March 16, 2015

Gas Laws

Chapter 14

Gas Laws

Overview:

Chapter 14: The Behavior of Gases• Gas Laws

> Boyle's, Charle's, Gay-Lussac's• Ideal Gas Law• Gases: Mixtures and Movements

3. GasesThe kinetic-molecular theory (KMT) can help you understand the behavior of gas molecules and the physical properties of gases. The theory provides a model of what is called an ideal gas.

An ideal gas is a hypothetical gas that perfectly fits all the assumptions of the kinetic-molecular theory.

There are five parts to this theory:

Kinetic-Molecular Theory of Gases1. Gases consist of large numbers of tiny particles that are far apart relative to their size.2. Collisions between gas particles and between particles and container walls are elastic collisions.

Elastic collision: one in which there is no net loss of total kinetic energy3. Gas particles are in continuous, rapid, random motion. They therefore possess kinetic energy, which is energy of motion.4. There are no forces of attraction between gas particles.5. The temperature of a gas depends on the average kinetic energy of the particles of the gas.

5. PressurePressure is defined as the force per unit area on a surface. The SI unit is Pascal (Pa)= N/m2.

Gas molecules exert pressure on any surface with which they collide. The pressure exerted by a gas depends on volume, temperature and the number of particles present.

PressureWe have many different units of pressure:

1 atm = 760 mm Hg and 760 Torr = 101.3 kPa

March 16, 2015

Pressure Conversion Practice

1. A pressure gauge records a pressure of 450 kPa. What is this measurement expressed in atmospheres and millimeters of mercury? (4.4 atm and 3376 mm Hg)

2. What pressure, in kPa and atm, does a gas exert at 385 mm Hg? (51.3 kPa, 0.507 atm)

Section 14.2 The Gas Laws

1. Boyle's LawPressure and Volume

2. Charles' LawTemperature and Volume

3. Gay-Lussac's LawPressure and Temperature

1. Boyle's LawBoyle's law: for a given mass of gas at constant temperature, the volume of the gas varies inversely with pressure.

1. Boyle's Law

P1 x V1 = P2 x V2

Example: A balloon contains 30.0 L of helium gas at 103 kPa. What is the volume of the helium when the balloon rises to an altitude where the pressure is only 25.0 kPa? (Assume the temperature remains constant)

Know:P1= 103 kPaV1= 30.0 LP2 = 25.0 kPaV2= ?

V2 = P1 x V1

P2

1. Boyle's LawPractice:1. Nitrous oxide (N2 O) is used as an anesthetic. The pressure on 2.50 L of N2 O changes from 105 kPa to 40.5 kPa. If the temperature does not change, what will the new volume be? (6.48 L)

March 16, 2015

2. Charles' LawCharles' Law: the volume of a fixed mass of gas is directly proportional to its Kelvin temperature if the pressure is kept constant.

2. Charles' LawA balloon inflated in a room at 24°C has a volume of 4.00 L. The balloon is then heated to a temperature of 58°C. What is the new volume if the pressure remains constant? (4.46 L)

Know:V1 = 4.00 LT1 = 24°CT2 = 58°CV2 = ?

1. Change both temperatures to Kelvin2. Rearrange equation to solve for V2

3. Gay-Lussac's Law

Gay-Lussac's Law: the pressure of a gas is directly proportional to the Kelvin temperature if the volume remains constant.

Why do auto tire manufacturers recommend checking for proper inflation before driving the car more than a mile?

3. Gay-Lussac's Law

The gas in a used aerosol can is at a pressure of 103 kPa at 25°C. If the can is thrown onto a fire, what will the pressure be when the temperature reaches 928°C? (415 kPa)

Known:P1 = 103 kPaT1 = 25°CT2 = 928°CP2 = ?

1. Change both temperatures to Kelvin2. Rearrange equation to solve for P2

4. The Combined Gas LawThe combined gas law allows you to do calculation for situations in which only the amount of gas is constant.

ExampleThe volume of a gas-filled balloon is 30.0 L at 313 K and 153 kPa pressure. What would the volume be at STP?

Both units of pressure must be the same along with both units of volume.

4. The Combined Gas LawPractice:

1. A gas 155 kPa and 25°C has an initial volume of 1.00 L. The pressure of the gas increases to 605 kPa as the temperature is raised to 125°C. What is the new volume? (0.342 L)

March 16, 2015

Derivation Real vs. IdealIdeal GasAn ideal gas would have to conform precisely to the assumptions of kinetic theory. Its particles could have no volume and there could be no attraction between particles in the gas.

An ideal gas DOES NOT exist!

Real Gas:The particles have volume, and there are attractions between the particles.

*Real gases differ most from an ideal gas at low temperatures and high pressures.

Real vs. Ideal

Section 14.3 Ideal GasesIn this section, you will learn how real gases differ from the ideal gases on which the gas laws are based.

· To calculate the number of moles of a contained gas requires an expression that contains the variable n.· Ideal gas constant (R) is 8.31 (L*kPa)/ (K*mol)

and 0.0821(L*atm)/ (K*mol)

PV=nRT

Section 14.3 Ideal GasesA deep underground cavern contains 2.24 x 106 L of

methane gas (CH4 ) at a pressure of 1.50 x 103 kPa and a temperature of 315 K. How many mols of CH4 does the cavern contain?

PV=nRTn=PV

RT

Known:P=1.50 x 103 kPaV= 2.24 x 106 LT=315 KR= 8.31 (L*kPa)/(K*mol)Solve for n

March 16, 2015

Practice:

1. When the temperature of a rigid hollow sphere containing 685 L of helium gas is held at 621 K, the pressure of the gas is 1.89 x 103 kPa. How many moles of helium does the sphere contain? (251 moles He)

Section 14.3 Ideal Gases Section 14.3 Ideal Gases

We can calculate density and molar mass using the ideal gas law:

Section 14.3 Ideal Gases

Calculate the density of CO2 in g/L at 0.900 atm and 55°C

Section 14.3 Ideal Gases

A greenish yellow gas of chlorine and oxygen has a density of 7.71 g/L at 36°C and 2.88 atm. Calculate the molar mass of this gas.

Section 14.3 Ideal Gases Practice

1. Find the molecular weight of a gas of which 5.03 g occupies a volume of 4.4 L when the pressure is 1.333 atm and the temperature is 65.5°C. (24 g/mol)