GasesGasesChapter 14Chapter 14

Section 14.1Section 14.1

Ideal GasIdeal Gas• Remember, these gas laws apply to

ideal (perfectly behaved) gases.• Ideal gases behave according to the

five assumptions made by kinetic molecular theory, and are as follows:

Kinetic Molecular TheoryKinetic Molecular Theory• Gas particles do not attract or repel each

other.• Gas particles are much smaller than the

spaces between them.• Gas particles are in constant, random

motion.• No kinetic energy is lost when gas

particles collide with each other or with the walls of their container.

• All gases have the same kinetic energy at a given temperature.

Boyle’s LawBoyle’s Law• At constant temperature, the

pressure exerted by a gas depends on the frequency of collisions between the particles and the container.

• If the same # of particles is squeezed into a smaller space, the # of collisions increases, thereby increasing the pressure.

Boyle’s Law EquationBoyle’s Law Equation• The equation that expresses Boyle’s

Law is:P1V1 = P2V2

ExampleExample• A sample of compressed methane

has a volume of 648 mL at a pressure of 503 kPa. To what pressure would the methane have to be compressed in order to have a volume of 216 mL?

ReasonablenessReasonableness• To determine whether your answer is

reasonable, notice that the gas is being squeezed into a smaller volume, which requires that the pressure is increased.

Practice Practice 1. What pressure will be needed to

reduce the volume of 77.4 L of helium at 98.0 kPa to a volume of 60.0 L?

2. A 250.0 mL sample of chlorine gas is collected when the barometric pressure is 105.2 kPa. What is the volume of sample after the barometer drops to 100.3 kPa?

Practice (cont’d)Practice (cont’d)3. A weather balloon contains 59.5 L of

helium at sea level, where the atmospheric pressure is 101.3 kPa. The balloon is released from a 4000 m mountaintop where the pressure is 61.7 kPa. What is the volume of the balloon when it is released?

4. Meteorologists want the balloon in problem 3 to float at an altitude of 35,000 m where the pressure is 575 kPa. What volume will the balloon have at that altitude?

Charles’s LawCharles’s Law• When the temperature of a sample of gas

is increased and the volume is free to change, the pressure of the gas does not increase.

• Instead the volume of the gas increases, with an increase in the Kelvin temperature.

• Charles’s Law is expressed as:V1 = V2

T1 T2

ExampleExample• A weather balloon contains 5.30 kL of

helium gas when the temperature is 12 degrees celsius. At what temperature will the balloon’s volume have increased to 6.00 kL?

PracticePractice5. A sample of SO2 gas has a volume of

1.16 L at a temperature of 23 degrees Celsius. At what temperature will the gas have a volume of 1.25 L?

6. A balloon is inflated with 6.22 L of helium at a temperature of 36 degrees celsius. What is the volume of the balloon when the temperature is 22 degrees celsius?

PracticePractice7. A student collects a 125.0 mL sample of

hydrogen. Later, the sample is found to have a volume of 128.6 mL at a temperature of 26 degrees celsius. At what temperature was the hydrogen collected?

8. A balloon has a volume of 10, 500 L if the temperature is 15 degrees celsius. If the temperature is -35 degrees celsius, what will be the volume of the balloon?

Gay-Lussac’s LawGay-Lussac’s Law• Gay-Lussac’s Law says that when

volume is constant, that pressure increases as temperature increases.

• It can be expressed as:P1= P2

T1 T2

THE COMBINED GAS LAW THE COMBINED GAS LAW AND AVOGADRO'S AND AVOGADRO'S PRINCIPLEPRINCIPLE

Section 14.2

Combined Gas LawCombined Gas Law• The three gas laws can be combined

into a single law, called the combined gas law.

• This relates pressure, volume, and temperature by the following equation:

P1 V1 = P2 V2

T1 T2

Using the Gas LawUsing the Gas Law• Using this equation, you can find any

value as long as you know the other five.

ExampleExample• A sample of nitrogen monoxide has a

volume of 72.6 mL at a temperature of 16 ̊C and a pressure of 104.1 kPa. What volume will the sample occupy at 24 ̊C and 99.3 kPa?

