A sample of gas has a volume of 12 liters at 0°C and 380 torr. What will be its volume when the pressure is changed to 760 torr at a constant temperature?

Feb 28, 2017

The new volume would be 6 liters.

Explanation:

$P V = n R T$

$P$ is pressure in atm (760 torr = 1 atm); $V$ is volume in liters; $n$ is the number of moles; $R$ is the constant 0.0821; $T$ is temperature in Kelvin.

$n$, $R$, and $T$ are constant; therefore, ${P}_{1} {V}_{1} = {P}_{2} {V}_{2}$

Convert the torr into atm

${P}_{1}$ = $\left(380 \text{torr")/(760 "torr} \times a t {m}^{- 1}\right)$ = $0.5$ atm
${P}_{2}$ = $\left(760 \text{torr")/(760 "torr} \times a t {m}^{- 1}\right)$ = $1$ atm

Set the volume

${V}_{1}$ = 12 L
${V}_{2}$ = $x$ L

${P}_{1} {V}_{1} = {P}_{2} {V}_{2}$
$0.5 \text{atm" times 12 "L}$ = $1 \text{atm" times x "L}$
$x$L = 6L

The new volume would be 6 liters.