# Why is the ideal gas law useful?

May 13, 2014

The ideal gas law is a simple equation of state that is followed very closely by most gases, particularly at high temperatures and low pressures.

• $P V = n R T$

This simple equation relates the pressure $P$, volume $V$, and temperature, $T$ for a fixed number of moles $n$, of nearly any gas. Knowing any two of the three main variables ($P , V , T$) allows you to calculate the third by rearranging the equation above to solve for the desired variable.

For consistency, it's always a good idea to use SI units with this equation, where the gas constant $R$ equals $8.314 \frac{J}{m o l - K}$. Here's an example:

What is the temperature of $3.3 m o l$ of helium gas confined to a $1.8 {m}^{3}$ vessel at a pressure of $6500 P a$?

• $T = \frac{P V}{n R} = \frac{6500 \times 1.8}{3.3 \times 8.314} = 426 K$

For high-precision work, more complicated equations of state have been developed for particular gases, especially for working at high pressures, but the ideal gas law provides an easy way to make good estimates for any gas with relatively small errors in most cases.