PracticePractice9. A sample of ammonia gas occupies a

volume of 1.58 L at 22 °C and a pressure of 0.983 atm. What volume will the sample occupy at 1.00 atm and 0 °C?

10. A student collects 285 mL of O2 gas at a temperature of 15 °C and a pressure of 99.3 kPa. The next day, the same sample occupies 292 mL at a temperature of 11 °C. What is the new pressure of the gas?

PracticePractice11. A balloon is inflated with 2.42 L of

helium at a temperature of 27 °C. Later, the volume of the balloon has changed to 2.37 L at a temperature of 19 ° C and a pressure of 99.7 kPa. What was the pressure when the balloon was inflated?

Avogadro’s PrincipleAvogadro’s Principle• According to Avogadro’s principle,

equal volumes of all gases at the same temperature and pressure, contain the same number of particles.

• In other words, at standard temperature and pressure (STP) [0 °C and 1.00 atm] gases occupy a volume of 22.4 L.

ExampleExample• What is the volume of 7.17 g of neon

gas at 24 °C and 1.05 atm, if the initial is STP.

PracticePractice12. How many moles of acetylene

(C2H2) gas occupy a volume of 3.25 L at STP?

13. Determine the volume of 12.3 g of formaldehyde gas (CH2O) at STP.

14.What is the volume of 1.000 kg of helium gas at 36 °C and a pressure of 98.7 kPa?

THE IDEAL GAS LAWTHE IDEAL GAS LAWSection 14.3

Ideal Gas LawIdeal Gas Law• The ideal gas law is a simpler, more

convenient way of relating pressure, volume, temperature and the number of moles.

PV = nRT• In this equation, n is the number of

moles and R is the Ideal gas constant.

R ValuesR Values• R includes the molar volume

correction.• It depends on the units that you need

for it.R= 8.314 L *kPa = 0.0821 L * atm = 62.4 L * mmHg

mol * K mol * K mol * K

ExampleExample• What pressure in atmospheres will

18.6 mol of methane exert when it is compressed in a 12.00 L tank at a temperature of 45 °C?

PracticePractice17. What is the pressure in atmospheres

of 10.5 moles of acetylene in a 55.0 L cylinder at 37 °C?

18. What volume does 0.056 mol of H2 gas occupy at 25 °C and 1.11 atm?

19. A sample of carbon monoxide has a volume of 344 mL at 85 °C and a pressure of 88.4 kPa. Determine the amount of moles of CO present.

Mass and Ideal Gas LawMass and Ideal Gas Law• Remember, that it is possible to

calculate the number of moles of a sample when you know the mass using the molar mass.

• We can also use the ideal gas expression to find the mass.

PV = mRT or PVM = mRTM .

ExampleExample• Determine the molar mass of an

unknown gas if a sample has a mass of 0.290 g and occupies a volume of 148 mL at 13 °C and a pressure of 107.0 kPa.

PracticePractice20.A 250.0 mL sample of a noble gas

collected at 88.1 kPa and 7 °C has a mass of 0.378 g. What is the molar mass of the gas? Identify the sample.

21.What volume is occupied by 1.000 g of H2O vapor at a temperature of 134 °C and a pressure of 0.0552 atm?

22.A 5.25 L tank contains 87.0 g of neon gas. At what temperature will the tank have a pressure of 19.0 atm?

GAS STOICHIOMETRYGAS STOICHIOMETRYSection 14.4

StoichiometryStoichiometry• Just like we can use moles to perform

stoichiometric calculations, with gases we can use volumes to perform stoichiometric calculations.

ExampleExample2NH3 (g) + H2SO4 (aq) (NH4)2SO4 (aq)

• What volume of NH3 gas, measured at 78 ° C and a pressure of 1.66 atm, will be needed to produce 5.00 X 103 g of (NH4)2SO4?

PracticePractice24.A piece of aluminum with a mass of

4.25 g is used to generate hydrogen gas by the following method.2 Al (s) + 6 HCl (aq) 2AlCl3 (aq) + 3H2 (g)

The hydrogen collected at a temperature of 15 °C and a pressure of 94.4 kPa. What volume of hydrogen is produced?