Question 5.4: Not all pollution is due to human activity. Natural sources,......
Not all pollution is due to human activity. Natural sources, including volcanoes, also contribute to air pollution. A scientist tries to generate a mixture of gases similar to those found in a volcano by introducing 15.0 g of water vapor, 3.5 g of SO_2 and 1.0 g of CO_2 into a 40.0-L vessel held at 120.0°C. Calculate the partial pressure of each gas and the total pressure.
Strategy As usual, we will begin by assuming that all the gases behave ideally. Then we can treat each gas separately to determine its partial pressure. Finally, sum these partial pressures to calculate the total pressure.
For all of the gases, T = 120°C = 393 K, and V = 40.0 L.
\mathrm{H}_{2}\mathrm{O}\!:\,15.0\;\mathrm{g}\;\mathrm{H}_{2}\mathrm{O}\times{\frac{1\;\mathrm{mol}\;\mathrm{H}_{2}\mathrm{O}}{18.0\;\mathrm{g}\;\mathrm{H}_{2}\mathrm{O}}}=0.833\;\mathrm{mol}
P_{\mathrm{H}_{2}\mathrm{O}}={\frac{(0.833\;\mathrm{mol})(0.08206\;{\mathrm L}\;\mathrm{atm\;mol}^{-1}\;{\mathrm K}^{-1})(393\;{\mathrm K})}{40.0\;{\mathrm L}}}=0.672\;\mathrm{atm}
\mathrm{SO_{2}}:\mathrm{3.5\ g\ SO_{2}}\times\mathrm{\frac{1\,\mathrm{mol\;SO_{2}}}{64.1\,\mathrm{g}\,S O_{2}}}=0.055\ \mathrm{mol}
P_{\mathrm{SO_{2}}}={\frac{(0.055\mathrm{~mol})(0.08206\mathrm{~L~atm~mol}^{-1}\mathrm{~K}^{-1})(393\mathrm{~K})}{40.0\mathrm{~L}}}=0.044\mathrm{~atm}
\mathrm{CO}_{2}:1.0~\mathrm{g}~\mathrm{CO}_{2}\times~\frac{1~\mathrm{mol}~\mathrm{CO}_{2}}{44.0~\mathrm{g}~\mathrm{CO}_{2}}=0.023~\mathrm{mol}
P_{\mathrm{CO_{2}}}={\frac{(0.023~\mathrm{mol})(0.08206~\mathrm{L~atm~mol}^{-1}~\mathrm{K}^{-1})(393~\mathrm{K})}{40.0~\mathrm{L}}}=0.018~\mathrm{atm}
Total pressure is the sum of these:
P_{tot} = P_{H_2O} + P_{SO_2} + P_{CO_2} = 0.672 + 0.044 + 0.018 = 0.734 atm
Note that you could also have used the total number of moles to find P_{tot} and then used mole fractions to find the partial pressures.
Analyze Your Answer It is possible to gain a feeling for quantities such as pressure and number of moles if you work a lot of these problems. In this case, we have almost a mole of gas in a volume of 40 L, and the temperature is somewhat high. Our result of 0.7 atm is not unreasonable.
Check Your Understanding A mixture containing 13.5 g of oxygen and 60.4 g of N_2 exerts a pressure of 2.13 atm at 25°C. What is the volume of the container, and what are the partial pressures of each gas?