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## Chapter 12 pp. 470-508

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Chapter 12 pp. 470-508

General properties & kinetic theory

- Gases are made up of particles that have (relatively) large amounts of energy.
- A gas has no definite shape or volume and will spread out to fill as much space as possible.
- A gas will exert a pressure on the walls of any container it is held in.
- As a result gases are easily compressed.

Pressure

- A pressure is exerted when the gas particles collide with the walls of the container. Pressure can be measured in a number of units.

1 atm = 760 mmHg = 760 torr = 101325 Pa = 101325 N/m2

Example #1

Use the factor labeling method to perform the following conversions

1. 1,657 mmHg to N/m2

2. 832 torr to atmospheres

3. 17.8 kPa to atmospheres

4. 120,000 Pa to mmHg

Kinetic theory

- The kinetic theory can be summarized by the five postulates below:

1. Gases are composed of tiny atoms or molecules (particles) whose size is negligible compared to the average distance between them. This means that the volume of the individual particles in a gas can be assumed to be negligible (close to zero).

2. The particles move randomly in straight lines in all directions and at various speeds.

The Rest of the Post…

3. The forces of attraction or repulsion between two particles in a gas are very weak or negligible (close to zero), except when they collide.

4. When particles collide with one another, the collisions are elastic (no kinetic energy is lost). The collisions with the walls of the container create the gas pressure.

5. The average kinetic energy of a molecule is proportional to the Kelvin temperature and all calculations should be carried out with temperatures converted to K.

Pressure and Volume relationships: Boyles Law

- Boyles Law states that, at constant temperature, pressure is inversely proportional to volume. This means that as the pressure increases the volume decreases and visa-versa.
- P1V1 = P2V2

Example #2

- If a 1.25 L sample of a gas at 56 torr is pressurized to 250 torr at a constant temperature what is the new volume?

2. The pressure on a 415 mL sample of gas is decreased form 823 mmHg to 791 mmHg. What will the new volume of the gas be?

Volume and Temperature relationships: Charles’s Law

- Charles’s Law states that, at constant pressure, volume is directly proportional to temperature. This means the volume of a gas increases with increasing temperature and visa-versa.
- V1T2 = V2T1

Example #3

1. A 12.0L sample of air is collected at 296K and then cooled by 15K. The pressure is held constant at 1.2 atm. Calculate the new volume of the air.

2. A gas has a volume of 0.672L at 35oC and 1 atm pressure. What is the temperature of a room where this gas has a volume of 0.535L at 1 atm?

Volume and Moles relationships: Avogadro’s Law

- Avogadro’s Law states that, at constant temperature and pressure, volume is directly proportional to the number of moles of gas present. This means the volume of a gas increases with increasing number of moles and visa-versa.
- V1n2 = V2n1

Example #4

- 1. A 13.3 L sample of 0.5 moles of oxygen gas is at a pressure of 1 atm and 25ºC. If all of the oxygen is converted to ozone (O3) what will be the volume of ozone produced?
- 2. If 2.11g of Helium gas occupies a volume of 12.0L at 28ºC, what volume will 6.50g occupy under the same conditions?

The Ideal Gas Law

- The combination of Boyle’s, Charles’s & Avogadro’s Laws leads to the formulation of the Ideal Gas Law.
- Most gases obey this law at temperatures above 0ºC and at pressures of 1 atm or lower.
- PV = nRT
- R = 0.08206 L·atm / mol·K

Different forms of Ideal GL

- n = mass / MW so…
- PV = (m/MW)RT
- Density = mass / V so…
- D = P·MW / RT

The General Gas equation

- P1V1n2T2 = P2V2n1T1
- If the number of moles of gas are constant in a problem, then we have the combined gas law…
- P1V1T2 = P2V2T1

Example #5

1. Assuming that the gas behaves ideally, how many moles of hydrogen gas are in a sample of H2 that has a volume of 8.16L at a temperature of 0ºC and a pressure of 1.2 atm?

2. A sample of aluminum chloride weighing 0.1g was vaporized at 350ºC and 1 atm pressure to produce 19.2cm3 of vapor. Calculate a value for the MW of aluminum chloride.

Deviations from ideal behavior

- At high pressures and low temperatures gas particles come close enough together to make the kinetic theory assumptions below become invalid:
- Gases are composed of tiny particles whose size is negligible compared to the average distance between them, and
- The forces of attraction or repulsion between two particles in a gas are very weak or negligible (close to zero)

Non-Ideality (cont)

- At this point gases are said to behave non-ideally or like real gases. This has two consequences.

