Question

If 3.31 moles of argon gas occupies a volume of 100 L what volume does 13.15 moles of argon occupy under the same temperature and pressure

Answer 1

397 L

Step-by-step explanation:

Recall the ideal gas law:

`\displaystyle PV = nRT`

If temperature and pressure stays constant, we can rearrange all constant variables onto one side of the equation:

`\displaystyle (P)/(RT) = (n)/(V)`

The left-hand side is simply some constant. Hence, we can write that:

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

Substitute in known values:

`\displaystyle \frac{(3.31 \text{ mol})}{(100 \text{ L})} = \frac{(13.15\text{ mol })}{V_2}`

Solving for V₂ yields:

`\displaystyle V_2 = \frac{(100 \text{ L})(13.15)}{3.31} = 397 \text{ L}`

In conclusion, 13.15 moles of argon will occupy 397* L under the same temperature and pressure.

(Assuming 100 L has three significant figures.)