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Chapter 15: Problem 102

Equilibrium is established in the reaction \(2 \mathrm{SO}_{2}(\mathrm{g})+\) \(\mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{SO}_{3}(\mathrm{g}) \quad\) at \(\quad \mathrm{a} \quad\) temperature \(\quad\) where \(K_{\mathrm{c}}=100 .\) If the number of moles of \(\mathrm{SO}_{3}(\mathrm{g})\) in the equilibrium mixture is the same as the number of moles of \(\mathrm{SO}_{2}(\mathrm{g}),\) (a) the number of moles of \(\mathrm{O}_{2}(\mathrm{g})\) is also equal to the number of moles of \(\mathrm{SO}_{2}(\mathrm{g}) ;\) (b) the number of moles of \(\mathrm{O}_{2}(\mathrm{g})\) is half the number of moles of \(\mathrm{SO}_{2} ;\) (c) \(\left[\mathrm{O}_{2}\right]\) may have any of several values; (d) \(\left[\mathrm{O}_{2}\right]=0.010 \mathrm{M}\)

Short Answer

Expert verified
The answers that match with \(K_c = 100\) are (c) \([O_2]\) may have any of several values and (d) \([O_2] = 0.010 M\).

Step by step solution

01

Exploring the known facts

We know that SO3 is produced from the reaction of SO2 and O2, with the reactant and product concentrations expressed through the equilibrium constant \(K_c = 100\). Also, we know the moles of SO2 and SO3 are equal.
02

Understanding the equilibrium constant

The equilibrium constant, Kc, is defined as the ratio of the concentrations of products to the reactants. For the reaction \(2SO_2 + O_2 \rightleftharpoons 2SO_3\), Kc would be represented as: \(K_c = [SO_3]^2 / ([SO_2]^2*[O_2])\). Because we know that the number of moles of \(SO_3\) is equal to the number of moles of \(SO_2\), we can simplify this formula to: \(K_c = 1 / [O_2]\)
03

Evaluating the options

With our simplified equation, we can check each of the suggested answers: (a) If the number of moles of \(O_2\) is equal to the number of moles of \(SO_2\), then \(K_c = 1\). This does not match the known \(K_c = 100\). (b) If the number of moles of \(O_2\) is half the number of moles of \(SO_2\), then \(K_c = 4\). This does not match the known \(K_c = 100\). (c) If \([O_2]\) has any value, this implies the possibility that \(K_c = 100\), which matches the known \(K_c = 100\). (d) If \([O_2] = 0.010 M\), then \(K_c = 1 / 0.010 = 100\), which matches the known \(K_c = 100\)

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Most popular questions from this chapter

For the dissociation of \(\mathrm{I}_{2}(\mathrm{g})\) at about \(1200^{\circ} \mathrm{C}\) \(\mathrm{I}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{I}(\mathrm{g}), K_{\mathrm{c}}=1.1 \times 10^{-2} .\) What volume flask should we use if we want 0.37 mol I to be present for every \(1.00 \mathrm{mol} \mathrm{I}_{2}\) at equilibrium?

In the reversible reaction \(\mathrm{H}_{2}(\mathrm{g})+\mathrm{I}_{2}(\mathrm{g}) \rightleftharpoons\) \(2 \mathrm{HI}(\mathrm{g}),\) an initial mixture contains \(2 \mathrm{mol} \mathrm{H}_{2}\) and 1 mol I \(_{2} .\) The amount of HI expected at equilibrium is (a) \(1 \mathrm{mol} ;\) (b) \(2 \mathrm{mol} ;\) (c) less than \(2 \mathrm{mol}\); (d) more than 2 mol but less than 4 mol.

In the reaction \(\mathrm{H}_{2} \mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}_{2}(\mathrm{aq}), K=1.0 \times\) \(10^{5}\) at \(25^{\circ} \mathrm{C} .\) Would you expect a greater amount of product or reactant?

For the dissociation reaction \(2 \mathrm{H}_{2} \mathrm{S}(\mathrm{g}) \rightleftharpoons 2 \mathrm{H}_{2}(\mathrm{g})+\) \(\mathrm{S}_{2}(\mathrm{g}), K_{\mathrm{p}}=1.2 \times 10^{-2}\) at \(1065^{\circ} \mathrm{C} .\) For this same reaction at \(1000 \mathrm{K},\) (a) \(K_{\mathrm{c}}\) is less than \(K_{\mathrm{p}} ;\) (b) \(K_{\mathrm{c}}\) is greater than \(K_{\mathrm{p}} ;(\mathrm{c}) K_{\mathrm{c}}=K_{\mathrm{p}} ;\) (d) whether \(K_{\mathrm{c}}\) is less than, equal to, or greater than \(K_{\mathrm{p}}\) depends on the total gas pressure.

One important reaction in the citric acid cycle is citrate(aq) \(\rightleftharpoons\) aconitate \((\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \quad K=0.031\) Write the equilibrium constant expression for the above reaction. Given that the concentrations of \([\text { citrate }(\mathrm{aq})]=0.00128 \mathrm{M},[\text { aconitate }(\mathrm{aq})]=4.0 \times\) \(10^{-5} \mathrm{M},\) and \(\left[\mathrm{H}_{2} \mathrm{O}\right]=55.5 \mathrm{M},\) calculate the reaction quotient. Is this reaction at equilibrium? If not, in which direction will it proceed?
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