The Foundations of Chemistry

R8.3145

You should now work Exercise 43.

We can now express R,the universal gas constant, to four digits in three different sets of units.

R0.08206 

m

L

o

a

l

t



m

K



8

m

.3

o

1

l

4

K

J

8.314 

k

m

Pa

o



l

d

K

m^3



The usefulness of the ideal gas equation is that it relates the four variables, P, V, n,

and T,that describe a sample of gas at one set of conditions.If any three of these vari-

ables are known, the fourth can be calculated.

EXAMPLE 12-8 Ideal Gas Equation

What pressure, in atm, is exerted by 54.0 grams of Xe in a 1.00-liter flask at 20.°C?

Plan

We list the variables with the proper units. Then we solve the ideal gas equation for Pand
substitute values.

Solution

V1.00 L n54.0 g Xe0.411 mol

T20.°C273°293 K P_?_

Solving PVnRTfor Pand substituting gives

P9.89 atm

EXAMPLE 12-9 Ideal Gas Equation

What is the volume of a gas balloon filled with 4.00 moles of He when the atmospheric pres-
sure is 748 torr and the temperature is 30.°C?

Plan

We first list the variables with the proper units. Then we solve the ideal gas equation for V
and substitute known values.

Solution

P748 torr0.984 atm n4.00 mol

T30.°C273°303 K V_?_

Solving PVnRTfor Vand substituting gives

1 atm



760 torr

(0.411 mol)


0.08

m

21

ol

L

K

atm

(293 K)



1.00 L

nRT



V

1 mol



131.3 g Xe

kPadm^3



molK

101.325 kPa22.414 dm^3



1 mol273.15 K

PV



nT

12-9 Summary of Gas Laws: The Ideal Gas Equation 451