) -ideal gas law = pressure vs volume vs amount vs temperature (PV = nRT) -r = 0.0821 L atm / mol K -moles = grams/molar mass -molar mass = grams / mole -density = P(MM) /RT -1 atm = 760 torr = 760 mmHg = 76 cmHg = 101.3 kPa
What are the units used for the ideal gas law?
-P = pressure, must be in atm -V = volume, must me in L -n = amount of gas, must be in moles -R = 0.0821, must me in L atm / mol K -T = temperature, must be in Kelvin -All units for the ideal gas law MUST be these units and no others (very picky)
What units can be used with Boyle's law?
-Pressure (P) can have any units as long as P1 and P2 have the same units -volume (V) can have any unites as long as V1 and V2 have the same units
What is the relationship between the root mean square speed and molar mass?
-RMS Speed is inversely proportional to the square root of the molar mass -As the RMS increases, the square root of the molar mass must decrease (and vice versa)
Dalton's Law
-States that the total pressure of a mixture of gases is equal to the sum of the individual (partial) pressures -Pt = P1 + P2 + P3... -The units of pressure must match
Volume
-The amount of space an object takes up -volume is determined by the size of the container (increase size = increase volume) -measured in L or mL
absolute zero
-The coldest temperature which is 0 Kelvin -It is the hypothetical temperature at which all molecular motion stops -at this temperature, particles cannot move, so therefore gases would not exist (this is why we use kelvin instead of Celsius because we can never have a temperature of 0 K for gases, so we will never be faced with the issue of dividing by 0 or with negative temperatures)
How to figure out if a relationship is direct or indirect:
-Tips for remembering which relationships are direct vs indirect: If the formula involves MULTIPLICATION (ex: PV = PV) then its an INDIRECT relationship. If the formula involves DIVISION (ex: P/T=P/T) then its a DIRECT relationship -DON'T ACCIDENTALLY USE FALSE LOGIC: If A is directly proportional to B, and B is indirectly proportional to C, then A is NOT also indirectly proportional to C -Ex: We know that Temperature is directly proportional to volume, and that volume is indirectly proportional to pressure. However, we can NOT conclude that temperature is also indirectly proportional to pressure (this conclusion proves to be WRONG per Gay Lussac's Law) -This is because each law exists under different conditions and requires that specific variables remain constant
What is the relationship between pressure and CELSIUS temperature?
-Unlike the relationship between pressure and KELVIN temperature (absolute temperature), the relationship between pressure and CELSIUS temperature is NOT direct -As celsius temperature increases, pressure will increase too, just not by the same factor
What units can we use for Charles' Law?
-Volume (V) can be any unit as long as V1 and V2 have the same units -Temperature (T) must be in Kevin
What is an ideal gas?
-a hypothetical gas that perfectly fits all the assumptions of the kinetic molecular theory and will conform to all gas laws -ideal gases will follow all four gas laws (Boyle, Charles, Gay Lussac, and combined) -in reality, many gases do not fit all the rules, and are therefore NOT considered ideal gases
What is the difference between a real gas and an ideal gas?
-a real gas is a gas that does not behave completely according to the assumptions of the kinetic-molecular theory -an ideal gas has no molecular volume, no attractive or repulsive forces, follows all the statements of the KMT and follows all the gas laws perfectly -In the real world, ideal gases DO NOT EXIST
What is the combined gas law?
-a single expression that combines Boyle's, Charles's and Gay Lussac's Laws -this gas law describes the relationship between temperature, pressure, and volume at a constant amount of gas
What is the ideal gas law?
-a special law that comes from the combined gas law but adds in an extra variable for the amount of gas -all other laws only work when the amount of gas was assumed to be constant, but this law allows a scientist to factor in different amounts of gas -The ideal gas law relates the amount of gas (in moles) to the volume it would occupy at a particular temperature and pressure
Kelvin
-a special unit for temperature -EVERYTHING IN THIS UNIT NEEDS TO BE IN KELVIN (NOT CELSIUS!!!!) -don't use a degree bubble -to convert from Celsius to Kelvin, add 273 and follow the sig fig rules for addition
What is the relationship between kinetic and potential energy?
