Question def0e

Mar 11, 2017

$\text{7.02 L}$

Explanation:

Avogadro's Law states that when temperature and pressure are kept constant, the volume of a gas is directly proportional to the number of moles of gas present in the container.

Mathematically, this is written as

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{{V}_{1} / {n}_{1} = {V}_{2} / {n}_{2}}}}$

Here

• ${V}_{1}$ and ${n}_{1}$ represent the volume and number of moles of gas at an initial state
• ${V}_{2}$ and ${n}_{2}$ represent the volume and the number of moles of gas at a final state

So, you know that initially, the balloon contained $4.51$ moles of gas and had an unknown volume ${V}_{1}$. After you add $1.25$ moles, the total number of moles of gas present in the balloon will be equal to

$\text{4.51 moles + 1.25 moles = 5.76 moles}$

The volume of the balloon went from ${V}_{1}$ to $\text{8.97 L}$. Right from the start, you can say that the volume increased, i.e. that

${V}_{1} < \text{8.97 L}$

because the number of moles of gas increased.

Rearrange the equation to solve for ${V}_{1}$

${V}_{1} / {n}_{1} = {V}_{2} / {n}_{2} \implies {V}_{1} = {n}_{1} / {n}_{2} \cdot {V}_{2}$

Plug in your values to find

V_1 = (4.51 color(red)(cancel(color(black)("moles"))))/(5.76color(red)(cancel(color(black)("moles")))) * "8.97 L" = color(darkgreen)(ul(color(black)("7.02 L")))#

The answer is rounded to three sig figs.

As predicted, the volume increased as a result of the increase in the number of moles of gas present in the balloon.