 # The air in a bicycle tire is bubbled through water and collected at 25^{\circ alka8q7 2021-11-17 Answered

The air in a bicycle tire is bubbled through water and collected at ${25}^{\circ }C$. If the total volume of gas collected is 5.45 L at a temperature of ${25}^{\circ }C$ and a pressure of 745 torr, how many moles of gas were in the bicycle tire?

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Step 1
$T=\left(25+273.15\right)K=298.15K$
${P}_{\to t}=745\to rr=745mmHg$
${P}_{{H}_{2}O}=23.78mmHg$
$V=5.45L$
${n}_{gas}=?$
Write down the known and unknown values.
Step 2
${P}_{\to t}={P}_{{H}_{2}O}+{P}_{gas}$
${P}_{gas}={P}_{\to t}-{P}_{{H}_{2}O}$
$=745mmHg--23.7mmHg$
$=721.3mmHg$
Use the gas-evolution equation based on Dalton's Law of partial pressures to calculate the partial pressure of the gas evolved.
Step 3
${P}_{gas}=\begin{array}{cc}721.3\mathrm{m̸}\mathrm{m̸}\mathrm{H̸}g& 1atm\\ & 760\mathrm{m̸}\mathrm{m̸}\mathrm{H̸}g\end{array}=0.94908atm$
Convert the partial pressure of the evolved gas into atmospheres.
Step 4
${P}_{gas}V={n}_{gas}RT\phantom{\rule{0ex}{0ex}}{n}_{gas}=\frac{{P}_{gas}V}{RT}\phantom{\rule{0ex}{0ex}}=\begin{array}{ccc}0.94908\mathrm{a̸}\mathrm{t̸}\mathrm{m̸}& mol\cdot \mathrm{K̸}& 5.45\mathrm{L̸}\\ & 0.08206\mathrm{L̸}\cdot \mathrm{a̸}\mathrm{t̸}\mathrm{m̸}& 298.15\mathrm{K̸}\end{array}=0.211mol$
Use the Ideal Gas Law to calculate the number of moles of the evolved gas.