A container has a volume of $9 L$ $9 L$ and holds $18 m o l$ $18 mol$ of gas. If the container is expanded such that its new volume is $48 L$ $48 L$ , how many moles of gas must be injected into the container to maintain a constant temperature and pressure?

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Answer 1 · 2016-08-23T01:05:48

$96 moles$ $96 "moles"$ of gas

Let's use Avogadro's law:

$\frac{v_{1}}{n_{1}} = \frac{v_{2}}{n_{2}}$ $v_1/n_1 = v_2/n_2$

The number 1 represents the initial conditions and the number 2 represents the final conditions.

• Identify your known and unknown variables:

$Knowns:$ $color(purple)("Knowns:"$
$v_{1}$ $v_1$ = 9 L
$v_{2}$ $v_2$ = 48 L
$n_{1}$ $n_1$ = 18 mol

$Unknowns:$ $color(marigold) ("Unknowns:"$
$n_{2}$ $n_2$

• Rearrange the equation to solve for the final number of moles:

$n_{2} = \frac{v_{2} \times n_{1}}{v_{1}}$ $n_2=(v_2xxn_1)/v_1$

• Plug in your given values to obtain the final number of moles:

$n_2=(48 cancelLxx18mol)/(9\cancel"L")$ = $96 mol$

A container has a volume of 9 L9L9 L and holds 18 mol18mol18 mol of gas. If the container is expanded such that its new volume is 48 L48L48 L, how many moles of gas must be injected into the container to maintain a constant temperature and pressure?