Gay-Lussac’s law: concept and formula

where:

• P  ₁ is the initial pressure;
• T  ₁  is the initial absolute temperature;
• P  ₂  is the final pressure;
• T  ₂ is the final absolute temperature.

Also, the units of absolute temperature are expressed in degrees Kelvin ( K ) and the units of pressure are expressed in pascals ( Pa ).

Examples of Gay-Lussac’s Law

Gay-Lussac’s Law explains the operation of different household appliances, such as the pressure cooker. In this case, the higher the temperature, the higher the pressure. Another everyday object where the Gay-Lussac Law applies is the tire of a car. For example, if the temperature decreases, the tire pressure of the car also decreases. In that case, air must be added to increase the pressure.

Problem to apply Gay-Lussac’s Law

A concrete problem that can be solved by applying Gay-Lussac’s Law would be to find the necessary temperature, in degrees Celsius , to change the pressure of 10 liters of a gas that has a pressure of 97.0 kPa at 25°C to the standard pressure, which is 101.325 kPa (kilopascals).

To solve this problem correctly, you must first convert 25°C to Kevin. This is very important, since the Kelvin scale measures absolute temperature. On both scales, 100 degrees separate the freezing and evaporation points of water, and 0°C corresponds to 273.15 K. Therefore, 25°C equals 298.15 K. 

Taking into account that the pressure of a gas with constant volume is directly proportional to its temperature, we must replace the Gay-Lussac Law equation with these values:

97.0 kPa / 298.15 K = 101.325 kPa / X

To know what the value of X is, we must perform the following operations:

X = (101.325kPa)x(298.15K)/(97.0kPa). With which we obtain that: X = 311.44 K

Then it only remains to subtract 273.15 to obtain the answer in degrees Celsius: X = 38.29° C

To recap, it is important to note that:

• The volume and quantity of the gas must be constant.
• If the temperature of the gas increases, the pressure increases.
• If the temperature decreases, the pressure also decreases.
• The temperature in Celsius must be converted to Kelvin in order to perform the equation correctly.

Bibliography

• Borneo, R. Gases. Problems solved. Series: Problems solved in Chemistry. Part 1. Ideal gases, gas laws. (2020). Spain. Raphael Borneo.
• Planas, O. (2021, December 8). Gay-Lussac’s Law: Formula, Statement, and Finder . Nuclear-energy.net. Available here .
• Chemtube. (2021, May 19). Gas Laws (III): Gay-Lussac’s Law . Available here .