Gas Laws

Why does a gas station sell liquid fuel?

Values and units

• P—mmHg, atm, torr, kPa, Pa

• T—k (could be given oC )

• V—ml,L,m3

• n—mol (could be given # of particles, mass)

(special cases)

• FM—g/mol (or kg/mol) D—g/L

• Rate or speed—m/s

Boyle’s Law

• Pressure & volume are inversely related

• PV=k

• P1V1=P2V2• When the pressure goes up, volume goes

down.

P

V

At a constant temperature!

For example:

If a sample of helium has a volume of 433 ml at a pressure of 88 kPa, what will its volume be if the pressure is increased to 2.8 atm?

Charles’ Law

• Temperature & volume are directly related

• V/T=k

• V1/T1=V2/T2• When the temperature goes up, volume

goes up.

T

V

At a constant pressure!

Charles’ Law

• Temperature & volume are directly related

• V/T=k

• V1/T1=V2/T2• When the temperature goes up, volume

goes up.

T

V

At a constant pressure!

Is it hot in here?

Charles’ Law

• Temperature & volume are directly related

• V/T=k

• V1/T1=V2/T2• When the temperature goes up, volume

goes up.

T

V

At a constant pressure!

You must use absolute temperatures

For example:

If a sample of oxygen has a volume of 2.4 m3 at 19oC, what will its volume be if the temperature is increased to 155oC?

For example:

If a sample of chlorine has a volume of 12 L at 38oC, at what temperature will its volume be 17 L?

Gay-Lussac’s Law

• Temperature & pressure are directly related

• P/T=k

• P1/T1=P2/T2• When the temperature goes up, pressure

goes up.

T

P

At a constant volume!

For example:

A tire is fairly flat (P=1200 mmHg) at -5oC on a cold morning. At what temperature would it reach its normal 3.5 atmospheres if you were to heat it up instead of pumping more air in?

Avogadro’s Law

• Volume & # of particles are directly related

• V/n=k

• V1/n1=V2/n2• When the number of particles goes up,

volume goes up.

n

V

At a constant pressure and temperature!

For example:

If nitrogen and hydrogen gasses are mixed in stoichiometric ratio (1:3) in a 120 L tank and the introduction of a catalyst allows the volume to fall to 110 L at the same pressure and temperature, what is K for the formation of ammonia?

Combined Gas Law

• Pressure, volume & temperature relationship

• PV/T=k

P1V1/T1=P2V2/T2

Combined Gas Law

P1V1/T1=P2V2/T2

• Solve for V2

• Solve for T1

Combined Gas Law

P1V1/T1=P2V2/T2

• Solve for V2 = P1V1T2/T1P2

• Solve for T2 = P2V2T1/P1V1

For example:

If a sample of hydrogen has a volume of 56 ml

at STP, what will its volume be 19oC and

.84 atm?

For example:

If a sample of hydrogen has a volume of 56 ml

at STP, what will its volume be 19oC and

.84 atm?

STP =standard temperature and pressure

= 273k, 1.00 atm

PS

• The standard molar volume for an ideal gas is:

at STP

22.4L/mol

22.4L/mol

PS

is about22.4L/mol

Ideal Gas Law

• Pressure, volume, temperature & mole relationship

• PV/nT=R

• P1V1/n1T1=P2V2/n2T2=R

PV=nRT

Ideal Gas constant

.0821 L atm/mol k

8.31 J/mol k

An ideal gas has particles of zero volume, with no attraction to each other!

Ideally…

A ? 3.8 ml .12 mol 58oC

B 725 mmHg

? 4.9 mol 198oC

C 325 kPa 2.9 m3 ? 257 k

D 1.2 atm 9.1 L .85 mol ?

Van der Waals Gas Law

• A more precise pressure, volume, temperature and mole relationship

• P V =nRT • (P+an2/V2)(V-nb)=nRT A little more realistic

Ideal behavior

Correction of the pressure to account for the real attraction between real

gas particles

Correction of the volume to account for the real

size of the gas particles

For example:

• Calculate the pressure of 2.000 mole NH3 in a 5.000 L container at 300.0 k with ideal behavior.

• Do the same with the van der Waals approximation (a=4.17, b=.0371)

• How do these two answers differ? Why?

Dalton’s law of partial pressures• The total pressure of a mixture of gasses is

the sum of the partial pressures.

P1+P2+…=Ptotal

• Even better: The pressure a single gas in a mixture exerts is that pressure that it would exert if it were in the container alone

For example:

• A flask contains 1.32 x 1023 atoms of Ne, 48 g Ar, 2.3 mol He and some xenon, at 27oC. If the flask has a volume of 24.0 L, what is the maximum amount of xenon it could hold if it will explode if the pressure exceeds 10.0 atm?

For example:

• A flask contains 2.9 mol O2, 4.1 mol NH3 and .5 mol CO2 The flask has a volume of 50.0 L, and a temperature of 550k. If a spark is introduced, the ammonia burns to form nitrogen monoxide and water vapor. Suppose the reaction goes to completion. What is the pressure in the flask after the reaction if the temperature remains constant?

Solution?

• After:

• 2.32 mol NO

• 3.48 mol H2O

• No O2

• 4.1-2.32=1.78 mol NH3 left over

• .5 mol CO2 unchanged

• 8.08 mol total7.30 atm.

Graham’s Law of Effusion

• The rate of effusion of a gas is inversely proportional to the square root of its molar mass

R1= M2

R2 M1

The heavy gas is slower!

PS

• Graham’s Law is used to separate U-235 (.7%) from U-238 (99.3%) by gas diffusion.

• A massively heavy gas, UF6, is prepared and allowed to escape slowly through a tiny opening. The 235UF6 is 1% lighter, so it escapes just a touch better. The second container might have up to 1.5% U-235

• Consider krypton and fluorine gasses.

• Which is faster?

• How many times as fast?

Now for a real speed.

The average velocity of particles in a sample of gas is likely zero, but the particles are moving

• The root mean square velocity (urms) of a gas depends on its mass and temperature.

• urms= 3kT/m or urms= 3RT/FM

Masses in kilograms!

What is the velocity of the particles in..

• Oxygen gas at 122 k?

• Helium at -29 oC?

• How do these answers differ? Why?