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Learning Goal:

To understand the ideal gas law and be able to apply it to a wide variety of situations.

The absolute temperature $T,$ volume $V,$ and pressure $p$ of a gas sample are related by the ideal gas law, which states that

$pV=nRT$

Here $n$ is the number of moles in the gas sample and $R$ is a gas constant that applies to all gases. This empirical law describes gases well only if they are sufficiently dilute and at a sufficiently high temperature that they are not on the verge of condensing.

In applying the ideal gas law, $p$ must be the absolute pressure, measured with respect to vacuum and not with respect to atmospheric pressure, and $T$ must be the absolute temperature, measured in kelvins $($that is$,$ with respect to absolute zero, defined throughout this tutorial as $-273C).$ If $p$ is in pascals and $V$ is in cubic meters, use $R=8\mathrm{.}3145\frac{J}{\text{m}\text{o}\text{l}*K}.$ If $p$ is in atmospheres and $V$ is in liters, use $R=0\mathrm{.}08206L*at\frac{m}{\text{m}\text{o}\text{l}*K}$ instead.

Part C

Some hydrogen gas is enclosed within a chamber being held at $200C$ with a volume of $0\mathrm{.}0250m^3.$ The chamber is fitted with a movable piston. Initially, the pressure in the gas is $1\mathrm{.}50{10}^{6}Pa(14\mathrm{.}8$atm$).$ The piston is slowly extracted until the pressure in the gas falls to $0\mathrm{.}950{10}^{6}Pa.$ What is the final volume $V_2$ of the container? Assume that no gas escapes and that the temperature remains at $200C.$

Enter your answer in cubic meters.

View Available Hint$($s$)$

$A$

$V_2$

$m^3$