Charles' Law

In 1787, the French inventor Jacques Charles, while investigating the inflation of his man‐carrying hydrogen balloon, discovered that the volume of a gas varied directly with temperature. This relation can be written as

 

equation

and is called Charles' law. For this law to be valid, the pressure must be held constant, and the temperature must be expressed on the absolute temperature or Kelvin scale .

Because the volume of a gas decreases with falling temperature, scientists realized that a natural zero‐point for temperature could be defined as the temperature at which the volume of a gas theoretically becomes zero. At a temperature of absolute zero, the volume of an ideal gas would be zero. The absolute temperature scale was devised by the English physicist Kelvin, so temperatures on this scale are called Kelvin ( K) temperatures. The relationship of the Kelvin scale to the common Celsius scale must be memorized by every chemistry student:

K = °C + 273.15

Therefore, at normal pressure, water freezes at 273.15 K (0°C), which is called the freezing point, and boils at 373.15 K (100°C). Room temperature is approximately 293 K (20°C). Both temperature scales are used in tables of chemical values, and many simple errors arise from not noticing which scale is presented.

Use Charles' law to calculate the final volume of a gas that occupies 400 ml at 20°C and is subsequently heated to 300°C. Begin by converting both temperatures to the absolute scale:

T 1 = 20°C = 293.15 K

T 2 = 300°C = 573.15 K

Then substitute them into the constant ratio of Charles' law:

  equation

When using Charles' law, remember that volume and Kelvin temperature vary directly; therefore, an increase in either requires a proportional increase in the other.

  • A gas occupying 660 ml at a laboratory temperature of 20°C was refrigerated until it shrank to 125 ml. What is the temperature in degrees Celsius of the chilled gas?