The Foundations of Chemistry

Summary of the ideal gas laws

1.The individual gas laws are usually used to calculate the changesin conditions for

a sample of gas (subscripts can be thought of as “before” and “after”).

Boyle’s Law P 1 V 1 P 2 V 2 (for a given amount of a gas

at constant temperature)

Charles’s Law 

V

T 1

1



V

T 2

2

 (for a given amount of a gas

at constant pressure)

Combined Gas Law 

P

T

1 V

1

1



P

T

2 V

2

2

 (for a given amount of a gas)

Avogadro’s Law 

V

n 1

1



V

n 2

2

 (for gas samples at the same

temperature and pressure)

2.The ideal gas equation is used to calculate one of the four variables P, V, n,and

T,which describe a sample of gas at any single set of conditions.

PVnRT

The ideal gas equation can also be used to calculate the densities of gases.

EXAMPLE 12-11 Ideal Gas Equation

Nitric acid, a very important industrial chemical, is made by dissolving the gas nitrogen dioxide,
NO 2 , in water. Calculate the density of NO 2 gas, in g/L, at 1.24 atm and 50.°C.

Plan

We use the ideal gas equation to find the number of moles, n, in any volume, V, at the spec-
ified pressure and temperature. Then we convert moles to grams. Because we want to express
density in g/L, we choose a volume of one liter.

Solution

V1.00 L n_?_

T50.°C273°323 K P1.24 atm

Solving PVnRTfor nand substituting gives

n0.0468 mol

So there is 0.0468 mol NO 2 /L at the specified Pand T. Converting this to grams of NO 2 per
liter, we obtain

Density2.15 g/L

You should now work Exercise 40.

46.0 g NO 2



mol NO 2

0.0468 mol NO 2



L

_?_g



L

(1.24 atm)(1.00 L)




0.0821 m

L

o

a

l

t



m

K

(323 K)

PV



RT

12-9 Summary of Gas Laws: The Ideal Gas Equation 453

See the Saunders Interactive

General Chemistry CD-ROM,

Screen 12.5, Gas Density.