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?

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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?

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Answer 1 · 2017-02-28T16:47:02

The new volume would be 6 liters.

Explanation:

$P V = n R T$ $PV = nRT$

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

$n$ $n$ , $R$ $R$ , and $T$ $T$ are constant; therefore, $P_{1} V_{1} = P_{2} V_{2}$ $P_1V_1 = P_2V_2$

Convert the torr into atm

$P_{1}$ $P_1$ = $\frac{380 torr}{760 torr \times a t m^{- 1}}$ $(380"torr")/(760 "torr" times atm^(-1))$ = $0.5$ $0.5$ atm
$P_{2}$ $P_2$ = $\frac{760 torr}{760 torr \times a t m^{- 1}}$ $(760"torr")/(760 "torr" times atm^(-1))$ = $1$ $1$ atm

Set the volume

$V_{1}$ $V_1$ = 12 L
$V_{2}$ $V_2$ = $x$ $x$ L

$P_{1} V_{1} = P_{2} V_{2}$ $P_1V_1 = P_2V_2$
$0.5 atm \times 12 L$ $0.5"atm" times 12 "L"$ = $1 atm \times x L$ $1"atm" times x "L"$
$x$ $x$ L = 6L

The new volume would be 6 liters.

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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?

1 Answer

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