The Foundations of Chemistry

EXAMPLE 12-3 Charles’s Law Calculation

A sample of nitrogen occupies 117 mL at 100.°C. At what temperature in °C would it occupy

234 mL if the pressure did not change?

Plan

We know the volume of the sample at one temperature and wish to know its temperature corre-

sponding to a second volume (constant pressure). We can solve Charles’s Law for the second

temperature. We must remember to carry out calculations with all temperatures expressed on

the Kelvin scale, converting to or from Celsius as necessary.

Solution

V 1 117 mL V 2 234 mL

T 1 100.°C273°373 K T 2 _?_

 and T 2 746 K

°C746 K
273° 473°C

The temperature doubles on the Kelvin scale, from 373 K to 746 K, so the volume doubles.

You should now work Exercise 24.

(234 mL)(373 K)



(117 mL)

V 2 T 1



V 1

V 2



T 2

V 1



T 1

446 CHAPTER 12: Gases and the Kinetic–Molecular Theory

Problem-Solving Tip:Be Careful of Units in Charles’s Law

Calculations

Which units for volume and temperature are appropriate for Charles’s Law calculations?

The equation 

V

T 1

^1 V

T 2

^2 can be written as V

V

1

2



T

T

1

2

. This involves a ratio of volumes,

so they can be expressed in any volume units—liters, milliliters, cubic feet—as long as

the sameunits are used for both volumes. But the relationship does not apply at allunless

the temperatures are both expressed on an absolute scale. Remember to express all

temperatures in kelvins for Charles’s Law calculations.

STANDARD TEMPERATURE AND PRESSURE

We have seen that both temperature and pressure affect the volumes (and therefore the

densities) of gases. It is often convenient to choose some “standard” temperature and pres-

sure as a reference point for discussing gases. Standard temperature and pressure (STP)

are, by international agreement, exactly 0°C (273.15 K) and one atmosphere of pressure

(760. torr).

THE COMBINED GAS LAW EQUATION

Boyle’s Law relates the pressures and volumes of a sample of gas at constant temperature,

P 1 V 1 P 2 V 2. Charles’s Law relates the volumes and temperatures at constant pressure,

12-7

12-6