Gas Law Applications

Edward A. Mottel

Department of Chemistry

Rose-Hulman Institute of Technology

Gas Law Applications

Reading Assignment: • Zumdahl Chapter 5.4, 5.6-5.8

This lecture concludes the topic of gas laws by describing the kinetic theory of gases and applying gaseous relationships to solve a variety of problems.

Gas Law Applications

Molecular weight determination Pressure measurements Isotope separation Stoichiometric reactions

Dumas Method of Molecular Weight Determination

The weight of a vapor is used to determine the approximate molecular weight of the compound.

Dumas Method of Molecular Weight Determination

A liquid is placed in anempty weighed retort.

The liquid is boiled untilis just completely

evaporates.

The tip of theglass retort issealed with a flame.

The mass of thetrapped gas is used inthe Ideal Gas equation

to calculate the MW

Dumas Method of Molecular Weight Determination

A gaseous sample was found to have the following composition:

1.6% H, 39.7% C, 58.7% Cl At 400. K and 870. torr, a 3.17 gram sample

occupies 0.500 liters.

Diagram an approachto determine the empirical formula

and the molecular formula of this compound.

Dumas Method of Molecular Weight Determination

Percentagecomposition

data

Approximate molecular weight

Molecularformula

Empiricalformula

GasData

1.6% H, 39.7% C,58.7% Cl

400. K and 870. torr,3.17 grams occupies 0.500 liters

Pressure MeasurementsBarometer

mercury

vacuumWhat forces determinethe height of themercuryin the glass tube?

Pressure MeasurementsManometer

mercuryPatm = 740. mm Hg

15.0 cm

10.0 cm

What is the pressureof the gas in the bulb?

open toatmosphere

Kinetic Theory of Gases

Gas is composed of discrete molecules. Molecules are in continuous motion. Molecular collisions are elastic. Molecules are small. The absolute temperature is proportional to

the average kinetic energy.

Kinetic Energy of Molecules

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

KE mv1

22

If an oxygen molecule has a velocity of1000. m·s-1, what will be the velocity of a

nitrogen molecule at the same temperature?

Boltzmann DistributionMaxwell Speed Distribution Law

P vMW

RTv e MW v RT

42

32

2 22

/

velocity or energy

num

ber

of m

olec

ules

The same gas at a given average temperaturehas a range of different velocities.

Boltzmann DistributionMaxwell Speed Distribution Law

velocity or energy

num

ber

of m

olec

ules average Gas velocity is a measure

of energy (temperature)

KE mv1

22

T2 > T1

Graham's Law of Effusion

Isotope separation

evacuatedchamber

mixedgases

pinhole leak

Graham's Law of Effusion

Isotope separation

Rate of effusion of gas A

Rate of effusion of gas B

MW of gas B

MW of gas A

Derive this equation from KE mv1

22

Graham's Law of Effusion

evacuatedchamber

mixedgases

pinhole leak

Which gas has a lower molecular weight?

Graham's Law of Effusion

Uranium hexafluoride (UF6) is a gas that has been used as a method to enrich the amount of uranium-235 used in nuclear reactions.

Uranium has two principle isotopes, uranium-235 and uranium-238.

Graham's Law of Effusion

How many enrichment cycles will be neededto raise the uranium-235 content from

the natural abundance 0.3% to 5%?

If the effusion method is used to separate235UF6 (MW = 349) from 238UF6 (MW = 352)

what will be the percentage enrichment per cycle?

Graham's Law of Effusion

Rate of effusion of 235UF6

Rate of effusion of 238UF6

MW of 238UF6=MW of 235UF6

352=

349= 1.0043

If the effusion method is used to separate35UF6 (MW = 349) from 238UF6 (MW = 352)

what will be the percentage enrichment per cycle?

Graham's Law of Effusion

eachenrichment

cycle1.0043 increase

1.0043 increase

1.0043 x 1.0043 increase

first cycle

second cycle

(1.0043)n increasenth cycle

Graham's Law of Effusion0.3%

naturalabundance

of U-235

5.0%required purity

of U-235for nuclearapplications

5.0%0.3% x (1.0043)n

5.0% / 0.3% = 16.7(1.0043)n

ln (16.7)n ln (1.0043)

n = 657 cycles

Non-ideal Behaviorvan der Waal Equation

intermolecular force correction (a)• collisions are not perfectly elastic

molecular volume correction (b)• molecules are not point masses

P an

VV bn nRTobs obs

2

Gas particles are molecules

Gas is composed of discrete particles of matter called molecules.• All molecules of the same substance are

the same.

Molecules are in continuous motion

Collide with each other and the walls that contain them.• The pressure of a gas is due to the

collision of molecules with the wall.

Molecular collisions are elastic

There is no net loss of kinetic energy. A perfectly insulated vessel will maintain the

same total kinetic energy (the temperature will remain constant).

Molecules are small

Molecules are small compared to the volume containing them.

• Molecules can be treated as point masses.• Gases are compressible because there is

a large distance between molecules.

Kinetic energy is proportional to absolute temperature

The absolute temperature of a gas is directly proportional to the average kinetic energy of the molecules.• The translational velocity of a molecule (a

measure of its kinetic energy) is proportional to its temperature.