Chapter 11: Gases

Mole Fraction

N partial / N total = P partial / P total You can use this to determine missing values

Boyles Law

PV=K or P1V1=P2V2 Pressure and volume are inversely proportional to one another at constant temperature. When volume increases, pressure decreases by the same factor. When pressure increases, volume decreases by the same factor.

What is the relationship between all the gas values using the principle of P1V1/N1T1= P2V2/N2T2

Pressure and Volume are inversely related Pressure and moles are directly related Pressure and temp are directly related Volume and moles are directly related Volume and temp are directly related Moles and temp are inversely related.

Relationships that can be determined from the ideal gas law

Pressure and volume are inversely proportional at constant temperature (to hold T constant, P and V must oppose one another) Pressure and temp are directly related at constant volume (to hold the volume constant, Pressure and Temp must mirror one another) Volume and Temp are directly proportional at constant pressure (to hold pressure constant, temperature and volume must mirror one another).

A property of a gas is that it exerts pressure on its container. What is pressure?

Pressure is force applied over a certain unit of area.

Mole to Volume ratio in a chemical reaction

The ratio between the moles of a gas is equal to the ratio between the volumes of a gas in a balanced chemical equation in which pressure and temperature are held constant. ONLY applies to gases, do not look at solids or liquids with this rule. This means that the ratio between moles of reactants and moles of products is equal to ratio between volume of reactants and volume of products.

Charles Law

V/T = K or V1/T1=V2/T2 Volume and temperature are directly proportional to one another at constant pressure. When volume increases, temperature increases by the same factor. When temperature increases, volume increases by the same factor.

What is the exception to the law of partial pressures?

VAPOR PRESSURE All gasses collected over water have vapor pressure in them and the way that the partial pressure of water vapor is measured is not the same as other gases. The only thing that determines the pressure of water vapor is temperature, and even this relationship is not proportional. As temperature increases, the pressure increases, yes (like normal), but the relationship is not directly proportional so the IGL does not work. Vapor pressure does not obey the other rules of the IGL!!!

So what is the relationship between volume and temperature at constant pressure? Apply the kinetic molecular theory.

Directly proportional. When temp increases, volume increases, when volume increases, temp increases, and same applies but opposite for decrease. You can apply THIS to the molecular theory because when temperature increases, the speed at which molecules travel also increases and if volume does not increase proportionally, then the pressure will change; so to maintain pressure at a constant, when that temp increases, the volume must do the same. When the temp decreases, volume must do the same.

What are the units for pressure?

1 atm= 760 torr= 760 mmHg 1 atm= 101,325 Pa

What are the five postulates of the KMT?

1. Molecules of a gas are in constant and random motion 2. The volume of the particles themselves are negligible 3. Forces of attraction and repulsion between particles are equal to 0 4. Collisions between particles and the walls of their container are perfectly elastic 5. The relationship between KE and absolute temp are directly proportional (this kinetic energy is the average of the particles in the gas, they do not have the same energy all the time, but just an average estimate). Look at study guide to analyze more deeply how these postulates relate to the mathematical concepts

How many liters does one mole of a gas occupy at STP (1 atm and 273 degrees kelvin)?

22.42 Liters

What is a gas?

A gas is a state of matter in which particles are farthest apart from one another, there is no definite shape or volume, meaning that the gas fills up its container completely. Gases are much less dense than liquids and solids, and are actually expressed in g/L rather than g/mL because of how low their density is.

What happens when temp is 0 degrees kelvin?

Absolute zero, the temp at which molecules stop moving and volume equals 0. This is not actually possible, though it makes sense conceptually.

Why is mole to volume ratio in chemical reactions different than avogadros law

Avo tells us that at constant temp and pressure, the relationship between moles and volume of the SAME gas given that one of the two variables change, is directly proportional. V1/N1=V2/N2 Volume to Mole ratio tells us that in TWO SEPERATE gasses, in a balenced chem equation, ratio between their volumes is the same as the ratio between moles at constant temp and P. V1/V2=N1/N2

So what is the relationship between volume and moles?

Directly proportional As V increases, n increases, as V decreases, n decreases by the same factors. In order to hold temperature and pressure constant, when the number of moles increases, volume would have to as well.

What are the factor relationships you can draw from ideal gas ratio?

