Gas Laws 10-2 and 10-3

Ideal Gas Law PV = nRT PV = nRT P = Pressure, in atm V = volume, in L n = number of moles T =Temperature, in Kelvins (K = C + 273) And R, the universal gas constant equals: (L)(atm)/(mol)(K)

Example 1 A steel tank has a volume of 438 L and is filled with 27.7 moles of O2 gas. Calculate the pressure of the O2 at 21ºC. A steel tank has a volume of 438 L and is filled with 27.7 moles of O2 gas. Calculate the pressure of the O2 at 21ºC.

Example 2 If 1.11 moles of gas with a volume of 0.73 L were at a temperature of 288 K, what would the pressure of the gas be? If 1.11 moles of gas with a volume of 0.73 L were at a temperature of 288 K, what would the pressure of the gas be?

Charles’s Law V = kT V = kT V/T = k V/T = k V 1 /T 1 = V 2 /T 2 V 1 /T 1 = V 2 /T 2 States there is a direct relationship between volume and temperature States there is a direct relationship between volume and temperature Assumes pressure is held constant Assumes pressure is held constant

Charles’s Law: Volume vs. Temperature

Example 1 A sample of gas occupies 24 m cubed at 100K. What volume would the gas occupy at 400 K? A sample of gas occupies 24 m cubed at 100K. What volume would the gas occupy at 400 K?

Example 2 Gas in a balloon occupies 2.5 L at 300 K (about room temperature). At what temperature will the balloon expand to 7.5 L? Gas in a balloon occupies 2.5 L at 300 K (about room temperature). At what temperature will the balloon expand to 7.5 L?

Boyle’s Law PV=k PV=k P 1 V 1 = P 2 V 2 P 1 V 1 = P 2 V 2 States that there is an inverse relationship between volume and pressure. States that there is an inverse relationship between volume and pressure. It is assumed that Temperature is held constant. It is assumed that Temperature is held constant.

Boyle’s Law: Volume vs. Pressure

Example 4 The gas in a 10.0 L container exerts a pressure of 100 kPa. What pressure is needed to compress the gas to 2.0 L while keeping the temperature constant? The gas in a 10.0 L container exerts a pressure of 100 kPa. What pressure is needed to compress the gas to 2.0 L while keeping the temperature constant?

Example 5 If the pressure of a 2.5 m3 sample of a gas is 1.5 atm, what volume will the gas occupy if the pressure is changed to 7.5 atm? If the pressure of a 2.5 m3 sample of a gas is 1.5 atm, what volume will the gas occupy if the pressure is changed to 7.5 atm?