# Ideal Gas Law

## Table of Contents

$$PV = nRT$$

Where

- \(P\) is the pressure of the gas,
- \(V\) is the volume of the gas,
- \(n\) is the number of moles of gas,
- \(R\) is the gas constant (see here for a table of R with various units), and
- \(T\) is the temperature of the gas.

“The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations.” - Wikipedia

## Sources #

## Example #

Kevin has a 1 liter container of a mysterious (ideal) gas at 1 atm and 300 K. What is the pressure of the gas if the volume is doubled?

There are two ways we could use the Ideal Gas Law to solve this problem:

- We could solve for \(n = \frac{PV}{RT}\) and then use that to solve for \(P_2 = \frac{nRT}{V_2}\)
- We could notice that the right side of the equation, \(nRT\) is a constant, since no moles of gas can escape, R is a constant by definition, and the temperature is not changed in the question. Since the right side is a constant, the left side must remain a constant. If the volume is doubled, then the pressure must thus be halved.