Feb 27, 2014

Avogadro's law states that, at the same temperature and pressure, equal volumes of all gases have the same number of molecules.

#### Explanation:

Another statement is, "Volume is directly proportional to the number of moles."

The volume increases as the number of moles increases. It does not depend on the sizes or the masses of the molecules.

V ∝ n, where $V$ is the volume, and $n$ is the number of moles.

$\frac{V}{n} = k$, where $k$ is a proportionality constant.

We can rewrite this as

${V}_{1} / {n}_{1} = {V}_{2} / {n}_{2}$

Equal volumes of hydrogen, oxygen, or carbon dioxide contain the same number of molecules.

STP is 0 °C and 1 bar.

One mole of an ideal gas occupies 22.71 L at STP. Thus, its molar volume at STP is 22.71 L

Example Problem

A 6.00 L sample at 25.0 °C and 2.00 atm contains 0.500 mol of gas. If we add 0.250 mol of gas at the same pressure and temperature, what is the final total volume of the gas?

Solution

The formula for Avogadro's law is:

${V}_{1} / {n}_{1} = {V}_{2} / {n}_{2}$

${V}_{1} = \text{6.00 L"; n_1 = "0.500 mol}$

V_2 = ?; color(white)(mml)n_2 = "0.500 mol + 0.250 mol = 0.750 mol"

V_2 = V_1 × n_2/n_1

${V}_{2} = \text{6.00 L" × (0.750 color(red)(cancel(color(black)("mol"))))/(0.500 color(red)(cancel(color(black)("mol")))) = "9.00 L}$