The Foundations of Chemistry

V 1 /T 1 V 2 /T 2. Combination of Boyle’s Law and Charles’s Law into a single expression
gives the combined gas law equation.

 (constant amount of gas)

When any five of the variables in the equation are known, the sixth variable can be
calculated.

EXAMPLE 12-4 Combined Gas Law Calculation

A sample of neon occupies 105 liters at 27°C under a pressure of 985 torr. What volume would
it occupy at standard temperature and pressure (STP)?

Plan

A sample of gas is changing in all three quantities P, V,and T.This suggests that we use the
combined gas law equation. We tabulate what is known and what is asked for, solve the combined
gas law equation for the unknown quantity, V 2 , and substitute known values.

Solution

V 1 105 L P 1 985 torr T 1 27°C273°300. K

V 2 _?_ P 2 760. torr T 2 273 K

Solving for V 2 ,

 so V 2 124 L

Alternatively, we can multiply the original volume by a Boyle’s Law factor and a Charles’s Law
factor. As the pressure decreases from 985 torr to 760. torr, the volume increases, so the Boyle’s
Law factor is 985 torr/760. torr. As the temperature decreases from 300. K to 273 K, the volume
decreases, so the Charles’s Law factor is 273 K/300. K. Multiplication of the original volume
by these factors gives the same result.

_?_L105 L124 L

The temperature decrease (from 300. K to 273 K) alone would give only a small decrease
in the volume of neon, by a factor of 273 K/300. K, or 0.910. The pressure decrease (from
985 torr to 760. torr) alone would result in a greater increasein the volume, by a factor
of 985 torr/760. torr, or 1.30. The result of the two changes is that the volume increases
from 105 liters to 124 liters.

EXAMPLE 12-5 Combined Gas Law Calculation

A sample of gas occupies 12.0 liters at 240.°C under a pressure of 80.0 kPa. At what temper-
ature would the gas occupy 15.0 liters if the pressure were increased to 107 kPa?

Plan

The approach is the same as for Example 12-4 except that the unknown quantity is now the
temperature, T 2.

273 K



300. K

985 torr



760. torr

(985 torr)(105 L)(273 K)



(760. torr)(300. K)

P 1 V 1 T 2



P 2 T 1

P 2 V 2



T 2

P 1 V 1



T 1

P 2 V 2



T 2

P 1 V 1



T 1

12-7 The Combined Gas Law Equation 447

Notice that the combined gas law

equation becomes

1.P 1 V 1 P 2 V 2 (Boyle’s Law)

when Tis constant;

2.  (Charles’s Law)

when Pis constant; and

3.  when Vis constant.

P 2



T 2

P 1



T 1

V 2



T 2

V 1



T 1