**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.