Question

A 0.19 mole sample of nitrogen gas occupies a volume of 2.25 L. What is the volume of 0.27 mol of nitrogen gas under the same conditions?

Answer 1

Step 1 - Discover the relation between moles and volume

The gas state equation states that:

`pV=\text{nRT}`

Since the exercise says that both pressure and temperature will remain the same ("under the same conditions"), and R is already a constant, we can obtain a direct relation between moles and volume:

`V=n((RT)/(P))\rightarrow V\propto n`

Since R, T and P will not vary, the quocient in parenthesis is a constant. Therefore, the volume will be directly proportional to the number of moles of gas.

Step 2 - using the relation to solve the problem

Since, as we saw, volume and moles are directly proportional to each other, we can set the following proportion to discover the new volume:

`\begin{gathered} 0.19\text{ moles of N2----2.25 L} \\ 0.27\text{ moles of N2-----x} \\ \\ x=(0.27*2.25)/(0.19)=3.19\text{ L} \end{gathered}`

So, the volume of 0.27 moles of N2 gas, under the same conditions, will be 3.19 L.