Gas Laws Chapters 13.1 + 14

Review Temperature Pressure Volume Average kinetic energy Collisions of gas particles between each other and container walls Volume Amount of space

Ideal Gas Don’t exist Model to explain behavior of all gases Make assumptions about some properties that good under certain conditions

Kinetic Molecular Theory The particles in a gas are constantly moving in rapid, random, straight-line motion. Gas particles have no volume compared to the volume of the gas. No attraction between particles All collisions are completely elastic

Gas Laws Boyle’s Law Charles’s Law Gay-Lussac’s Law Combined Gas Law Avogadro’s Law Ideal Gas Law

Boyle’s Law Relationship between pressure and volume Constant Temperature Mathematical relationships As pressure is decreasing, volume is increasing As pressure is increasing, volume is decreasing

Boyle’s Law V P Inverse

Boyle’s Law PV = constant Temperature remains constant

Example A 40 L sample of gas at 1atm of pressure is compressed to 10 L. What is the new pressure of the gas? P1V1 = P2V2 (1atm)(40L) = P2(10L) P2 = 4 atm

Example The pressure of a 25 L sample is changed from 2 atm to 0.4 atm. What is the new volume of the gas? P1V1 = P2V2 (2atm)(25L) = (0.4atm)V2 V2 = 125 L

Charles’s Law Relationship between volume and temperature Constant Pressure Mathematical relationships As temperature is increasing, volume is increasing As temperature is decreasing, volume is decreasing

Charles’s Law T V Direct

Charles’s Law V/T = constant Temperature must be in Kelvin Pressure remains constant Temperature must be in Kelvin

Example A 4L sample of gas at 300K is heated to 600K. What is the new volume?

Example A gas occupying 45L at 27°C is cooled until its volume is 15L. What is the new temperature of the gas?

Gay-Lussac's Law Relationship between pressure and temperature Constant Volume Mathematical relationships As temperature is increasing, pressure is increasing As temperature is decreasing, pressure is decreasing

Gay-Lussac's Law T P Direct

Gay-Lussac's Law P/T = constant Temperature must be in Kelvin Volume remains constant (rigid container) Temperature must be in Kelvin

Example In a rigid container, a sample of gas at 1 atm and 300K is heated to 400K. What is the pressure at this temperature?

Example A sample of gas at 101.3 kPa and 27°C is heated until its pressure is 3.5atm. What is the new temperature?

Review Boyle’s Law Charles’s Law Gay-Lussac's Law

Question How often do only 2 properties of a gas change while the other remains constant? Rarely Need a gas law that incorporates all three properties (PTV) changing

Combined Gas Law Combines Boyle’s, Charles’s, and Gay-Lussac's Laws together

Example A gas at 5atm is heated and compressed from 10L at 100K to 5L at 200K. What is the new pressure?

Example A gas at 2atm and 27°C occupies 10L of space. What is the new volume when it is cooled to STP?

Real Life

Review 1 mole of ANY gas occupies 22.4L of volume at STP

Avogadro’s Law Relationship between the amount of gas and the volume of the gas Mathematical relationships As the amount of gas increases, volume increases As the amount of gas decreases, volume decreases

Avogadro’s Law n V Direct

Avogadro’s Law V/n = constant Pressure and Temperature remains constant

Avogadro’s Law Equal volumes of gas at the same Temperature and Pressure have the same number of particles At the same temperature and pressure, which sample contains the same number of moles of particles as 1 liter of O2(g)? A. 1 L Ne(g) B. 0.5 L SO2(g) C. 2 L N2(g) D. 4 L H2O(g)

Review Boyle’s Law Charles’s Law Gay-Lussac’s Law Avogadro’s Law

All Together Now Constant If we add Avogadro’s Law into the Combined Gas Law: Constant

Ideal Gas Law PV = nRT R = Universal Gas Constant Ideal Gases follow assumptions of the Kinetic Molecular Theory

Kinetic Theory of Gases The particles in a gas are constantly moving in rapid, random, straight-line motion. Gas particles have no volume compared to the volume of the gas. No attraction between particles All collisions are completely elastic

Ideal Gases When do real gases act most like an ideal gas? High Temperature Low Pressure When do real gases act least like an ideal gas? Low Temperature High Pressure