From P1V1/N1T1= P2V2/N2T2... Determine what is constant and cancel. Let's say you have P1/N1T1=P2/N2T2. If you double P and you 1/2 T, what happens to N. Well N has to do whatever P does because that is direct. So we start with doubling N. Then we do the inverse of whatever T does, so instead of halving, we double it again. So we end up multiplying N by 4. So if we have 1/2x4 ---> 2/8x2, that is proportional and we know we have done our job correctly. This is the logic you will use when asked questions regarding what takes place when arbitrary changes are made to two variables. The same applies if you recieve a balenced chemical equation. The change in moles is presented in the equation, but you may be given another change, like change in temp... Based on these principles determine what happens to the missing value.

It is important to note that we are looking at what kind of particles in a chemical equation when talking about avogadros law?

GAS PARTICLES ONLY!!! These rules do not apply to solids and liquids.

What is the purpose of the Ideal Gas Law

It combines the principles of Boyle's Law, Charles's Law, and Avogadro's Law into a single equation. The equation is PV=nRT. You can then set up a ratio to account for changes in any of these values to solve for an unknown using P1V1/N1T1= P2V2/N2T2 This ratio is also the basis for the relationships that exist between all the gas values. If any part of the ratio is constant, you can cross it out on both sides to obtain a refined equation that only takes into account the values that are changing.

What is the relationship between velocity of a particle and mass?

Lighter molecules travel faster than heavier ones

Combined Gas Law

P1V1/T1=P2V2/T2 If you are given 5/6 of the variables, then you can solve for the sixth. Temperature must always be in Kelvin, but pressure and volume just have to be the same on both sides.

Relationship between total moles and total pressure and partial pressure and moles.

Ptotal= Ntotal x R x T/ V Ppartial= Npartial x R x T/ V Grams can be thrown into this, at which point the only thing you are looking for is moles.

Grahams Law of Effusion

Rate of Effusion 1 / Rate of Effusion 2 = √(MM2 / MM1) Thinking about wording. If gas A is 0.45 times faster than gas B, you are comparing A to B so your rate ratio is A/B. Then, MM1 is A, on bottom, and MM 2 (B) is on top. Because .45 is less than 1, you know A is moving slower than B and thus, is heavier than B. When you set up your MM ratio, A is on bottom and should be the one with a heavier mass. You can equate everything to .45 because you know that is the ratio between A:B. From here, you can calculate the missing MM. Double check your work by determining if the missing MM makes sense. Is A heavier than B?

So when we are talking about the pressure of a water vapor, what should you look at?

Temperature only, and specifically, the temperature listed in the table.

So the pressure of a gas is dependent upon the forces between the molecules and...

The container

Effusion

The passage of a gas through a tiny hole into an evacuated chamber

Avogadros Law

The relationship between volume and moles is directly proportional at constant temperature and pressure. V1/n1=V2/n2, so as volume increases, moles of particles increases by the same factor. When volume decreases, moles of particles decrease by the same factor. They are directly proportional at constant temperature and pressure. So two objects with the same volume at constant temperature and pressure will have the same number of moles.

Dalton's Law of Partial Pressures

The total pressure of a gas is the sum of all its partial pressures (the individual gases that comprise the system).

So what is the relationship between pressure and volume at constant temperature?

They are Inversely Related. As pressure increases, volume decreases, and as pressure decreases, volume increases. Think about the weight on the piston

What are the two factors that determine the average speed (velocity) of a gas particle. What is the equation for RMS.

1. Temperature and Molar Mass 2. Vrms= √(3RT/MM)

Under what conditions are gases most likely to behave like ideal gases?

At high temperature and low pressure. At high temps and low pressure, the distance between molecules is so big and speed of the molecules is so fast that the volumes of the gases themselves and the forces between them are negligible, as stated by the KMT. However, when pressure is high, particles are tightly packed and because overall volume has decreased, the volume of each particle may no longer be negligible. When temp is low, the particles are moving more slowly, so forces of attraction or repulsion between them is also no longer negligible.

How to determine the partial pressure of a gas collected over water

When you are given the pressure of a gas collected over water, you need to take the total pressure and subtract the tabulated vapor pressure to determine the partial pressure of the specific gas. Once you have determined the partial pressure of the specific gas, you can apply chemical reaction, ideal gas, stoichiometry rules like normal to obtain information about the other properties of the gas.