Gas LawsGas Laws

10-2 and 10-310-2 and 10-3

Ideal Gas LawIdeal Gas Law

PV = nRTPV = 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: 0.0821 (L)(atm)/(mol)(K)

Example 1Example 1

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

Example 2Example 2

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

Charles’s LawCharles’s Law

V = kTV = kT V/T = kV/T = k VV11/T/T11 = V = V22/T/T22

States there is a States there is a direct relationship direct relationship between volume and between volume and temperaturetemperature

Assumes pressure is Assumes pressure is held constantheld constant

Charles’s Law: Volume vs. TemperatureCharles’s Law: Volume vs. Temperature

546, 1094

373, 748

272, 546

200, 403

100, 19950, 100

0

200

400

600

800

1000

1200

0 200 400 600

Temperature (K)

Vo

lum

e (

mL

)

Example 1Example 1

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

Example 2Example 2

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

Boyle’s LawBoyle’s Law

PV=kPV=kPP11VV11 = P = P22VV22

States that there is an States that there is an inverseinverse relationship relationship between between volumevolume and and pressurepressure..

It is assumed that It is assumed that TemperatureTemperature is held is held constant.constant.

Boyle’s Law: Volume vs. PressureBoyle’s Law: Volume vs. Pressure

100, 500

150, 333

200, 250250, 200

350, 143450, 110

0

100

200

300

400

500

600

0 100 200 300 400 500

Pressure (kPa)

Vo

lum

e m

L

Example 4Example 4

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

Example 5Example 5

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