# Aballoon with a volume of 8.00 Lis known to contain 1.200 moles of gas. How many moles of gas remain if some of the gas is released and the new volume is 5.25 L? Assume temperature and pressure remain constant.

Dec 27, 2016

The amount of gas remaining is 0.788 mol.

This problem is an example of Avogadro's Law, which states,

The volume occupied by a gas is directly proportional to the number of moles of gas present in the container, if the pressure and the temperature are held constant.**

In symbols,

$\textcolor{b l u e}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} {V}_{1} / {n}_{1} = {V}_{2} / {n}_{2} \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$

In this problem,

${V}_{1} = \text{8.70 L"; n_1 = "1.200 mol}$
${V}_{2} = \text{5.25 L"; n_2 = "?}$

n_2 = n_1 × V_2/V_1 = "1.200 mol" × (5.25 color(red)(cancel(color(black)("L"))))/(8.00 color(red)(cancel(color(black)("L")))) = "0.788 mol"