-as kinetic energy increases, potential energy decreases -as kinetic energy decreases, potential energy increases -this is because kinetic energy turns into potential energy and vice versa when in an ideal closed system with no energy loss
What is an indirect/inverse relationship?
-as one variable increases, the other decreases -if x varies indirectly with y, then 1/x varies directly with y (so the first graph would be a curve but the second graph would be a line)
What is the relationship between density and molar mass?
-as the molar mass increases, the density increases (direct relationship) -This is because if a given amount of gas has a high molar mass than its individual molecules have more mass in a given volume than smaller, lighter molecules would -the more mass something has in a given volume, the higher the density
What is the relationship between volume and pressure of gas?
-as volume increases, pressure decreases -as volume decreases, pressure increases -thus, the relationship between pressure and volume is indirect
What is the relationship between amount of gas and pressure of gas?
-at a constant temperature and volume, if we increase the number of gas particles, then the pressure increases -direct relationship (one goes up, the other goes up by the same factor; one goes down, the other goes down by the same factor)
How do polar molecules deviate from ideal gas behavior?
-by unequally sharing electrons, polar molecules create an attraction between molecules which violates ideal gas behavior
What does the Kinetic Molecular Theory tell us about gases?
-gas particles move in straight lines are don't deviate from this path until they collide with something -gas particles are always moving -the direction of gas particles cannot be predicted because it is random -there are no attractive or repulsive forces among the particles, and because of this, a gas can never be liquified or solidified according to this theory (but in the real world this is not always the case)
How does high molar mass cause a gas to deviate from ideal gas behavior?
-high molar mass means larger molecular volume which violates ideal gas behavior because ideal gases are not supposed to have molecular volume -this means that elements with the LOWEST molar mass are the most ideal
Volume to Volume ratio
-just like substances in an equation have a mole to mole ratio, their coefficients also form a volume to volume ratio -the volume to volume ratio is the exact same thing as mole to mole ratio except the units on the coefficients will be in Liters, not moles
Amount of particles
-measured in moles -one mole of gas = 6.02 x 10²³ particles of gas
What units can we use for Gay Lussac's Law?
-pressure (P) can be in any unit as long as P1 and P2 have the same units -temperature (T) must be in Kelvin (remember, its because we don't want to get stuck needing to divide by zero)
What is the relationship between pressure and collisions?
-pressure is caused by collisions between gas particles AND between the gas particles and the walls of the container -The more gases collide with the walls of the container, the higher the pressure -factors that affect pressure are causing changes in pressure BECAUSE they are increasing or decreasing collisions
Which relationships are direct?
-pressure vs moles -Temperature (K) vs kinetic energy -temperature (K) vs pressure -temperature (K) vs volume -volume vs moles -density vs molar mass -density vs pressure -mole fraction or volume percent vs partial pressure (?)
Which relationships are indirect/inverse?
-pressure vs volume -density vs volume (for the equation D = mass/volume) -density vs temperature -rate of effusion vs square root of the gas's molar mass
Volume percentage
-ratio of solute-to-solution volume expressed as a percentage -The volume percentage is NUMERICALLY EQUAL to the mole fraction because of Avogadro's law which says that volume and moles are proportional at a constant temperature and pressure
Graham's Law
-states that the rate of effusion or diffusion of a gas is inversely proportional to the square root of the gas's molar mass -Rate A / Rate B = Square root of molar mass B / square root of molar mass A -always put the larger molar mass in the numerator -sig figs do not matter if the original numbers given were from the periodic table
Gay Lussac's Law (Also called Amonton's law in the txbk)
-summarizes the relationship between Pressure and temperature -states that for a given volume of a gas, as the temperature of an enclosed gas increases, the pressure of a gas is directly proportional
Boyle's law
-summarizes the relationship between pressure and volume -states that for a given amount of gas at a constant temperature, the volume of a gas varies inversely with pressure
Charles' Law
-summarizes the relationship between temperature and volume -states that for a given mas of a gas at constant pressure, the volume of the gas is directly proportional to its temperature in Kelvin
What is the ONLY thing that can change kinetic energy?
