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.

Pi=Xi PP_i = X_i\ P   (5.10)

Gas N2_2 O2_2 H2_2O SO2_2
Mole fraction 0.751 0.149 0.080 0.020
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Pi=Xi PtotalP_i = X_i\ P_{total}
PN2P_{N_2} = (0.751)(750. torr) = 563 torr
PO2P_{O_2} = (0.149)(750. torr) = 112 torr
PH2OP_{H_2O} = (0.080)(750. torr) = 60 torr
PSO2P_{SO_2} = (0.020)(750. torr) = 15 torr

The desired total pressure of 750 torr can also be expressed as 0.987 atm. So

ntotal=PVRT=(0.987 atm)(15.0 L)(0.08206 L atm mol1 K1)(303 K)=0.595 moln_{\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}

ni=Xintotaln_i = X_in_{total}
nN2=(0.751)(0.595)=0.447n_{N_2} = (0.751)(0.595) = 0.447 mol
nO2=(0.149)(0.595)=8.87×102n_{O_2} = (0.149)(0.595) = 8.87 × 10^{−2} mol
nH2O=(0.080)(0.595)=4.8×102n_{H_2O} = (0.080)(0.595) = 4.8 × 10^{−2} mol
nSO2=(0.020)(0.595)=1.2×102n_{SO_2} = (0.020)(0.595) = 1.2 × 10^{−2} mol

Check Your Understanding A mixture of SO2_2(g) and SO3_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?

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