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A 100 mL flask contained $\mathrm{H}_2$ at 200 torr, and a 200 mL flask contained He at 100 torr. The two flask were then connected so that each gas filled their combined volume. Assume, no change in temperature, total pressure is
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Verified Answer
The correct answer is:
133.33 torr
Given,
$\begin{aligned} \mathrm{p}_{\mathrm{H}_2} & =200 \text { torr } \\ \mathrm{V}_{\mathrm{H}_2} & =100 \mathrm{~mL} \\ \mathrm{p}_{\mathrm{He}} & =100 \text { torr }\end{aligned}$
$\begin{array}{rlrl} & \mathrm{V}_{\mathrm{He}} & =200 \mathrm{~mL} \\ & & \mathrm{n}_{\mathrm{H}_2} & =\frac{\mathrm{pV}}{\mathrm{RT}}=\frac{20000}{\mathrm{RT}} \\ \therefore & & \mathrm{n}_{\mathrm{He}} & =\frac{\mathrm{pV}}{\mathrm{RT}}=\frac{20000}{\mathrm{RT}}\end{array}$
Total number of moles $=\mathrm{n}_{\mathrm{H}_2}+\mathrm{n}_{\mathrm{He}}$
$=\frac{20000}{R T}+\frac{20000}{R T}=\frac{40000}{R T}$
$\begin{aligned} & \text { Total volume }=300 \mathrm{~mL} \\ & \text { Total pressure }(\mathrm{p}) \quad=\frac{\mathrm{n}}{\mathrm{V}} \mathrm{RT}\end{aligned}$
$\begin{aligned} & =\frac{40000 \times \mathrm{RT}}{\mathrm{RT} \times 300}=\frac{400}{3} \\ & =133.33 \mathrm{torr}\end{aligned}$
$\begin{aligned} \mathrm{p}_{\mathrm{H}_2} & =200 \text { torr } \\ \mathrm{V}_{\mathrm{H}_2} & =100 \mathrm{~mL} \\ \mathrm{p}_{\mathrm{He}} & =100 \text { torr }\end{aligned}$
$\begin{array}{rlrl} & \mathrm{V}_{\mathrm{He}} & =200 \mathrm{~mL} \\ & & \mathrm{n}_{\mathrm{H}_2} & =\frac{\mathrm{pV}}{\mathrm{RT}}=\frac{20000}{\mathrm{RT}} \\ \therefore & & \mathrm{n}_{\mathrm{He}} & =\frac{\mathrm{pV}}{\mathrm{RT}}=\frac{20000}{\mathrm{RT}}\end{array}$
Total number of moles $=\mathrm{n}_{\mathrm{H}_2}+\mathrm{n}_{\mathrm{He}}$
$=\frac{20000}{R T}+\frac{20000}{R T}=\frac{40000}{R T}$
$\begin{aligned} & \text { Total volume }=300 \mathrm{~mL} \\ & \text { Total pressure }(\mathrm{p}) \quad=\frac{\mathrm{n}}{\mathrm{V}} \mathrm{RT}\end{aligned}$
$\begin{aligned} & =\frac{40000 \times \mathrm{RT}}{\mathrm{RT} \times 300}=\frac{400}{3} \\ & =133.33 \mathrm{torr}\end{aligned}$
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