Question

A container has a volume of `4 L` and holds `3 mol` of gas. If the container is expanded such that its new volume is `9 L`, how many moles of gas must be injected into the container to maintain a constant temperature and pressure?

Answer 1

`3.75` `"mol"`

Explanation:

To solve this problem, we can use the volume-quantity relationship of gases, illustrated by Avogadro's law:

`(n_1)/(V_1) = (n_2)/(V_2)`

where

• `n_1` and `n_2` are the initial and final quantities, in `"mol"`, of the gas, and

• `V_1` and `V_2` are the initial and final volumes of the gas, usually in `"L"`

Since we're trying to find how many moles of gas are needed to inject, we'll rearrange the equation to solve for `n_2`:

`n_2 = (n_1V_2)/(V_1)`

Our known quantities are

• `n_1 = 3` `"mol"`

• `V_1 = 4` `"L"`

• `V_2 = 9` `"L"`

Plugging these values into the equation, we have

`n_2 = (n_1V_2)/(V_1) = ((3"mol")(9cancel("L")))/(4cancel("L")) = 6.75` `"mol"`

This is the total final volume; we were asked to find how many moles needed to be injected. To find this, we simply subtract the initial value from the final value:

`n_"need" = 6.75` `"mol" - 3` `"mol" = color(red)(3.75` `color(red)("mol"`

Thus, to maintain a constant temperature and pressure, you must inject `color(red)(3.75` moles of gas into the container.

If you follow the rules for significant figures, the answer is technically `4` moles, but questions like this with one significant figure are universally disliked... one significant figure is too uncertain for most people :)