THE GAS LAWS

BOYLE’S LAWThe inverse relationship between pressure and volumeIt states that the volume of a sample of gas changes inversely with the pressure of the gas as long as the temperature and the amount of the gas remain constant.

When the pressure of the gas decreases, the volume of the gas increases.When the pressure of a gas increases, the volume of the gas decreases.

P1V1 = P2V2

SAMPLE PROBLEMS:1. A tank of nitrogen has a volume of 14.0 L and a pressure of 760.0 mmHg. Find the volume of the nitrogen when its pressure is changed to 400.0 mmHg while the temperature is held constant.

2. A 200-L helium gas at a pressure of 280C and a pressure of 2.0 atm was transferred to a tank with a volume of 68.0 L. What is the internal pressure of the tank if the temperature is maintained?

3. A balloon contains 14.0 L of air at a pressure of 760 torr. What will the volume of the air be when the balloon is taken to a depth of 10 ft in a swimming pool, where the pressure is 981 torr? The temperature of the air does not change.

CHARLES’ LAWStates that the Kelvin temperature and the volume of a gas are directly related when there is no change in pressure or amount of gas.The relationship between volume and temperature was first observed by French physicist and balloonist Jacques Charles.

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SAMPLE PROBLEMS

1. A balloon has a volume of 2500.0 mL on a day when the temperature is 30.00C. If the temperature at night falls to 10.00C, what will the volume of the balloon if the pressure remains constant?

2. Find the final temperature of a 2.00- L gas sample at 20.00C cooled until it occupies a volume of 500 mL.

Do the ff. exercises:

1. A sample of freon gas used in air conditioner has a volume of 325.0 L and a pressure of 96.3 kPa at 200C. What will the pressure of the gas be when its volume is 975.0 L at 200C?

2. A balloon contains 30.0L of helium gas at 100 kPa. What is the volume when the balloon rises to an altitude where the pressure is only 25.0 kPa?

3. What is the volume of a sample of thane at 467K and 2.25 atm if it occupies 1.405 L at 300K and 2.25 atm?

4. The gas in a 1.00-L bottle at 250C can be put into a 0.946 bottle at the same pressure if the temperature is reduced. What temperature is required?

THE COMBINED GAS LAW

The two gas laws can be combined and treated as a single law which describes the relationship among the pressure, volume and temperature of a constant amount of gas.

SAMPLE PROBLEMS:

1. A given mass of gas has a volume of 800.0 mL at –23.00C and 300.0 torr. What would the volume of the gas be at 27.00C and 600.0 torr of pressure? The amount of gas is constant.

2. A 5.0 –L air sample at a temperature of –50.00C has a pressure of 107.0 kPa. What will the new pressure be if the temperature is raised to 100.00C and the volume expands to 7.0 L?

3. A 3.50-L gas sample at 200C 200C and a pressure of 86.7 kPa is allowed to expand to a volume of 8.0 L. The final pressure of the gas is 56.7 kPa. What is the final temperature of the gas?

5. A weather balloon is filled with 16.0 L of helium at a temperature of 260C and a pressure of 700 mm hg. What is the pressure of the helium in the balloon in the upper atmosphere when the temperature is -330C and the volume becomes 35.oL

THE IDEAL GAS LAW

The law that describes the pressure, volume, temperature, and number of moles of a gas.

PV= nRTWhere:

P= pressure of the gasV= volume of the gasn= amount of gasR= ideal gas constantT= temperature of the gas

At STP,P= 1.0 atm= 101.325 kPaV= 22.4 Ln= 1.0 moleT= 273 KR= 0.0821 atm x L/ mol x K = 8.31kPa x L/ mol x K

SAMPLE PROBLEMS:

1. What volume will 1.27 mol of helium gas occupy at STP?

2. How many moles of gas are contained in a 50.0-L cylinder at a pressure of 100.0 atm and a temperature of 35.00C?

3. What pressure will be exerted by 0.450 mol of a gas at 250C if it is contained in a vessel whose volume is 0.65 L?

4. You fill a rigid steel cylinder with a volume of 20.0 L with nitrogen gas to a final pressure of 20 000 kPa at 270C. How many moles of nitrogen gas does the cylinder contain?

Answer the following exercises:

1. A deep underground cavern contains 2.24 x 106 L of methane gas(CH4) at a pressure of 1,500 kPa and a temperature 420C. How many kg of methane does this gas deposit contain?

2. The volume of a gas- filled balloon is 30.0 L at 40.00C and 150 kPa pressure. What volume will the balloon have at STP?

3. The volume of a sample of CO is 405 mL at 10.0 atm and 467 K. What volume will it occupy at 4.29 atm and 467 K?

4. When a rigid hollow sphere containing 680 L of helium gas is heated from 300 K to 600 K, the pressure of the gas increases to 1 800 kPa. How many moles of helium are in the sphere?

5. A container with an initial volume of 1.0 L is occupied by a gas at a pressure of 150 kPa at 250C. By changing the volume, the pressure of the gas increases to 600 kPa as the temperature is raised to 1000C. What is the new volume?

GAY- LUSSAC’S LAW

Temperature and pressure relationshipThe pressure of a gas is directly related to its Kelvin temperature.

This means that an increase in temperature increases the pressure of a gas, and a decrease in temperature decreases the pressure of the gas as long as the volume and number of moles of the gas remain constant.

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SAMPLE PROBLEMS:1. The gas left in a used aerosol can is at a pressure of 100 kPa at 270C. If the can is thrown onto a fire, what will the internal pressure be when its temperature reaches 9270C?

2. The pressure in automobile tire is 200 kPa at a temperature of 270C. At the end of a journey on a hot sunny day, the pressure has risen to 223 kPa. What is the temperature of the air in the tire?

AVOGADRO’S LAW

Equal volumes of gases at the same temperature and pressure contain equal numbers of particles.

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SAMPLE PROBLEMSIf 23.1 g of oxygen occupies a volume of 5.0 L at a particular pressure and temperature, what volume will 2.5 g of oxygen gas occupy under the same conditions?

Determine the volume in liters occupied by 0.202 mol of a gas at STP.How many oxygen molecules are in 3.3 liters of oxygen gas at STP?

Determine the volume in liters occupied by 14.0 g of N2 at STP.What volume is occupied by 4.02 x 1022 molecules of H2 at STP?

DALTON’S LAW

At constant volume and temperature, the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of the component gases.

Ptotal= P1+P2+P3……

SAMPLE PROBLEMSDetermine the total pressure of a gas mixture that contains oxygen, nitrogen, and helium if the partial pressures of the gases are 20.0 kPa, 46.7 kPa, and 26.7 kPa respectively.

A balloon contains mostly He and a little methane. The partial pressure of helium is 101.2 kPa. If the pressure inside the balloon is 101.3 kPa, what is the partial pressure of methane?A 5.73- L flask at 250C contains 0.0388 mol of N2, 0.1 47 mol of CO, and 0.0803 mol of H2. What is the pressure in the flask in atm and kPa?