# A container has a volume of 21 L and holds 14 mol of gas. If the container is compressed such that its new volume is 7 L, how many moles of gas must be released from the container to maintain a constant temperature and pressure?

Dec 31, 2016

9.33 moles

#### Explanation:

Assuming ideal gas behavior where n = PV/RT , with a constant temperature and pressure, the ratio of the volume change in L is the same as the ratio of the change in the total number of moles of gas in the container.
${\left({n}_{1} \cdot \frac{P V}{T}\right)}_{1} = {\left({n}_{2} \cdot \frac{P V}{T}\right)}_{2}$

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

$\frac{{n}_{2}}{14} / = \left(\frac{7}{21}\right)$

$\left({n}_{2}\right) = \left(\frac{7}{21}\right) \cdot \left(14\right)$ = 4.67 moles

SO, to retain 4.67 moles from the original 14, 9.33 moles of gas must be released.