Gas LawsAlex Daro, Brian Kuttler, and Max O'Donnell

• Gases have mass• Gases are easy to compress• Gases fill to their container• Diffusion is when gases move

through other gases• Gases exert pressure

Properties of Gases

• Gases consist of small particles• Particles must be separated by a

large distance• Particles are in constant motion• Pressure results when particles

collide with a container's wall• Kinetic energy of the gas depends

on the temperature of the gas

Kinetic Molecular Theory

• An increase in temperature will make gas particles move faster• An increase of temperature also

makes gas particles spread apart (Increase in volume)

Temperature's Effect

• An increase in pressure decreases volume and compresses particles• The particles also become less

dense and spread out

Pressure's Effect

• A decrease in volume results in greater pressure which makes the particles move closer together • As volume increases temperature

increases

Volume's Effect

• atm• torr (mm Hg)• Pa• kPa1 atm = 760 torr = 101,325 Pa =

101.3 kPa• All answers involving pressure must

be in atm unless stated otherwise

Pressure Units

• P1V1 = P2V2

• This states that pressure and volume have an inverse relationship• (780 torrs)(2 Liters) = (? P)(5 Liters)• (78/76 atm)(2 Liters)• 2.05 = ?P(5 Liters)• 2.05(atms * Liters)/(5 liters)• .41 atm = ?P

Boyle's Law

• V1/T1 = V2/T2

• This states that volume and temperature have a direct relationship• (300mL N)/(30°C) = (?V)(90°C) • (10 mL/°C) = (?V)(90°C)• (.1mL) = (?V)

Charles' Law

• P1/T1 = P2/T2

• This states that pressure and temperature have a direct relationship• (760mmHg)/(200K) = (?P)(300K) • (3.8 mmHg/K) = (?P)(300K)• (.01 mmHg) = (?P)• (.00002 atm) = (?P)

Gay-Lussac's Law

• P1V1/T1 = P2V2/T2

• This is a combination of other gas laws• (2atm)(3.2 L)/?T = (4.5atm)(5

L)/(200K)• 6.4atm*L/?T=.1125atm*L/K• 6.4atm*L=.1125atm*L/K(?T)• ?T = 60 K

Combined Gas Law

• PV = nRT• R = .0821L*atm/(mol*K)• n = Number of moles• P = Pressure• V = Volume• T = Temperature

Ideal Gas Law

• 2atm(5) = 3moles*R*?T• 10 atm*L = .2463 ?T• 40 K = ?T

Ideal Gas Law Problem

• Each gas and a mixture of gas has its own pressure and the total pressure of the mixture is the sum of the partial pressures of the component gases• PT=P1+P2+P3+...

Dalton's Law of Partial Pressure

• If the total pressure of the gas is 1atm and the pressure of hydrogen gas is .2atm then what is the pressure of the nitrogen gas?• 1atm=.2atm+P2

• .8atm = P2

Practice Problem

• Rates of effusion of gases at the same temperature and pressure are inversely proportional to the square roots of their molar masses• (rate of effusion of A)/(rate of

effusion of B) = (root MB)/(root MA)• The rates are found in grams/mole

Graham's Law of Effusion

• What is the rate of effusion of oxygen(O2) and hydrogen(H2)?• √(32 grams/mol)/√(2.016 grams/mol)• Hydrogen effuses 3.98 times faster

than oxygen

Practice Problem

• Diffusion is the rate at which particles move away from the initial point in space.

Graham's Law of Diffusion

#1 5atm(2 Liters) = 4atm(xliters)• 10atm*L/4atm = xliters• x = 2.5 Liters#2 920torr(5 Liters) = xatm(2 Liters)• 1.2atm(5 Liters) = xatm(2 Liters)• 1.2atm*5Liters/2 Liters = x atm• x atm = 3 atm

Boyles Law Practice Problems

#1 5atm/100K = 10atm/xK• 1atm/20K(xK) = 10 atm• xK = 10atm/(1atm/20K)• xK = 200 K#2 15atm/10K = xatm/200K• 15atm/10k(200K) = xatm• xatm = 300 K

Charles Law Practice Problems

#1 5Liters/ 20K = 21Liters/ xK• 1Liter/4K (xK)= 21 Liters• xK = 21Liters/(1liter/4K)• xK = 84K#2 .6Liters/50K = xLiters/21K• .6Liters/50K*21K = xLiters• xLiters = .252 Liters

Gay-Lussac's Law Practice Problems

1.(3atm)(2.2 L)/?T = (4.5atm)(6 L)/(200K)(6.6atm*L)/(?T)=(.135atm*L/K)(48.89K)=(?T)

2. (?atm)(4.3 L)/200K = (3atm)(3 L)/(273K)(?atm)(4.3L)/200K = (.03atm*L/K)(?atm)(4.3L) = (6atm*L)(?atm) = (1.4atm)

Combined Gas Law Practice Problems

1. 1atm(3L)=?n*R*273K(3atm*L)=(?n)(22.4L*atm/(mol))(.13moles)=(?n)

2. ?atm(4L)=3*R*273K?atm(4L)=67.24L*atm/(mol)?atm=16.84atm

Ideal Gas Law Practice Problems

1) If the pressure of Hydrogen gas is .35 atm and Nitrogen gas is .47 atm and Oxygen gas is .24 atm what is the total pressure?

.35 + .47 + .24 = PTPT = 1.06

Dalton's Law of Partial Pressures Practice Problems

2) If the total pressure of gases is 3.01 atm then what is the pressure of Oxygen gas if the pressure of Hydrogen gas is 1.11 atm and the pressure of Nitrogen gas is .87 atm?

3.01 atm = P1 atm + 1.11 atm + .87 atm

3.01 atm = P1 atm + 1.98 atmP1 atm = 1.03 atm

Dalton's Law of Partial Pressures Practice Problems Cont.

1) What is the rate of effusion of Oxygen gas (O2) and Nitrogen gas (N2)?

√(32 grams/mol)/√(28.02 grams/mol)Nitrogen effuses 1.069 times faster

than oxygen

Graham's Law of Effusion

2) What is the rate of effusion of Nitrogen gas (N2) and Hydrogen gas (H2)?

√(28.02 grams/mol)/√(2.016 grams/mol)

Hydrogen effuses 3.728 times faster than oxygen

Graham's Law of Effusion Cont.