Avogadro's gas law states the volume of a gas is proportional to the number of moles of gas present when temperature and pressure are held constant. This example problem demonstrates how to use Avogadro's law to determine the volume of a gas when more gas is added to the system.

### Avogadro's Law Problem

A 6.0 L sample at 25 °C and 2.00 atm of pressure contains 0.5 moles of a gas. If an additional 0.25 moles of gas at the same pressure and temperature are added, what is the final total volume of the gas?

**Solution:**

Avogadro's law can be expressed by the formula:

V_{i}/n_{i} = V_{f}/n_{f}

where

V_{i} = initial volume

n_{i} = initial number of moles

V_{f} = final volume

n_{f} = final number of moles

For this example, V_{i} = 6.0 L and n_{i} = 0.5 moles.

When 0.25 moles are added

n_{f} = n_{i} + 0.25 moles

n_{f} = 0.5 moles = 0.25 moles

n_{f} = 0.75 moles

The only variable remaining is the final volume.

V_{i}/n_{i} = V_{f}/n_{f}

Solve for V_{f}

V_{f} = V_{i}n_{f}/n_{i}

V_{f} = (6.0 L x 0.75 moles)/0.5 moles

V_{f} = 4.5 L/0.5 V_{f} = 9 L

Check to see if the answer makes sense. You would expect the volume to increase if more gas is added. Is the final volume is greater than the initial volume? Yes. This check is useful since it is easy to put the initial number of moles in the numerator and the final number of moles in the denominator. If this happened, the final volume answer would be smaller than the initial volume.

**Answer:**

The final volume of the gas is 9.0 L.

### Notes Regarding Avogadro's Law

- Unlike Avogadro's number, Avogadro's law was actually proposed by Amedeo Avogadro. In 1811, he hypothesized two samples of an ideal gas with the same volume and at the same pressure and temperature contained the same number of molecules.

- Avogadro's law is also called Avogadro's principle or Avogadro's hypothesis.
- Like the other ideal gas laws, Avogadro's law only approximates the behavior of real gases. Under conditions of high temperature or pressure, the law is inaccurate. The relation works best for gases held at low pressure and ordinary temperatures. Also, smaller gas particles (e.g., helium, hydrogen, nitrogen) yield better results than larger molecules, which are more likely to interact with each other.

- Another mathematical relation used to express Avogadro's law is:

V/n = k

where V is the volume, n is the number of moles of the gas, and k is the proportionality constant. It's important to note this means the ideal gas constant is *the same* for all gases.