Unit 10—Gas Laws

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Name Class Period Kinetic Molecular Theory of Gases

The kinetic molecular theory is based on the idea that particles of matter are always in .

An ideal gas is an gas that perfectly fits all the assumptions of the kinetic molecular theory.

The assumptions of the kinetic molecular theory of gases are as follows: 1. Gases consist of large numbers of tiny particles that are in continuous, rapid, random motion

and are relative to their size. The particles of an ideal gas are said to occupy volume and are .

2. Collisions between gas particles and between the particles and container walls are . An elastic collision is one in which there is no net loss of .

3. There are no forces of or between the particles of an ideal gas. This means that ideal gases do not exhibit hydrogen bonding, London forces or dipole-dipole interactions.

4. The average kinetic energy of gas particles depends on the of the gas. A warmer gas sample has a average kinetic energy than a cooler gas sample.

Some differences between real gases and ideal gases are:

1. Ideal gas particles have volume. Real gases particles occupy a volume.

2. The particles of an ideal gas attractive forces on each other. Real gas particles experience

between the particles.

3. Real gases can be and sometimes by cooling and by applying pressure.

Ideal gases be liquefied or solidified.

The conditions in which real gases behave the most like ideal gases are:

1. temperature

2. pressure

Which types of gas molecules deviate the most from ideal gas behavior?

1. molecules deviate more from ideal gas behavior than nonpolar molecules. This is because the intermolecular forces of attraction are usually in polar molecules.

2. molecules deviate more from ideal gas behavior than small diatomic molecules. This is because the particles take up more .

Unit 10—Gas Laws

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Boyle’s Law, Charles’ Law and Gay-Lussac’s Law

Property and Definition Unit Other Units and Unit Conversions

Volume 1000 cm3 = 1000 mL = 1 L

Temperature Celcius (Reminder: Standard temperature = )

Pressure 1 atm = 1 atm = 1 atm = (Reminder: Standard pressure = )

Amount No other unit; can be converted to grams using molar mass

Boyle’s Law states . The formula for Boyle’s Law is: Example: A given mass of gas occupies a volume of 12 L when under a pressure of 2.0 atm. Assuming no change in temperature, what will the volume be if the pressure is changed to 3.0 atm? Charles’s Law states . The formula for Charles’s Law is: Example: A given mass of gas occupies a volume of 1.2 L at a temperature of 27°C and a pressure of 1 atm. What will the volume be if the temperature is increased to 77°C and the pressure remains unchanged? Gay Lussac’s Law states . The formula for Gay Lussac’s Law is:

Example: A quantity of acetylene in a steel cylinder is under a pressure of 1.2 atm at 27°C. What will be the pressure of the gas if the temperature is increased to 87°C?

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Combined Gas Law The formula for the combined gas law is:

Example: 400. mL of a gas at -23°C and a pressure of 750. mm Hg will occupy what volume if the temperature is increased to 77°C and the pressure is decreased to 700. mm Hg?

Practice Problems: 1. A sample of nitrogen gas has a pressure of 2.5 atm at a temperature of 25°C. What temperature

is required to increase the pressure to 4.0 atm, assuming that the volume is fixed and amount of gas does not change?

2. The volume of a sample of gas is 200. mL at 275 K and 92.1 kPa. What will the new volume of the gas be at 350. K and 98.5 kPa?

3. A given mass of gas occupies a volume of 640 mL at 47°C and 650 mm Hg. What will the new temperature be if the volume is decreased to 210 mL and the pressure remains unchanged?

4. A given mass of gas occupies a volume of 50.0 L when under a pressure of 10.0 atm. Assuming no change in temperature, what will be the new pressure if the volume is changed to 75.0 L?

Day 1—Graham’s Law Graham’s Law of Diffusion/Effusion The velocity of two gases can be compared using the following formula:

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Which gas diffuses faster? Hydrogen or nitrogen? What is the ratio of the rates of diffusion? How would the ratio of the rates of diffusion for hydrogen and nitrogen change if the temperature were increased? A sample of hydrogen effuses through a porous container about 9 times faster than an unknown gas. Estimate the molar mass of the unknown gas. If a molecule of neon gas travels at an average of 400 m/s at a given temperature, estimate the average speed of a molecule of butane gas, C4H10, at the same temperature.

Dalton’s Law of Partial Pressures and the Ideal Gas Law Dalton’s law of partial pressure states that the

.

The formula for Dalton’s law of partial pressure is:

Air contains oxygen, nitrogen, carbon dioxide, and trace amounts of other gases. What is the partial pressure of oxygen (𝑃𝑂2) at 760 mm Hg of pressure if 𝑃𝑁2 = 593.4 mm Hg, 𝑃𝐶𝑂2 = 0.3 mm Hg, 𝑃𝑜𝑡ℎ𝑒𝑟 =

7.1 mm Hg?

