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A sample of gas with an initial volume of 28.4 L at a pressure of 724 mm Hg and a temperature of 303 K is compressed to a volume of 15.5 L and warmed to a temperature of 379 K. What is the final pressure of the gas?

User CBono
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1 Answer

12 votes
12 votes

To solve this question, we need to use the combined gas equation which is given as


\begin{gathered} (P_1V_1)/(T_1)=(P_2V_2)/(T_2) \\ p=\text{pressure} \\ v=\text{volume} \\ t=\text{temperature} \end{gathered}

Now we should write down the given data


\begin{gathered} v_1=28.4l \\ p_1=724\operatorname{mm}hg \\ T_1=303K \\ v_2=15.5L \\ T_2=379K \\ p_2=\text{ ?} \end{gathered}

So, we would use the previous equation i wrote down.


\begin{gathered} (p_1v_1)/(t_1)=(p_2v_2)/(t_2) \\ (724*28.4)/(303)=(p_2*15.5)/(379) \\ 67.8600=(p_2*15.5)/(379) \\ 15.5p_2=67.86*379 \\ 15.5p_2=25718.94 \\ \text{divide both sides by the coefficent of p2} \\ (15.5p_2)/(15.5)=(25718.94)/(15.5) \\ p_2=1659.28\operatorname{mm}hg \end{gathered}

From the calculations above, the final pressure of the gas is 1659.28mmHg

User Grifos
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