-temperature -ALL gases have the SAME Kinetic energy as long as they are at the same temperature because kinetic energy is NOT effected by the type of particle
what is the relationship between molar mass and effusion or diffusion?
-the SMALLER the molar mass, the HIGHER the rate of diffusion or effusion -this is because lighter objects have faster speeds
pressure
-the amount of force exerted per unit area of a surface -measured in kPA, mmHg, torr, or atm -determined by volume, amount, or temperature
effusion
-the escape of a gas through a tiny pinhole in a container of gas -gases with LOWER molar masses effuse more quickly
What is the ideal gas constant?
-the ideal gas constant is a value denoted by R and equals about 0.0821 -R has units of Liter atmospheres per mole Kelvin -R has other values when different units are used -R's value serves to connect all the other variables in the ideal gas law, which is why the other units must match the units used for R
Molar mass / molar weight
-the mass in grams of one mole of a substance -the molar mass of a substance will NOT change even if temperature, pressure, volume, or amount do change -Moles = grams / molar mass -This ^^ expression can be substituted for moles in the ideal gas law to solve for molar mass -NOTE: on Earth, mass = weight, so molar mass is the same thing as molar weight
mole fraction (X)
-the ratio of the number of moles of solute to the total number of moles of solution (basically, its the moles of an individual gas divided by the sum of the moles of all the gases in the mixture)
root mean square speed
-the square root of the average of the squared speeds of the gas molecules in a gas sample (basically the average speed or rate of gas particles) -the higher the root mean square speed, the lower the molar mass, and the lower the time it takes to diffuse -Don't need to know this formula
diffusion
-the tendency of gas particles to spontaneously spread out until uniformly distributed -gas particles move from highly concentrated areas to less concentrated areas (the original area will be more concentrated at first)
molar volume
-the volume occupied by 1 mole of a gas at standard temperature and pressure -ALL gases have the same molar volume at STP which is 22.414 L -the molar volume of a gas can act as a conversion factor between moles and volume when performing dimensional analysis
Units of pressure
1 atm = 101.3 kPa = 101,300 Pa = 760 torr = 760 mmHg
What are the three factors that affect gas pressure?
1. Adding or removing gas (amount) 2. Increasing or decreasing the size of the container (volume) 3. Adding or removing heat (temperature)
Under what conditions will gases NOT act ideal?
1. High pressure 2. Low temperature 3. High molar mass 4. Polar molecules (however, most gases WILL act ideal under most conditions)
What four variables are generally used to describe a gas?
1. pressure 2. volume 3. temperature 4. Amount
What are the two things gas pressure depends on?
1. the amount of gas 2. the kinetic energy of its particles
concentration
A measurement of how much solute exists within a certain volume of solvent
What is a gas?
A state of matter with no definite shape or volume
diffusion vs effusion
Diffusion- the movement of particles from regions of higher density to regions of lower density (ex: a scent spreading throughout a room) Effusion- the passage of gas under pressure through a tiny opening (ex: air leaking from a balloon)
Note on Graham's Law:
If Oxygen diffuses twice as fast as a random gas, then the rate of O2 is 2 and the rate of gas X is 1. This means that if gas X takes 2 seconds to diffuse, then O2 takes 1 second to diffuse (the RATE and the TIME are NOT THE SAME THING)
What is the relationship between partial pressure, total pressure, volume percentage, and mole fraction?
Pg = (Pt)(X) -Pg = partial pressure -Pt = total pressure -X = mole fraction or volume percent
What units can be used for Avogadro's Law?
V = volume (any units as long as they are consistent) n = moles
How does low temperature cause a gas to deviate from being ideal?
low temperature --> gas particles slow down and come closer together --> attractive and repulsive forces increase which violates the behaviors of ideal gases
How does high pressure cause a gas to deviate from being ideal?
more pressure --> gas particles are pushed closer together --> more attractive and repulsive forces occur which violates the Ideal Gas behaviors
potential energy
stored energy that results from the position or shape of an object
total pressure
sum of all partial pressures
partial pressure
the contribution each gas in a mixture of gases makes to the total pressure
kinetic energy
the energy an object has due to its motion (kinetic energy is increased by increasing temperature, which causes particles to move faster)