The Behavior of Gases Chapter 14

Section 1 Properties of Gases

Section 1 Learning Targets 14.1.1 – I can explain why gases are easier to compress than solids or liquids are. 14.1.2 – I can describe three factors that affect gas pressure.

Compressibility Compressibility – a measure of how much the volume of matter decreases under pressure. Gases are easily compressed because of the space between the particles.

Factors Affecting Gas Pressure The amount of gas, volume, and temperature are factors that affect gas pressure. Pressure (P) in kilopascals (kPa) Volume (V) in liters (L) Temperature (T) in Kelvin (K) Number of moles (n) in mole (mol)

Amount of Gas You can use kinetic theory to predict and explain how gases will respond to a change of conditions. As you add more gas particles the pressure increases.

Amount of Gas Once the pressure exceeds the strength of the container the container will burst.

Aerosol cans depend on the movement of gas from a region of high pressure to a region of low pressure. Pushing the spray button creates an opening between the inside of the can and the outside.

The gas flows through the opening to the lower pressure region outside. The movement of the gas propels the paint out of the can until the gas can no longer propel paint out.

Volume You can raise the pressure exerted by a contained gas by reducing its volume. The more a gas is compressed the greater the pressure.

Temperature As a gas is heated, the temperature increases and the average kinetic energy also increases.

When the volume of a container is held constant and the temperature increases and the pressure increases.

Section 2 The Gas Laws

Section 2 Learning Targets 14.2.1 – I can describe the relationships among the temperature, pressure and volume of a gas. 14.2.2 – I can use the combined gas law to solve problems.

Answer the following questions based on the graph from the previous slide. When the volume is 2.0L, what is the pressure? What would the pressure be if the volume were increased to 3.0L? Based on the shape of the graph, describe the general pressure-volume relationship.

Boyle’s Law: Pressure and Volume If the temperature is constant, as the pressure of a gas increases, the volume decreases.

Boyle’s law – states that for a given mass of gas at a constant temperature, the volume of the gas varies inversely with pressure.

Example: Nitrous oxide (N2O) is used as an anesthetic. The pressure on 2.50L of N2O changes from 105kPa to 40.5kPa. If the temperature does not change, what will the new volume be?

Answer the following questions based on the graph from the previous slide. What is the unit of temperature? What happens to the volume as the temperature rises? If the temperature of a gas were 0K, what would the volume of the gas be?

Charles’s Law: Temperature and Volume As the temperature of an enclosed gas increases, the volume increases, if the pressure is constant.

Charles’s law – states that the volume of a fixed mass of gas is directly proportional to its Kelvin temperature if the pressure is kept constant.

Example: If a sample of gas occupies 6.80L at 325°C, what will its volume be at 25°C if the pressure does not change? (HINT: temps need to be in Kelvin first)

How can you tell from the picture that there is a fixed amount of gas in the cylinder? Describe what is happening in the cylinder as it’s being heated.

Gay-Lussac’s Law: Pressure and Temperature As the temperature of an enclosed gas increases, the pressure increases, if the volume is constant.

Gay-Lussac’s law – states that the pressure of a gas is directly proportional to the Kelvin temperature if the volume remains constant.

Example: A sample of nitrogen gas has a pressure of 6.58kPa at 539K. If the volume does not change, what will the pressure be at 211K?

P V Boyle’s Law Gay-Lussac’s Law Charles’s Law T

The Combined Gas Law Combined gas law – describes the relationships among the pressure, temperature, and volume of an enclosed gas.

The combined gas law allows you to do calculations for situations in which only the amount of gas is constant.

P V Boyle’s Law Combined Gas Law Gay-Lussac’s Law Charles’s Law T

P Boyle’s Law V T Gay-Lussac’s Law Charles’s Law

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

Section 3 Ideal Gases

Section 3 Learning Targets 14.3.1 – I can compute the value of an unknown using the ideal gas law. 14.3.2 – I can compare and contrast real and ideal gases.

Ideal Gas Law The combined gas law is good when the amount of gas does not change – this does not always stay constant though.

To calculate the number of moles of a contained gas requires an expression that contains the variable n. The number of moles is directly proportional to the number of particles and can be introduced into the combined gas law by dividing each side by n.

Ideal gas constant – (R) has the value of 8.31 (L•kPa)/(K•mol). Ideal gas law – includes the variables of P, V, T, and n. P is the pressure (units of kPa) V is the volume (units of L) T is the temperature (units of K) n is the number of moles (units of mol)

PV=nRT Song

Example: When the temperature of a rigid hollow sphere containing 685L of helium gas is held at 621K, the pressure of the gas is 1.89x103kPa. How many moles of helium does the sphere contain?

Ideal Gases and Real Gases An ideal gas is one that follows the gas laws under all conditions of temperature and pressure. Real gases differ most from an ideal gas at low temperatures and high pressures.

Answer the following questions based on the graph from the previous slide. What are the values of (PV)/(nRT) for an ideal gas at 20,000 and 60,000 kPa? What variable is responsible for the differences between the two (CH4) curves? How does an increase in pressure affect the (PV)/(nRT) ratio for real gases?

Section 4 Gases: Mixtures and Movements

Section 4 Learning Targets 14.4.1 – I can relate the total pressure of a mixture of gases to the partial pressures of the component gases. 14.4.2 – I can explain how the molar mass of a gas affects the rate at which the gas diffuses and effuses.

Dalton’s Law Partial pressure – the contribution of each gas in a mixture makes to the total pressure. In a mixture of gases, the total pressure is the sum of the partial pressures of the gases.

Dalton’s law of partial pressures – states that 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.

Example: Determine the total pressure of a gas mixture that contains oxygen, nitrogen, and helium. The partial pressures are: PO2 = 20kpa, PN2 = 46.7kPa; and PHe = 26.7kPa.

Graham’s Law Diffusion – tendency of molecules to move toward areas of lower concentration until the concentration is uniform throughout.

Bromine gas is put in a cylinder and after several hours you can see how the gas has diffused.

Effusion – a gas escapes through a tiny hole in its container. Gases of lower molar mass diffuse and effuse faster than gases of higher molar mass.

Thomas Graham’s Contribution Scottish chemist Thomas Graham studied rates of effusion in the 1840’s Relates to KE = ½ mv2. Kinetic energy of the particles (KE) is related to the mass (m) and their velocity (v).

Graham’s law of effusion – states that the rate of effusion of a gas is inversely proportional to the square root of the gas’s molar mass.

Example: Determine the rate of effusion for helium compared to nitrogen. This result tells me that the helium effuses/diffuses faster than the nitrogen at the same temperature.