The Gas Laws

Proportionality Directly Proportional As one variable goes up the other goes up, or as one variable goes down the other goes down Both variables do the same thing Indirectly Proportional As one variable goes up the other goes down The two variables do the opposite thing

Boyle’s Law P 1 V 1 = P 2 V 2 Temperature is constant Pressure (P) and volume (V) are indirectly proportional

Cartesian Diver 1.Draw or describe the initial observation 2.Claim: If the pressure inside the bottle is increased then… 3.What are the variables? (list in table) 4.What is the Gas Law relationship? (write the gas law and proportionality) Demo

Marshmallow Madness 1.Draw or describe the initial observation 2.Claim: If the pressure inside the syringe is decreased then… 3.What are the variables? (list in table) 4.What is the Gas Law relationship? (write the gas law and proportionality) Demo

Example 1 A helium balloon was compressed from 4.0L to 2.5L at a constant temperature. If the pressure of the gas in the 4.0L balloon is 210 kPA, what will the pressure be at 2.5L? Given: V 1 = 4.0LV 2 = 2.5L P 1 = 210 kPaP 2 = ? P 1 V 1 = P 2 V 2 (210 kPa) × (4.0L) = P 2 × (2.5L) P 2 = 336 kPa ≈ 340 kPa

Example 2 A sample of neon gas occupies 0.200L at atm. What will be its volume at 29.2 kPa pressure? Given: V 1 = 0.200L V 2 = ? P 1 = atm P 2 = 29.2 kPa P 1 V 1 = P 2 V 2 (87.1 kPa) × (0.200L) = (29.2 kPa) × V 2 V 2 = 0.597L **Units must match for each variable (doesn’t matter which one is converted) atm kPa 1 atm = 87.1 kPa

Charle’s Law V 1 V 2 T 1 T 2 Pressure is constant Temperature must be in Kelvin Volume (V) and temperature (T) are directly proportional =

1.Draw or describe the initial observation 2.Claim: If the temperature inside the flask is decreased then… 3.What are the variables? (list in table) 4.What is the Gas Law relationship? (write the gas law and proportionality) Demo Balloon in a Bottle

Example 1 A gas ample at 40.0°C occupies a volume of 2.32L. If the temperature is raised to 75.0°C, what will the volume be, assuming the pressure remains constant? Given: T 1 = 40.0°C = 313KT 2 = 75.0°C = 348K V 1 = 2.32LV 2 = ? V 1 V 2 T 1 T 2 = 2.32L V = V 2 = 2.58L

Example 2 A gas ample at 55.0°C occupies a volume of 3.50L. At what new temperature in kelvin will the volume increase to 8.00L? Given: T 1 = 55.0°C = 328KT 2 = ? V 1 = 3.50LV 2 = 8.00L V 1 V 2 T 1 T 2 = 3.50L T 2 = T 2 = 750K

Gay-Lussac’s Law P 1 P 2 T 1 T 2 Volume is constant Temperature must be in Kelvin Pressure (P) and temperature (T) are directly proportional =

Can Crusher 1.Draw or describe the initial observation 2.Claim: If the temperature inside the bottle is increased and suddenly decreased then… 3.What are the variables? (list in table) 4.What is the Gas Law relationship? (write the gas law and proportionality) Demo

Boiling Water 1.Draw or describe the initial observation 2.Claim: If the temperature inside the flask is decreased then… 3.What are the variables? (list in table) 4.What is the Gas Law relationship? (write the gas law and proportionality) Demo

Egg in a Bottle 1.Draw or describe the initial observation 2.Claim: If the temperature inside the bottle is increased then… 3.What are the variables? (list in table) 4.What is the Gas Law relationship? (write the gas law and proportionality) Demo

Example 1 The pressure of a gas in a tank is 3.20 atm at 22.0°C. If the temperature rises to 60.0°C, what will be the gas pressure in the tank? Given: P 1 = 3.20 atmP 2 = ? T 1 = 22.0°C = 295KT 2 = 60.0°C =333K P 1 P 2 T 1 T 2 = 3.20 atm P 2 295K 333K = P 2 = 3.61 atm

Example 2 A rigid container has a gas at constant volume at 665 torr pressure when the temperature is 22.0C. What will the pressure be if the temperature is raised to 44.6C? Given: P 1 = 665 torrP 2 = ? T 1 = 22.0°C = 295KT 2 = 44.6°C =317.6K P 1 P 2 T 1 T 2 = 665 torr P 2 295K 317.6K = P 2 = 716 atm