A sample of gas occupies a volume of 50.0 milliliters in a cylinder with a movable piston. The pressure of the sample is 0.90 atmosphere and the temperature is 298 K. What is the volume of the sample at STP?

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A sample of gas occupies a volume of 50.0 milliliters in a cylinder with a movable piston. The pressure of the sample is 0.90 atmosphere and the temperature is 298 K. What is the volume of the sample at STP?

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Answer 1 · 2015-12-19T01:08:54

The new volume is 41 mL.

Explanation:

Use the combined gas law $\frac{P_{1} V_{1}}{T_{1}} = \frac{P_{2} V_{2}}{T_{2}}$ $(P_1V_1)/T_1=(P_2V_2)/T_2$ .
$STP=273.15 K and 1 atm$ $"STP=273.15 K and 1 atm"$

Given/Known
$P_{1} = 0.90 atm$ $P_1="0.90 atm"$
$V_{1} = 50.0 mL$ $V_1="50.0 mL"$
$T_{1} = 298 K$ $T_1="298 K"$
$P_{2} = 1 atm$ $P_2="1 atm"$
$T_{2} = 273.15 K$ $T_2="273.15 K"$

Unknown
$V_{2}$ $V_2$

Solution
Rearrange the equation to isolate $V_{2}$ $V_2$ and solve.

$\frac{P_{1} V_{1}}{T_{1}} = \frac{P_{2} V_{2}}{T_{2}}$ $(P_1V_1)/T_1=(P_2V_2)/T_2$

$V_{2} = \frac{P_{1} V_{1} T_{2}}{T_{1} P_{2}}$ $V_2=(P_1V_1T_2)/(T_1P_2)$

$V_2=(0.90cancel"atm"xx50.0"mL"xx273.15cancel"K")/(298cancel"K"xx1cancel"atm")="41 mL"$

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A sample of gas occupies a volume of 50.0 milliliters in a cylinder with a movable piston. The pressure of the sample is 0.90 atmosphere and the temperature is 298 K. What is the volume of the sample at STP?

1 Answer

Explanation:

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