# Avogadro's Law

There is even more we can do with good old **P V** = **n R T**. The first part of this section introduced you to Avogadro's Law. One mole of any gas takes up a volume of 22.4 liters at standard temperature and pressure (STP). If we go back to the comparison of two formulas of the Ideal Gas Law, we have:

__P1 V1 = n1 R T1
__P2 V2 = n2 R T2

The **R**'s are the same, so they can be cancelled. At standard temperature, **T _{1}** =

**T**=

_{2}**273K**, and the

**T**'s can be cancelled. At standard pressure,

**P**=

_{1}**P**=

_{2}**1 atmosphere**, and the

**P**'s can be cancelled. When all the canceling has been done,

__V1__ = __n1
__V2 n2

If the volume is proportional to the number of mols of a gas, there is a constant, k, that we can use in the formula, **V** = **k n**, to express the proportionality of **V** and **n**. What is that proportionality constant? At standard temperature and pressure, the pressure is one atmosphere and the temperature is 273K. The Universal Gas Constant is still 0.0821 Liter - atmospheres per mol - degree. Let's set **n** at one to find out what **k** is.

P V = n R T and V = n R T/P

V = (1 mol) (0.0821 L - A/ mol - K) (237 K) / (1 A)

Cancel the mols, the A's (for Atmosphere) and the K's. Do the math.

V = 22.4 Liters

We have seen this number before in Avogadro's Law, and this is where it comes from. When n is one mol and V is 22.4 Liters, k is 22.4 Liters/mol.

**1 mol of any gas at STP = 22.4 liters**