Question #24a0b

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Answer 1 · 2017-04-15T15:08:41

The final volume will be 38.7 L.

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.

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

In a more usable form, Avogadro's Law becomes

$color(blue)(|bar(ul(color(white)(a/a)V_1/n_1 = V_2/n_2color(white)(a/a)|)))" "$

We can rearrange this equation to get

$V_2 = V_1 × n_2/n_1$

In your problem,

$V_1 = "49.0 L"; n_1 = "1.90 mol"$
$V_2 = "?"; color(white)(mmll)n_2 = "(1.90 - 0.400) mol" = "1.50 mol"$

∴ $V_2 = "49.0 L" × (1.50 color(red)(cancel(color(black)("mol"))))/(1.90 color(red)(cancel(color(black)("mol")))) = "38.7 L"$