March 22, 2014

Kinetic Molecular Theory• A model to explain the physical properties of ideal

gases

1. Gas particles are much smaller than the distances between them.

2. Gas particles do not attract or repel each other.

3. Gas particles are in constant, random motion. Collisions are elastic

4. The average kinetic energy of the gas molecules is directly proportional to the temperature of the gas (K)

March 22, 2014

Kinetic Energy and Temperature• Temperature = measure of average kinetic energy

of the particles in a sample of matter• Kinetic energy and temperature are directly

proportional.

KEavg=1/2mv2

KEavg=3/2RT

The higher the temperature, the faster the molecules are moving.

March 22, 2014

Maxwell-Boltzman Distribution

March 22, 2014

Maxwell-Boltzman Distribution

At the same temperature, all gasses have the same average kinetic energy.

March 22, 2014

Maxwell-Boltzman Distribution

March 22, 2014

Diffusion and Effusion

Diffusion = random movement of particles from area of higher concentration to area of lower concentration

March 22, 2014

Example 1:

If two bottles of the same gasses where gas 1 has a molar mass of 32g/mol and gas 2 has a molar mass of 20 g/mol, which gas will have a greater rate of diffusion?

March 22, 2014

Gas Laws: Relates volume, pressure, temperature, and amount of gas

1. Temperature2. Pressure3. Volume4. Amount

kelvinatm, psi, mmHglitersmoles

variable unitssymbol

TPVn

K= ºC + 273

March 22, 2014

What is pressure?

P= forcearea

force exerted by gas molecule in a collision

surface area force is determined by:➀ how fast molecule is traveling ➁ mass of molecule➂ number of collisions

March 22, 2014

1atm = 760 mmHg = 760 torr = 29.9 in. Hg = 101.3 kPa = 14.7 psi

Units and conversions for pressure

March 22, 2014

Barometer measures atmospheric pressure

March 22, 2014

Manometer measures pressure of confined gas

height difference indicates pressure of gas relative to atmospheric pressure.

Example 2: What is the pressure of the confined gas if the height of the mercury is 155 mm and the atmospheric pressure is 775mmHg?

March 22, 2014

Volume

1 mol of a gas at STP (standard temperature and pressure) has a volume of 22.4 L.

STP: 273K and 1 atm

Example 3: What is the volume of a gas if you have 4g of oxygen gas at STP?

March 22, 2014

Gas Laws!

1. Boyle's Law

2. Charles's Law

3. Gay-Lussac's Law

4. Combined Gas Law

5. Ideal Gas Law

March 22, 2014

1. Boyle's Law• Relates pressure and volume of gas when

temperature and amount (n) is constant

March 22, 2014

pressure (atm)

Boyle's Law

volu

me

(L)

March 22, 2014

March 22, 2014

Example 4: The volume of a gas at 99.0 kPa is 300.0mL. If the pressure is increased to 188 kPa, what will be the new volume?

March 22, 2014

Example 5: A sample of neon gas occupies 0.220L at 0.860 atm. What will be its volume at 29.2 kPa?

March 22, 2014

Volume of a given mass of gas is directly proportional to its temperature at constant pressure.

2. Charles's Law• Relates temperature and volume of gas when

pressure and amount (n) is constant

March 22, 2014

Example 6: A gas sample at 40.0º C occupies a volume of 2.32 L. If the temperature is raised to 75.0ºC, what will the volume be, assuming pressure remains constant?

March 22, 2014

Example 7: A gas at 89º C occupies a volume of 0.67L. At what celsius temperature will the volume increase to 1.12L (constant pressure and amount).

March 22, 2014

3. Gay-Lussac's Law• Relates pressure and temperature of gas when

volume and amount (n) is constant

March 22, 2014

Example 8: the pressure of a gas in a tank is 3.20atm at 22.0ºC. If the temperature rises to 60.0ºC, what will be the gas pressure in the tank?

March 22, 2014

Example 9: A gas in a sealed container has a pressure of 125 kPa at a temperature of 30.0ºC. If the pressure in the container is increased to 201 kPa, what is the new temperature?

March 22, 2014

Combined Gas Law• Can combine Boyle's, Charles's, and Gay-Lussac's

law into one law: relates T, P, V of a fixed amount of gas.

*If you know this law, you can derive any of the other three laws.

March 22, 2014

Example 10:

A helium-filled balloon at sea level has a volume of 2.1 L at 0.998 atm and 36ºC. If it is released and rises to an elevation at which the pressure is 0.900 atm and the temperature is 28ºC, what will be the new volume of the balloon?

March 22, 2014

Example 11:

At 0.00ºC and 1.00 atm pressure, a sample of gas occupies 30.0mL. If the temperature is increased to 30.0ºC and the entire gas sample is transferred to a 20.0mL container, what will be the gas pressure inside the container?

March 22, 2014

PV=nRT

Ideal Gas Law• Combines all four variables: P, T, V, and n

R = gas constant

Value depends on units of pressure:

March 22, 2014

Example 12: What is the volume of 1 mole of gas at STP?

March 22, 2014

Example 13:

Calculate the number of moles of gas contained in a 3.0L vessel at 3.00x102 K with a pressure of 1.50 atm.

March 22, 2014

March 22, 2014

Example 14:

Determine the celsius temperature of 2.49 moles of gas contained in a 1.00 L vessel at a temperature of 143 kPa.

March 22, 2014

Example 15:

Calculate the number of molecules of air in a breath of air whose volume is 2.5 L at a body temperature of 37ºC and a pressure of 100kPa.

March 22, 2014

Gas Laws and Stoichiometry! Hooray• remember...PV=nRT (n is moles of gas)• 1 mol of any gas at STP has a volume of 22.4L

March 22, 2014

Example 16: What is the volume of water vapor that can be produced from 25.0g of oxygen gas at a temperature of 35ºC and a pressure of 1.3atm?

2H2 + O2 ⟶"2H2O

March 22, 2014

Dalton's Law of Partial Pressures

The pressure of a gas mixture is the sum of the partial pressures of the gases present.

The partial pressure is the pressure that the gas would exert if it were alone in a container.

*Doesn't matter what the identity of the gas is--what matters is total moles of particles. You can use PV=nRT to figure out P at a given V and T.

March 22, 2014

Ptotal = P1 + P2 + P3....

Dalton's Law of Partial Pressures

March 22, 2014

Example 17: A mixture of neon and argon gases exerts a total pressure of 2.39 atm. The partial pressure of the neon alone is 1.84 atm, what is the partial pressure of the argon?

March 22, 2014

In a lab, when a gas is collected over water, the partial pressure of water vapor must be taken into account.

Ptotal = PH2O vapor + Pgas

March 22, 2014

March 22, 2014

Example"20:"A"450"mL"sample"of"hydrogen"is"collect"over"water"at"12"C."""The"pressure"of"the"hydrogen"and"water"vapor"mixture"is"78.5"kPa.""What"is"the"partial"pressure"of"the"dry"hydrogen"gas?"

March 22, 2014

Example 21: A sample of oxygen gas is saturated with water vapor at 27ºC. The total pressure of the mixture is 772 torr and the vapor pressure of water is 26.7 torr at 27ºC. What is the partial pressure of the oxygen gas?

March 22, 2014

Example 23: A 500. mL sample of O2 gas at 24ºC was prepared by the following equation:

2H2O2 (aq) 2H2O(g) + O2(g)

The oxygen prepared was collected by displacement of water. The total pressure of gas collected was 755mmHg.

1. What is the partial pressure of O2? (The vapor pressure of water at 24ºC is 23mmHg)

2. How many moles of O2 were prepared?