# Question 24a0b

Apr 15, 2017

The final volume will be 38.7 L.

#### Explanation:

We can use Avogadro's Law to solve this problem.

The volume of a fixed mass of a gas is directly proportional to the number of moles if the temperature and pressure are constant.

$\frac{V}{n} = k$

In a more usable form, Avogadro's Law becomes

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

We can rearrange this equation to get

V_2 = V_1 × n_2/n_1#

${V}_{1} = \text{49.0 L"; n_1 = "1.90 mol}$
${V}_{2} = \text{?"; color(white)(mmll)n_2 = "(1.90 - 0.400) mol" = "1.50 mol}$
${V}_{2} = \text{49.0 L" × (1.50 color(red)(cancel(color(black)("mol"))))/(1.90 color(red)(cancel(color(black)("mol")))) = "38.7 L}$