Chapter 14 The Behavior of Gases

Properties of Gases 14.1

Compressibility Gases can expand to fill all of the available space Gases are easily compressible (ability to be compressed into a smaller volume) Compressibility is a measure of how much the volume of matter decreases under pressure

Key Question Why are gases easier to compress than solids or liquids Key Question Why are gases easier to compress than solids or liquids? The space between the gas particles makes it possible for gases to be compressed.

Factors Affecting Gas Pressure Gas particles move along straight-line paths until they collide with other gas particles Gas particles are in constant random motion Concerning the kinetic theory, we assume that there are no forces of attraction or repulsion among particles in a gas, which allows the gas particles to move freely Pressure, volume, temperature, and the number of moles are variables that are used to describe a gas

Key Question What are the three factors that affect gas pressure Key Question What are the three factors that affect gas pressure? Gas, volume, and temperature

Amount of Gas The kinetic theory is used to explain how gases will respond to a change of conditions Gas particles exert pressure on a container, this pressure is due to the collisions between the gas particles Increasing the number of particles causes an increase in the pressure WHY?

Assume the volume and temperature are constant! What happens to the pressure of a container when the following occurs?: Assume the volume and temperature are constant! Doubling the number of gas particles DOUBLES Tripling the number of particles TRIPLES The number of particles are cut in half Drop by half

Volumes Volume and pressure has an indirect relationship Pressure is increased when the volume is decreased (smaller container, use of a piston) The more the gas is compressed the greater the increase in pressure

Particles move faster, causing more collisions on the container Temperature When the temperature of a gas is increased the pressure is increased WHY? Particles move faster, causing more collisions on the container

Gas Laws 14.2

How are the pressure and volume of a gas related? Boyle’s Law Key Question How are the pressure and volume of a gas related? At constant temperature, the pressure of the gas increases and the volume of the gas decreases. Boyle’s law states that for a given mass of gas at constant temperature, the volume of the gas varies inversely with pressure

Boyle’s Equation Constant Temperature P1V1 = P2V2

Practice: Using Boyle’s Law Page 457, Numbers 9 and 10 (blue book) Page 419, Numbers 7 and 8 (red book)

How are the temperature and volume of a gas related? Charle’s Law Key Question How are the temperature and volume of a gas related? As the temperature of an enclosed gas increases, the volume increases if the pressure is constant. Charle’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

Charle’s Equation Constant Pressure V1 = V2 T1 T2

Practice Using Charle’s Law Blue Book page 459, Numbers 11 and 12 Red Book page 421, Numbers 9 and 10

How are the pressure and temperature of a gas related? Gay-Lussac’s Law Key Question How are the pressure and temperature of a gas related? 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

Gay-Lussac’s Equation Constant Volume P1 = P2 T1 T2

Practice: Gay-Lussac’s Law Blue Book page 461, Numbers 13 and 14 Red Book page 423, Numbers 11 and 12

How are the pressure, volume, and temperature of a gas related? The Combined Gas Law Combined gas law combines Boyle’s Law, Charle’s Law, and Gay-Lussac’s Law Key Question How are the pressure, volume, and temperature of a gas related? When only the amount of gas is constant, the combined gas law describes the relationship among pressure, volume, and temperature.

Number of Moles are Constant The Combined Gas Law Equation Number of Moles are Constant P1V1 = P2V2 T1 T2

Practice: Combined Gas Law Blue Book page 462, Numbers 15 and 16 Red Book page 424, Numbers 13 and 14

Ideal Gases 14.3

Ideal Gas Law The ideal gas law includes all four variables that relate to gases (V, P, T, and n) Ideal Gas Law Equation PV = nRT R is the ideal gas constant that has the value of 0.0821 L atm/mol K Key Question How can you calculate the amount of a contained gas when the pressure, volume, and temperature are specified? When known values of P, V, and T are provided the ideal gas law may be used to calculate the number of moles of the gas.

Practice: Ideal Gas Law Blue Book page 465, Numbers 26 and 27 page 466, Numbers 28 and 29 Red Book page 427, Numbers 23 and 24

Ideal Gases and Real Gases KEY QUESTION Under what conditions are real gases most likely to differ from ideal gases? Low temperatures and high pressures! Think about the distance between molecules and intermolecular forces.

Gases: Mixtures and Movements 14.4

Dalton’s Law The contribution each gas in a mixture makes to the total pressure is called the partial pressure Key Question How is the total pressure of a gas mixture related to the partial pressures of the component gases? 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 Each component gas exerts its own pressure independent of the pressure exerted by the other gases

Practice: Dalton’s Law of Partial Pressure Blue Book page 471, Numbers 37 and 38 Red Book page 434, Numbers 31 and 32

The type of particle is important ! Graham’s Law Two processes that involves the movement of molecules in a gas: Diffusion is the tendency of molecules to move toward areas of lower concentration until the concentration is uniform throughout Effusion a gas escapes through a tiny hole in its container The type of particle is important ! Key Question How does the molar mass of a gas affect the rate at which the gas diffuses or effuses? Gases of lower mass diffuse and effuse faster than gases of higher molar mass.

Thomas Graham’s Law of Effusion 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 (may also be applied to diffusion) An increase in mass is balanced by a decrease in velocity If two objects with different masses have the same kinetic energy, the lighter object must move faster

Comparing Effusion Rates The rate of effusion is related only to a particles speed; therefore, Graham’s law of effusion is written as followed: RateA = √ molar massB RateB molar massA The rates of effusion of two gases are inversely proportional to the square roots of their molar masses