Question 11.4: A sample of gas has an initial volume of 158 mL at a pressur......
A sample of gas has an initial volume of 158 mL at a pressure of 735 mm Hg and a temperature of 34 °C. If the gas is compressed to a volume of 108 mL and heated to a temperature of 85 °C, what is its final pressure in millimeters of mercury?
Step-by-Step
GIVEN:
P_1 = 735 mm Hg
t_1 = 34 °C t_2 = 85 °C
V_1 = 158 mL V_2 = 108 mL
FIND: P_2
RELATIONSHIPS USED
\frac{P_{1}V_{1}}{T_{1}}\;=\;\frac{P_{2}V_{2}}{T_{2}} (Combined gas law, presented in this section)
\frac{P_{1}V_{1}}{T_{1}}\;=\;\frac{P_{2}V_{2}}{T_{2}} \\ P_{2}=\frac{P_{1}V_{1}T_{2}}{T_{1}V_{2}} \\ \begin{array}{c}{{T_{1}=34\ +\ 273\ =\ 307~\mathrm{ K }}}\\ {{T_{2}=85\ +\ 273\ =\ 358~\mathrm{ K }}}\end{array} \\ P_{2}={\frac{735\;\mathrm{mm~Hg}\ \times\,158\;\mathrm{\cancel{mL}}\ \times\;358\;\mathrm{\cancel{K}}}{307\;\mathrm{\cancel{K}}\times108\;\mathrm{\cancel{mL}}}} \\ = 1.25 \times 10^3 mm HgThe answer has the correct units, mm Hg. The answer is reasonable because the decrease in volume and the increase in temperature should result in a pressure that is higher than the initial pressure.
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