Concise Physical Chemistry

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

12 IDEAL GAS LAWS

P(v)

v

FIGURE 1.4 The probability density of molecular velocities in a spherical velocity space.

density drops off as a Gaussian function. In between these two approaches to zero,

the probability density must go through a maximum as shown in Fig. 1.4.

PROBLEMS AND EXERCISES

Exercise 1.1 The Combined Gas Law

Combine Boyle’s law and Charles’s law to obtain the combined gas law.

Solution 1.1 Take an ideal gas under the arbitrary conditionsp 1 V 1 T 1 and convert

it top 2 V 2 T 2 by a two-step process, varying the pressure first and the temperature

second. After the pressure is changed fromp 1 top 2 , according to Boyle’s law, the

volume, still atT 1 , is at an intermediate valueVx

p 1 V 1 =p 2 Vx T 1 =const

Vx=

p 1 V 1

p 2

Now change the temperature toT 2 at constantp 2. By Charles’s law, the volume goes

fromVxtoV 2

Vx

T 1

=

V 2

T 2

p 2 =const

Vx=T 1

V 2

T 2

Now equateVxfrom the equations above:

p 1 V 1

p 2

=T 1

V 2

T 2

p 1 V 1

T 1

=

p 2 V 2

T 2