Gas Laws

Chapter 14

Mrs. Hayen, Fall ‘03

Kinetic Molecular Theory

Gas particles do not attract or repel each other.

Gas particles are much smaller than the spaces between them.

Gas particles are in constant, random motion.

No kinetic energy is lost when gas particles collide with each other or with the walls of their container.

All gases have the same kinetic energy at the same temperature.

Three factors that affect gases:

Temperature: A measure of the kinetic energy of a gas Measured in ºC or in K

Volume: A measure of the amount of space the gas occupies

(equal to vol. of container) Measured in L or mL

Pressure: A measure of the number of times the molecules collide

(with each other and/or with the walls of the container) Measured in mm Hg, kPa, or atm.

(SI unit for pressure)

Important InfoSTP = Standard Temperature & Pressure

0 °C 1 atm273 K 101.3 kPa

760 mmHg

Pressure unit conversions:1 atm = 760 mmHg = 101.3 kPa

Temperature unit conversions:Kelvin = °C + 273

Temperature should always be in Kelvin units for gas law problemsThe “Big Three…”

Boyle’s LawPressure is inversely related to volume.

[In other words: as pressure increases, volume decreases.]

P1V1 = P2V2

Example: A sample of compressed methane has a volume of 648 mL at a pressure of 503 kPa. To what pressure would the methane have to be compressed in order to have a volume of 216 mL?

Answer: 1510 kPa

Charles’ LawVolume is directly proportional to temperature.

[In other words: as temperature increases, volume increases.]

V1/T1 = V2/T2

Example: A weather balloon contains 5.30 kL of He gas when the temperature is 12 ºC. At what temperature will the balloon’s volume have increased to 6.00 kL?

Answer: 50 ºC

Gay-Lussac’s LawPressure is directly proportional to temperature.

[In other words: as temperature increases, pressure increases.]

P1/T1 = P2/T2

Example: Pressure inside a jelly jar before it is sealed is 1.75 atm at 25 ºC. Volume is constant. After the jar is heated to 100. ºC, what is the new pressure?

Answer: 2.19 atm

Combined Gas LawThe combined laws of Boyle, Charles, and Gay-Lussac:

P1V1 /T1 = P2V2 /T2

Example: A student collects 285 mL of O2 gas at 15 ºC and a pressure of 99.3 kPa. The next day, the same sample occupies 292 mL at a temperature of 11 ºC. What’s the new pressure?

Answer: P2 = 95.6 kPa

Avogadro’s principleThe principle that equal volumes of all gases at the same conditions of temperature and pressure have the same number of molecules.

I mol = 22.4 L @ STP

Now you can interrelate the following for any gas:

Mass, moles, pressure, volume, and temperature

Example: What is the volume of 7.17 g of Ne (g) at 24 º C and 1.05 atm?

Answer: 8.24 L Ne

Gases can be ideal or real:Ideal gases follow the principles of the kinetic molecular theory and obey the previous laws exactly.

Real gases show slight deviations from the laws.

However, at normal (not extreme) temperatures and pressures, these deviations can be ignored and therefore the gases we discuss can be treated as ideal gases.

Ideal Gas Law

The equation that relates moles, pressure, volume, and temperature and adjusts for conditions other than STP

PV = nRT

where n = number of moles & R= ideal gas constant

R= 8.314 L•kPa = 0.0821 L•atm mol•K mol•K

Ideal Gas Law (cont’d)

Example: What pressure (in atm) will 18.6 mol of methane exert when it is compressed in a 12.00-L tank at a temperature of 45 ºC?

R= 8.314 L•kPa = 0.0821 L•atm mol•K mol•K

Answer: 40.5 atm

Dalton’s LawEach gas in a mixture exerts pressure independently of the other gases.

The total pressure of a mixture is equal to the sum of the pressures of the individual gases.

PTotal = P1 + P2 + P3 +… Pn

Example: Air is made up of four main gases: N2, O2, Ar, and CO2. Air presusre at sea level is approximately 760 mm Hg. Calculate the partial pressure of O2 given the following: N2 = 594 mm Hg; Ar = 7.10 mm Hg; CO2 = 0.27 mm Hg.

Answer: 158.63 mm Hg

Graham’s LawGases move from areas of high concentration to areas of low concentration based on their molecular mass.

[In other words, the bigger the molecule, the slower it will diffuse.]

Identify formula & understand concept only.

Rate A = molar mass B

Rate B molar mass A

Know these laws:

Boyle’s Law

Charles’ Law

Gay-Lussac’s Law

Combined Gas Law

Ideal Gas Law

Dalton’s Law

Graham’s Law

Gas StoichiometryAmmonium Sulfate can be prepared by a reaction between ammonia gas and sulfuric acid. The skeleton equation is:

NH3 (g) + H2SO4 (NH4)2SO4 (aq)

What volume of ammonia gas, measured at 78ºC and a pressure of 1.66 atm, will be needed to produce 5.00 X 103 g of ammonium sulfate?

[You have to balance the equation first!]

2

Answer: 1310 L