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The pressure of a gas collected over water can be calculated by the vapor pressure of the water from the total pressure. The amount of water vapor present is very sensitive to . 0.750 L of a gas is collected over water at 25.0°C with a total pressure of 747.8 mm Hg. What is the pressure of the dry gas?

Temperature (°C)

Pressure (mm Hg)

-10 2.1

-0 3.2

0 4.6

5 6.5

10 7.0

15 9.2

20 17.5

25 23.8

30 31.8

Avogadro’s law states that

This means that the volume of a gas is proportional to the number of moles of the gas.

The ideal gas law equation allows for the quantity of the gas to be considered. The ideal gas law is as follows: The 3 different values for R, are: The value of R you should use depends upon the unit of being used in the calculation.

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1. What volume will 1.2 mol of N2 occupy at 17°C and 2.0 atm? 2. What pressure in atmospheres, will 0.80 mol of gas in a volume of 2.0 L exert if the temperature

is 27°C? 3. At what Celsius temperature will 0.20 mol of gas in a 1.5 L cylinder exert a pressure of 2.8 atm? 4. At 27°C the gas in a 920 mL flask exerts a pressure of 730 mm Hg. How many grams of nitrogen

gas are in the flask? Finding Molar Mass or Density from the Ideal Gas Law 1. At 28°C and 0.974 atm, 1.00 L of gas has a mass of 5.16 g. What is the molar mass of this gas? 2. What is the density of a sample of ammonia

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Stoichiometry of Gases 1. What mass in grams of hydrogen peroxide must be used to produce 1.00 L O2(g), measured at

25C and 1.00 atm? The reaction is 2H2O2(aq) → O2(g) + 2H2O(g)

2. How many liters of oxygen, measured at 740 mm Hg and 24C, are required to burn 1.00 g of octane, C8H18(l), to carbon dioxide and water?

2C8H18(g) + 25O2(g) → 16CO2(g) + 18H2O(g)

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Phase Changes The six phase changes are:

1. Solid → Liquid

Example:

2. Liquid → Solid

Example:

3. Liquid → Gas

a. Evaporation – occurs at the of a liquid.

Example:

b. Boiling – occurs when the

Example:

4. Gas → Liquid

Example:

5. Solid → Gas

Example:

6. Gas → Solid

Example:

, and are endothermic processes.

, and are exothermic processes.

A vapor pressure curve can be used to represent the of a substance at various .

Any point along a vapor pressure curve for a compound represent the

of the substance.

The normal boiling point of a substance occurs when the vapor pressure is equal to .

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At what temperature will ethanol boil when the atmospheric pressure is 200 mm Hg?

What vapor pressure would be needed to make water boil at 80°C?

Which substance has the strongest intermolecular forces of attraction? Heating and Cooling Curves Here is a heating curve for water.

1. Segment AB:

2. Segment BC:

Point B -

Between Points B and C -

Point C -

3. Segment CD:

4. Segment DE:

Point D -

Between Points D and E -

Point E -

5. Segment EF: The amount of energy required to vaporize a sample of water is much

than the amount of energy required to melt than same amount of water.

A

B C

D E

F

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1. Segment FE:

2. Segment ED:

Point E -

Between Points E and D -

Point D -

3. Segment DC:

4. Segment CB:

Point C -

Between Points C and B -

Point B -

5. Segment BA:

20.0 g of an unknown substance is heated from 30.0°C to 120°C as illustrated in the graph below.

a. At what temperature does the substance freeze? b. At what temperature does the substance melt? 55°C c. At what temperature does the substance boil? d. At what temperature does the substance boil?

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Phase Diagrams A phase diagram is a

The triple point indicates the temperature and pressure conditions at which the of the substance can coexist at equilibrium.

The triple point of water is at °C and atm.

The critical point of a substance

The critical temperature is the temperature above which the substance

regardless of pressure.

The critical temperature for water is °C.

The critical pressure is the at which the substance can exist as a liquid at the critical temperature.

The critical pressure for water is atm.

Using the phase diagram for water, at roughly what pressure will water be a gas at 0°C?

Within what range of pressures will water be a liquid at temperatures above its normal boiling point?

What phase change is occurring as the temperature of ice is increased from -50°C to 50°C at 1 atm of pressure?

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Use the phase diagram below to answer the following questions.

Indicate the property to the system that is changing and name the phase change for each section of the diagram.

A → B

C → D

E → F

G → H

B → A

D → C

F → E

H → G

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Notice that the solid-liquid equilibrium line does not slope the same for both diagrams. What this means is that when is increased, a normal substance will change from a , but water will change from a . This is due to the in water. The lattice structure formed by ice causes the solid phase to be than the liquid phase which is why ice floats on water.