Page 32 - Physical chemistry eng

1.4 EQUATIONS OF STATE AND THE IDEAL GAS LAW 9

EXAMPLE PROBLEM 1.1
Starting out on a trip into the mountains, you inflate the tires on your automobile to a
5
recommended pressure of 3.21 * 10 Pa on a day when the temperature is –5.00°C.
You drive to the beach, where the temperature is 28.0°C. (a) What is the final pressure
in the tires, assuming constant volume? (b) Derive a formula for the final pressure,
assuming more realistically that the volume of the tires increases with increasing pres-
where g is an experimentally determined constant.
f
i
f
i
sure as V = V A1 + gCP - P DB
Solution
a. Because the number of moles is constant,
P V P V P V T
f f
i i f
i i
= ; P = ;
f
T i T f V T
f i
P V T V (273.15 + 28.0)
i i f
5
= = 3.21 * 10 Pa * i * 5
P f = 3.61 * 10 Pa
V T V i (273.15 - 5.00)
f i
P V A1 + gCP - P DB
P V f i f i
i i
b. = ;
T i T f
P T = P T A1 + gCP - P DB
f i
f
i f
i
2
P T g + P T (1 - P g) - P T = 0
i f
f i
i
f i
2
2
-T (1 - P g) ; 2T (1 - P g) + 4T T gP i
i
i
i f
i
i
P =
f
2T g
i
We leave it to the end-of-chapter problems to show that this expression for P has the
f
correct limit as g : 0 .
In the SI system, the constant R that appears in the ideal gas law has the value TABLE 1.2 The Ideal Gas
-1 -1
8.314 J K mol , where the joule (J) is the unit of energy in the SI system. To sim- Constant, R, in Various Units
plify calculations for other units of pressure and volume, values of the constant R with
-1
different combinations of units are given in Table 1.2. R = 8.314 JK mol -1
-1
3
R = 8.314 Pa m K mol -1
-1
R = 8.314 * 10 -2 L bar K mol -1
-1
EXAMPLE PROBLEM 1.2 R = 8.206 * 10 -2 L atm K mol -1
-1
Consider the composite system, which is held at 298 K, shown in the following figure. R = 62.36 L Torr K mol -1
Assuming ideal gas behavior, calculate the total pressure and the partial pressure of
each component if the barriers separating the compartments are removed. Assume that
the volume of the barriers is negligible.
He Ne Xe
2.00 L 3.00 L 1.00 L
1.50 bar 2.50 bar 1.00 bar