Answer to Question #71241 in General Chemistry for Paul

Question

The volume of a sample of gas measured at 15.45oC and 0.167 atm pressure is 4.50 L. What must the final volume be in order for the gas to have a final pressure of 0.817 atm at 150.0oC?

Answer 1

We use the ideal gas law:
PV=nRT, where
P is the pressure of the gas,
V is the volume of the gas,
n is the number of moles of gas,
R is the universal gas constant,
T is the absolute temperature of the gas.

In our case number of moles is constant. So transform the equation and write it for the initial (indexed with “0”) and final (indexed with “1”) state of the system:
PV/T=nR = constant.
P1V1/T1 = P0V0/T0.
Therefore V1 = P0V0*T1/(T0 * P1)

Note that T is measured in kelvins. To convert from ºC to kelvins we have to add 273.2.
Thus T0 = 15.45+273.2=288.65 K; T1 = 150.0+273.2 = 423.2 K.
P is measured in Pa. 1 atm = 101 325 Pascal. So P0 = 0.167 atm = 0.167*101325 = 16921 Pa;
P1 = 0.817 atm = 0.817*101325 = 82783 Pa.
V can be expressed in liters.

Calculations:
V1 = 16921 Pa * 4.50L * 423.2K / (288.65K * 82783 Pa) = 1.35 L.

Answer:
The final volume must be 1.35 L.