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Chapter 5: Problem 98

Equal moles of sulfur dioxide gas and oxygen gas are mixed in a flexible reaction vessel and then sparked to initiate the formation of gaseous sulfur trioxide. Assuming that the reaction goes to completion, what is the ratio of the final volume of the gas mixture to the initial volume of the gas mixture if both volumes are measured at the same temperature and pressure?

Short Answer

Expert verified
The ratio of the final volume of the gas mixture to the initial volume of the gas mixture, when measured at the same temperature and pressure, is 3:4.

Step by step solution

01

Write the balanced chemical equation

Determine the balanced chemical equation for the reaction involving sulfur dioxide (SO2), oxygen (O2), and sulfur trioxide (SO3). The balanced chemical equation is: 2 SO2(g) + O2(g) -> 2 SO3(g)
02

Analyze the stoichiometry of the reaction

From the balanced chemical equation, we can see that 2 moles of SO2 react with 1 mole of O2 to produce 2 moles of SO3. Since equal moles of SO2 and O2 are involved initially, we can say that half of the moles of O2 react with SO2 to form SO3.
03

Calculate moles of each gas after the reaction

Let's assume that initially there are x moles of SO2 and x moles of O2 in the reaction vessel. After the reaction, SO2 consumption is x moles (as reaction goes to completion), and O2 consumption is (1/2)x moles (by stoichiometry of the balanced equation). Therefore, the moles of the remaining O2 will be [(x - (1/2)x] = (1/2)x moles. Since 2 moles of SO3 are produced for each 1 mole of O2 consumed, the moles of SO3 produced will be (2 * (1/2)x) = x moles.
04

Determine the initial and final volume ratio

According to the combined gas law, at constant temperature and pressure, the volume of a gas depends only on the number of moles. Since initially, there are x moles of SO2 and x moles of O2, the initial volume of the gas mixture will be proportional to a total of (x + x) = 2x moles. After the reaction, there are x moles of SO3 and (1/2)x moles remaining of O2, the final volume of the gas mixture will be proportional to (x + (1/2)x) = (3/2)x moles. The ratio of the final volume to the initial volume will be: \(\frac{Final\:Volume}{Initial\:Volume} = \frac{(3/2)x\:moles}{2x\:moles}\)
05

Simplify the ratio

Simplify the expression above to obtain the ratio of the final volume to the initial volume: \(\frac{Final\:Volume}{Initial\:Volume} = \frac{(3/2)x\:moles}{2x\:moles} = \frac{3}{4}\) So, the ratio of the final volume of the gas mixture to the initial volume of the gas mixture, when measured at the same temperature and pressure, is 3:4.

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Most popular questions from this chapter

Trace organic compounds in the atmosphere are first concentrated and then measured by gas chromatography. In the concentration step, several liters of air are pumped through a tube containing a porous substance that traps organic compounds. The tube is then connected to a gas chromatograph and heated to release the trapped compounds. The organic compounds are separated in the column and the amounts are measured. In an analysis for benzene and toluene in air, a 3.00-L sample of air at 748 torr and \(23^{\circ} \mathrm{C}\) was passed through the trap. The gas chromatography analysis showed that this air sample contained \(89.6\) ng benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) and \(153 \mathrm{ng}\) toluene \(\left(\mathrm{C}_{7} \mathrm{H}_{8}\right)\). Calculate the mixing ratio (see Exercise 121 ) and number of molecules per cubic centimeter for both benzene and toluene.

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