First slide

Gaseous state

Question

A quantity of hydrogen gas occupies a volume of 30.0 mL at a certain temperature and pressure. What volume would half this mass of hydrogen occupy at triple the absolute temperature if the pressure were one-ninth that of the original gas?

Moderate

A

27O mL
B

90 mL
C

405 mL
D

135 mL

Solution

$p_{1} V_{1} = n_{1} {RT}_{1} p_{2} V_{2} = n_{2} {RT}_{2} \Rightarrow \frac{p_{1}}{9} V_{2} = \frac{n_{1}}{2} R (3 T_{1}) \frac{n_{1} {RT}_{1}}{V_{1}} \frac{V_{2}}{9} = \frac{n_{1}}{2} R (3 T_{1}) ∴ V_{2} = \frac{27 V_{1}}{2} = 13 .5 \times 30 mL = 405 mL$

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