Concise Physical Chemistry

c01 JWBS043-Rogers September 13, 2010 11:20 Printer Name: Yet to Come

6 IDEAL GAS LAWS

1.5 THE MOLE FRACTION

Recognizing that the pressure of each gas is directly proportional to the number

of moles through the same constant, we may write the pressure fraction as amole

fraction:

Xi=

ni

∑

i

ni

The pressure of a real gas follows Dalton’s law only as an approximation, but the

number of particles (measured in moles) is not dependent upon ideal behavior; hence

the summation of mole fractions

Xtotal=

∑

i

Xi

is exactfor ideal or nonideal gases and for other states of matter such as liquid and

solid mixtures and solutions.

1.6 EXTENSIVE AND INTENSIVE VARIABLES

Massmis anextensivevariable. Densityρis anintensivevariable. If you take twice

the amount of a sample, you have twice as many grams, but the density remains the

same at constantpandT. Molar quantities are intensive. For example, if you double

the amount of sample under at constantpandT, the molar volume (volumeper mole)

Vmremains the same just as the density did.

1.7 GRAHAM’S LAW OF EFFUSION

Knowing the molar gas constant R= 8 .314 J K−^1 mol−^1 = 0 .08206 L atm K−^1

mol−^1 , which follows directly from measurements ofpandVon known amounts of

a gas at specific values ofT, one can determine the atomic or molecular weight of an

independent sample within the limits of the ideal gas approximation. Another way

of finding the molecular weight of a gas is through Graham’s law of effusion, which

states that the rate of escape of a confined gas through a very small hole is inversely

proportional to its particle weight—that is, its atomic or molecular weight. This being

the case, measuring the rate of effusion of two gases—one of known molecular weight

and the other of unknown molecular weight—gives the ratio MWknown/MWunknown

and hence easy calculation of MWunknown.

Aside from important medical applications (dialysis), Graham’s work also focused

attention on the random motions of gaseous particles and the speeds with which they

move. We can rationalize Graham’s law as the result of a very largeensembleof