Non-Ideality (cont)

- Under these real conditions the actual volume occupied by the gas is smaller than one would expect when assuming the size of particles is negligible. Since in a small volume the size of the particles is not negligible, the observed volume is larger than it really is. This necessitates the need to correct the volume by subtracting a factor.

Non-Ideality (cont)

- Under these real conditions the actual pressure of a gas is higher than one would expect when assuming there was no attractive forces between the molecules. Because the particles are attracted to one another they collide with the walls with less velocity and the observed pressure is less than it really is. This necessitates the need to correct the pressure by adding a factor.

Van der Waal’s Equation for Real Gases

(P + a(n/V)2)·(V-nb) = nRT

a and b are constants, where a corrects for intermolecular forces and b corrects for molecular volume

Example #6

- You want to store 165g of CO2 gas in a 12.5L tank at room temperature (25ºC). Calculate the pressure the gas would have using (a) the ideal gas law and (b) the van der Waals equation. (For CO2, a = 3.59 atm·L2/mol2 and b = 0.0427 L/mol)

Molar Volume

- We have seen how Avogadro's law states that equal volumes of all gases at constant temp and pressure will contain equal numbers of moles.
- The volume of one mole of any gas is called its molar volume and can be calculated using the ideal gas equation.

PVm = nRT

Molar Volume (cont)

- By applying the data, pressure (P) = 1atm, temp (T) = 273K, the gas constant (R) = 0.08206 L·atm·mol-1 K-1, number of moles (n) = 1 mol, the molar volume (Vm) can be found.
- A simple calculation finds its value to be 22.4L.
- That is to say, for one mole of any ideal gas, at standard temp and pressure (s.t.p), the volume it occupies will be 22.4 L.

Example #7

- Calculate the mass of ammonium chloride required to produce 22L of ammonia (at s.t.p) in the reaction below.

2NH4Cl(s) + Ca(OH)2(s) 2NH3(g) + CaCl2(s) + 2H2O(g)

Example #8

- What mass of potassium chlorate must be heated to give 3.25L of oxygen at s.t.p?
- 2KClO3(s) 2KCl(s) + 3O2(g)

Example #9

- Barium carbonate decomposes according to the equation below. Calculate the volume of carbon dioxide produced at s.t.p when 9.85g of barium carbonate is completely decomposed.
- BaCO3(s) BaO(s) + CO2(g)

Example #10

- What volume of oxygen (at s.t.p.) is required to burn exactly 1.5L of methane (CH4)
- CH4(g) + 2O2(g) CO2(g) + 2H2O(g)

Distribution of Molecular Speeds

- When considering the kinetic theory postulate #2 introduces the idea that all of the gas particles move at different speeds
- and postulate #5 that the speed (velocity), and therefore the kinetic energy, is dependent upon the temperature.

Greatest number of particles are moving with this energy

Root Mean Square of the energy of the particles

A typical plot showing the variation in particle speeds is shown below for hydrogen gas at 273K..

Root Mean Square

- The root-mean-square-speed is the square root of the averages of the squares of the speeds of all the particles in a gas sample at a particular temperature.

μrms = (3RT / MW)1/2

Where R = universal gas constant = 8.3145 kg·m2/s2 mol·K, T = temperature in Kelvin, MW = molar mass of the gas in kg/mol.

Example #11

- Determine the μrms of hydrogen gas at 25ºC. Determine the μrms of nitrogen gas at 25ºC.
- Determine the μrms of argon gas at 25ºC.
- Determine the μrms of the gases in questions 1, 2 and 3 at a temperature of 50ºC.
- What can be said quantitatively about the μrms of a gas in relation to its molar mass and its temperature?

Grahams Law of Effusion and Diffusion

- Effusion is the process in which a gas escapes from one chamber of a vessel to another by passing through a very small opening.
- Grahams Law of effusion states that the rate of effusion is inversely proportional to the square root of the density of the gas at constant temperature.

Grahams Law of Effusion and Diffusion

- Diffusion is the process by which a homogeneous mixture is formed by the random motion and mixing of two different gases.
- Grahams Law of diffusion states that the rate at which gases will diffuse is inversely proportional to the square roots of their respective densities and molecular masses.

Dalton’s Law of Partial Pressures

- Dalton’s Law states that in a mixture of gases the total pressure exerted by the mixture is equal to the sum of the individual partial pressures of each gas.
- PT = P1 + P2 + P3 + …+ Pn

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