Chapter 10Gases

No…not that kind of gas

Kinetic Molecular Theory of Gases

Kinetic Molecular Theory of Gases –

Based on the assumption that gas molecules are always moving.

Assumptions of Gas Molecules

1. Gases consist of lots of tiny particles that are very far apart. Caron dioxide particles take up 1000x space of liquid or solid.

2. Collisions of the gas particles are elastic – no net loss of energy.

3. Gas particles are in constant random motion.

4. No attraction or repulsion between gas particles.

5. Average energy of gas depends on temperature of gas.

Ideal Gases

Ideal gases follow all 5 assumptions of the kinetic molecular theory.

Real gases act like ideal gases at 1 atm and room temperature.

Real gases don’t follow the assumptions of KMT at very low temperatures and at very high pressures because these gases at low temp. and high press. are becoming a liquid or solid. Therefore, will not act like a gas.

Properties of Gases

Gases don’t have definite shape or volume. They flow, have low density, are compressible and can diffuse and effuse.

Diffusion – mixing of two gases by random motion

Effusion – process where a gas passes through a small opening.

Pressure

Pressure = force per unit area

Calculate the force for getting your foot stomped on by a) athletic shoe heel

b) stiletto high heel.

Measurements of Pressure

Barometer measures atmospheric pressure.

Units for Pressure (memorize)

1 atm = 760 mm Hg = 760 torr = 101.3 kPa

atm = atmosphere kPa = kilopascal

mm Hg = millimeters of mercury

STP = standard temp and press = 1 atm, 0C

Pressure

For gases in a container…

Pressure is caused by gas molecules colliding with the WALL of the container

The more collisions with the wall, the higher the pressure.

Gas Laws

Gas laws relates 4 variables of gases to each other:

1. pressure , P

2. temp, T must be in kelvin

3. volume , V

4. amount of gas, n must be in moles

Boyle’s Law

Boyle’s Law: The pressure is inversely proportional to the volume.

PV = k OR P1V1 = P2V2

Illustrate and graph. Pg 314

Boyle's Law, As the pressure increases the volume decreases proportionally

http://www.grc.nasa.gov/WWW/K-12/airplane/aboyle.html

Charles’ Law

Charles Law – volume of gas is directly proportional to the Kelvin temp.

V = k OR V1 = V2

T T1 T2

Illustrate by example and graph p318.

Charles' Law, As the temperature increases the volume increases proportionally

Gay Lussac’s Law

Gay Lussac’s Law: Pressure of a gas is directly proportional to the Kelvin temperature.

P = k OR P1 = P2

T T1 T2

Illustrate by example and graph pg 319

Gay Lussac's Law, At constant volume as the temperature increases the pressure increases proportionately

Avogadro’sLaw

Avogadro’s Law - Gas volume is directly proportional to the amount of gas.

V = k OR V1 = V2

n n1 n2

Illustrate by example and graph.

Combined Gas Law – shows the relationship between pressure, volume, temperature, and amount of gas.

Combined Gas Law

P1V1 = P2V2

n1T1 n2T2

P = pressure in mmHg, torr, kPa, as long as P1 & P2 are same units.

V = volume in L, mL as long as V1 & V2 are same units

n = number of molesT = temperature in Kelvin K = °C + 273 must be Kelvin in all gas law calculations.

Demonstrate what happens to the combined gas law when a variable does not change.

Therefore, any variable held constant or not mentioned can be dropped from the combined gas law equation.

Practice Problems

1. A fixed amount of helium gas is compressed from 4 L to 2.5 L at a constant temperature. If the pressure of a gas in the 4.0 L volume is 210 kPa, what will the pressure be at 2.5 L?

2. The pressure of a fixed amount of gas in a tank is 3.20 atm at 22.0 ºC. If the temperature rises to 60 ºC, what is the new gas pressure in the tank if the volume is constant?

3. A fixed mass of gas at 40ºC occupies a volume of 2.32 L. If the temperature is raised to 75ºC, what is the new volume if the pressure remains constant?

4. A gas at 110 kPa and 30C fills a flexible container with an initial volume of 2 L. If the temperature is raised to 80ºC, and the pressure is increased to 440 kPa, what is the new volume?

5. The volume of a sample of gas is 200 mL at 275 K and 92.1 kPa. What is the temperature of the gas if the volume increases to 450 mL and the pressure increases to 98.5 kPa?

Dalton’s Law of Partial Pressure

Dalton’s Law of partial pressures – the total pressure of a gas mixture is equal to the pressures of each of the individual gases added together.

Pt = P1 + P2 + P3 + …

Illustrate how a gas is collected by water displacement. Appendix A table gives water vapor pressure at different temperatures. Pg. 899

Examples

1. A mixture of a gases contains argon and neon. If the partial pressure of neon is 1.84 atm, what is the partial pressure of argon at 1816.4 mm Hg?

2.

888 mL of oxygen is collected over water with a temperature of 27C. The total pressure of the gases is 55.8 kPa. What is the partial pressure of the dry gas?

3. Some hydrogen gas is collected over water at 20C. The levels of water inside and outside the gas collection bottle are the same. The partial pressure of hydrogen is 742.5 torr. What is the barometric pressure at the time the gas collected?

Chapter 11

Gases Part II

Avogadro’s Law

Avogadro’s Law – Equal volumes of gases at the same temp and press have the same number of molecules. Illustrate.

Standard Molar Volume of a Gas –

Volume of mole of gas at STP = 22.414 L

1 mole gas = 22.4 L (STP)

Examples

1. A chemical reaction produced 0.0680 moles of oxygen gas. What is the volume at STP?

2. What is the mass of 98 mL of sulfur dioxide at STP?

Ideal Gas Law

Ideal Gas Law – relationship between P, V, n, T for one gas alone.

PV = nRT

P = press in atm

V = volume in L

n = moles

R = universal gas constant

= 0.0821 Latm

molK

T = Kelvin

Memorize the value and units of RSee different values of R on pg. 342

1. What is the volume, in liters, of 0.250 moles of oxygen gas at 20C and 0.974 atm?

2. What is the volume of 25.36 g of nitrogen gas, N2, at 0C and 765 mm Hg?

3.

a. What is the molar mass of a 1.00 liter gas at 28C and 0.974 atm. The gas has a mass of 5.16 g?

b. What is the density of the gas?

Gas Stoichiometry

Review the 4 steps of stoichiometry problems:

Step 1

Step 2

Step 3

Step 4

Volume – Volume Calculations

1. What will be the volume of oxygen at STP needed for the complete combustion of 0.350 L of propane, C3H8?

Volume – Mass Calculations

2. How many grams of calcium carbonate must be decomposed to produce 5.00 L of carbon dioxide at STP? CaCO3 CaO + CO2

Gas Stoichiometry with New Conditions

1. Tungsten is produced for light bulbs by this reaction:

WO3 + 3H2 W + 3H2O

How many liters of hydrogen at 35C and 0.980 atm are needed to react completely with 875 g of tungsten oxide?

2. What volume of chlorine gas at 38C and 1.63 atm is needed to react completely with 10.4 g of sodium to form NaCl?

Graham’s Law of Effusion

The rates of effusion of gases at the same temp and press are inversely proportional to the square roots of their molar masses.

Rate of effusion of A = MB = densityB

Rate of effusion of B = MA densityA

Examples

1. Compare the rates of effusion of hydrogen and oxygen at the same temp and press.