Question 5.5: An experiment is designed to determine the effect of sulfur ......
An experiment is designed to determine the effect of sulfur dioxide, one of the EPA criteria pollutants, on plants. Among the variations used is a mixture that has the mole fractions given in the following table.
If the desired total pressure is 750. torr, what should the partial pressures be? If the gas is to be in a 15.0-L vessel held at 30°C, how many moles of each substance are needed?
Strategy We know the mole fractions and the desired total pressure. So we can calculate partial pressures using the relationship defined in Equation 5.10. From the total pressure and the volume, we can calculate the total number of moles and thereby the number of moles of each gas.
P_i = X_i\ P (5.10)
| Gas | N_2 | O_2 | H_2O | SO_2 |
| Mole fraction | 0.751 | 0.149 | 0.080 | 0.020 |
P_i = X_i\ P_{total}
P_{N_2} = (0.751)(750. torr) = 563 torr
P_{O_2} = (0.149)(750. torr) = 112 torr
P_{H_2O} = (0.080)(750. torr) = 60 torr
P_{SO_2} = (0.020)(750. torr) = 15 torr
The desired total pressure of 750 torr can also be expressed as 0.987 atm. So
n_{\mathrm{total}}={\frac{P V}{R T}}={\frac{(0.987~{\mathrm{atm}})(15.0~\mathrm{L})}{(0.08206~\mathrm{L~atm~mol^{-1}~K^{-1})(303~K)}}}=0.595~\mathrm{mol}
n_i = X_in_{total}
n_{N_2} = (0.751)(0.595) = 0.447 mol
n_{O_2} = (0.149)(0.595) = 8.87 × 10^{−2} mol
n_{H_2O} = (0.080)(0.595) = 4.8 × 10^{−2} mol
n_{SO_2} = (0.020)(0.595) = 1.2 × 10^{−2} mol
Check Your Understanding A mixture of SO_2(g) and SO_3(g) is to be prepared with a total pressure of 1.4 atm. If the mole fractions of the gases are 0.70 and 0.30, respectively, what are the partial pressures? If the mixture is to occupy 2.50 L at 27°C, what mass of each gas is needed?