### Gay-Lussac's Law Definition

Gay-Lussac's law is an ideal gas law where at constant volume, the pressure of an ideal gas is directly proportional to its absolute temperature (Kelvin). The formula for the law may be stated as:

P_{i}/T_{i} = P_{f}/T_{f}

where

P_{i} = initial pressure

T_{i} = initial temperature

P_{f} = final pressure

T_{f} = final temperature

The law is also known as the Pressure Law. Gay-Lussac formulated the law around the year 1808.

Other ways of writing Gay-Lussac's law make it easy to solve for pressure or temperature of a gas:

P_{1}T_{2} = P_{2}T_{1}

P_{1} = P_{2}T_{1} / T_{2}

T_{1} = P_{1}T_{2} / P_{2}

### What Gay-Lussac's Law Means

Basically, the importance of this gas law is that increasing the temperature of a gas causes its pressure to rise proportionally (assuming the volume doesn't change. Similarly, decreasing the temperature causes pressure to fall proportionally.

### Gay-Lussac's Law Example

If 10.0 L of oxygen exerts 97.0 kPa at 25°C, what temperature (in Celsius) is needed to change its pressure to standard pressure?

To solve this, first you need to know (or look up) standard pressure. It's 101.325 kPa. Next, remember gas laws apply to absolute temperature, which means Celsius (or Fahrenheit) must be converted to Kelvin. The formula to convert Celsius to Kelvin is:

K = °C + 273.15

K = 25.0 + 273.15

K = 298.15

Now you can plug the values into the formula to solve for the temperature.

T_{1} = P_{1}T_{2} / P_{2}

T_{1} = (101.325 kPa)(298.15) / 97.0

T_{1} = 311.44 K

All that's left is to convert the temperature back to Celsius:

C = K - 273.15

C = 311.44 - 273.15

C = 38.29°C

Using the correct number of significant figures, the temperature is 38.3°C.

### Gay-Lussac's Other Gas Laws

Many scholars consider Gay-Lussac to be the first to state Amonton's law of pressure-temperature.

Amonton's law states that the pressure of a certain mass and volume of a gas is directly proportional to its absolute temperature. In other words, if the temperature of a gas is increased, so does it's pressure, providing its mass and volume remain constant.

The French chemist Joseph Louis Gay-Lussac is also credited for other gas laws, which are sometimes called "Gay-Lussac's law". Gay-Lussac stated that all gases have the same mean thermal expansivity at constant pressure and the same temperature range. Basically, this law states many gases behave predictably when heated.

Gay-Lussac is sometimes credited as being the first to state Dalton's law, which says that the total pressure of a gas is the sum of the partial pressures of individual gases.