Question

Question #def0e

Answer 1

`"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

`color(blue)(ul(color(black)(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

`"4.51 moles + 1.25 moles = 5.76 moles"`

The volume of the balloon went from `V_1` to `"8.97 L"`. Right from the start, you can say that the volume increased, i.e. that

`V_1 < "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 * 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.