MU #1 Kinetic molecular theory describes the relationships of pressure, volume, temperature, velocity, and frequency and force of collisions among gas molecules. 

The combined gas law  (See table T) is the relationship between pressure, volume, and temperature for ideal gases.

Note: Temperature has to be expressed in Kelvins. To convert Celsius degrees (^oC) to kelvins (K) and vice versa see table T

K = ^oC + 273

Example

At STP a gas has a volume of 20 L. If the pressure increases to 2 atm and the temperature decreases to 200 K, what is the

new volume? Hint: For STP refer to table A.

Using P1 V1 / T1 = P2 V2 / T2 solve for V2

V2 = P1 V1 T2 / P2 T1 = (1 atm) (20 L) (200 K) / (2 atm) (273 K) = 7 L

Problems

1. A sample of gas confined to a volume of 10 liters at 273 K and 2 atm is subjected to a pressure increase of .5 atm and a temperature decrease of 10^oC. What is the new volume?

At constant temperature, T1 and T2 are the same, therefore they cancel out of the combined gas law formula. The relationship between pressure and volume at constant temperature is called Boyle's law.

Example

Therefore, at constant temperature, as the pressure increases the volume decreases or the volume of a gas is inversely proportional to the pressure applied on it.

When Boyle's law is graphed the line is a hyperbola.

Problem

1. Explain the gas law in terms of the KMT.

2. A storage container holds 400 liters of a gas at 2 atm. If the pressure is increased to 5 atmospheres at constant temperature, what will be the volume of the gas?

At constant pressure, P1 and P2 are the same, therefore they cancel out of the combined gas law formula. The relationship between volume and temperature at constant pressure is called Charles' law.

Example

Therefore, at constant pressure, as the temperature increases the volume increases or the volume of a gas is directly proportional to its temperature.

When Charles' law is graphed the line is positive.

Problems

1. Explain the gas law in terms of the KMT

2. At constant pressure and 27^oC, a gas has a volume of 150 mL. If the T is increased to 327^oC, what will be the new volume?

At constant volume, V1 and V2 are the same, therefore they cancel out of the combined gas law formula. The relationship between temperature and pressure at constant volume is called Gay-Lussac's law.

Example

Therefore, at constant volume, as the temperature increases the pressure increases or the pressure of a gas is directly proportional to its temperature.

When Gay-Lussac's law is graphed the line is positive.

Problem

1. Explain the gas law in terms of KMT

2. Water vapor is contained in a close container. In the morning the temperature was 25^oC and by noon the temperature increased by 10^oC. If the pressure inside the container was 2 atm in the morning, what is the pressure at noon?

At constant volume and temperature, the total pressure of a mixture of gases is the sum of the partial pressure of each gas (Dalton's law)

P_total = P₁ + P₂ + P₃  ........

Example

Problems

1. Gas samples A, B, and C are contained in a system at STP. The partial pressure of sample A is .2 atm and the partial pressure of sample B is .3 atm. What is the partial pressure of sample C?

MU #2 Equal volumes of different gases at the same temperature and pressure contain an equal number of particles.

Example

Note: 1 mole of molecules = 6.02 x 10²³ molecules

TEST YOUR UNDERSTANDING

1/07

6/07

8/07

6/02

1 Which graph shows the pressure-temperature relationship expected for an ideal gas?

2 At the same temperature and pressure, which sample contains the same number of moles of particles as 1 liter of O₂(g)?

            (1) 1 L Ne(g)  (2) 2 L N₂(g)         (3) 0.5 L SO₂(g)        (4) 1 L H₂O(l)

1/03

A gas occupies a volume of 40.0 milliliters at 20^oC. If the volume is increased to 80.0 milliliters at constant pressure, the resulting temperature will be equal to

(1) 20^oC x 80.0 mL /  40.0 mL       (2) 20^oC x 40.0 mL / 80.0 mL            (3) 293 K x 80.0 mL / 40.0 mL      (4) 293 K x 40.0 mL / 80.0 mL                  

6/03

1  Base your answers on the diagram below, which shows a piston confining a gas in a cylinder.

Graph the general relationship between the pressure and the volume of an ideal gas at constant temperature.

2 The gas volume in the cylinder is 6.2 milliliters and its pressure is 1.4 atmospheres. The piston is then pushed in until the gas volume is 3.1 milliliters while the temperature remains constant.

        a) Calculate the pressure, in atmospheres, after the change in volume. Show all work.

        b) Record your answer.   

8/03

20 At the same temperature and pressure, 1.0 liter of CO( g) and 1.0 liter of CO₂ (g) have
        (1) equal masses and the same number of molecules (3) equal volumes and the same number of molecules

        (2) different masses and a different number of molecules (4) different volumes and a different number of molecules

1/04

40 The volume of a gas is 4.00 liters at 293 K and constant pressure. For the volume of the gas to become 3.00 liters, the Kelvin temperature must be equal to

 42 Which graph best represents the pressure-volume relationship for an ideal gas at constant
temperature?

6/04

Base your answers to questions 75 through 78 on the following  formation. A weather balloon has a volume of 52.5 liters at a temperature of 295 K. The balloon is released and rises to an altitude where the temperature is 252 K.

75 How does this temperature change affect the gas particle motion?
76 The original pressure at 295 K was 100.8 kPa and the pressure at the higher altitude at 252 K is 45.6 kPa. Assume the balloon does not burst. Show a correct numerical setup for calculating the volume of the balloon at the higher altitude.

77 What Celsius temperature is equal to 252 K?
78 What pressure, in atmospheres (atm), is equal to 45.6 kPa?

8/04

39 A gas occupies a volume of 444 mL at 273 K and 79.0 kPa. What is the final kelvin temperature when the volume of the gas is changed to 1880 mL and the pressure is changed to 38.7 kPa?

                (1) 31.5 K (2) 292 K (3) 566 K (4) 2360 K

1/05

19 At STP, 4 liters of O₂ contains the same total number of molecules as

                (1) 1 L of NH₃ (2) 2 L of Cl₂ (3) 8 L of He (4) 4 L of CO₂

40 A sample of helium gas has a volume of 900. milliliters and a pressure of 2.50 atm at 298 K. What is the new pressure when the temperature is changed to 336 K and the volume is decreased to 450. milliliters?

                (1) 0.177 atm (2) 4.43 atm (3) 5.64 atm (4) 14.1 atm

6/05

Base your answers to questions 77 through 79 on the information and diagrams below. Cylinder A contains 22.0 grams of CO₂(g) and cylinder B contains N₂(g). The volumes, pressures, and temperatures of the two gases are indicated under each cylinder.

77 What is the total number of moles of CO₂(g) in cylinder A?

78 Explain why the number of molecules of N₂(g) in cylinder B is the same as the number of molecules of CO₂(g) in cylinder A.

79 The temperature of the CO₂(g) is increased to 450. K and the volume of cylinder A remains constant. In the space in your answer booklet, show a correct numerical setup for calculating the new pressure of the CO₂(g) in cylinder A.

1/06

6/06

70 When the air bag inflates, the nitrogen gas is at a pressure of 1.30 atmospheres, a temperature of 301 K, and has a volume of 40.0 liters. In the space in your answer booklet, calculate the volume of the nitrogen gas at STP. Your response must include both a correct numerical setup and the calculated volume.

8/06

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