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Chapter 15: Problem 32

Consider the equilibrium \(\mathrm{Na}_{2} \mathrm{O}(s)+\mathrm{SO}_{2}(g) \rightleftharpoons\) \(\mathrm{Na}_{2} \mathrm{SO}_{3}(s)\) (a) Write the equilibrium-constant expression for this reaction in terms of partial pressures. (b) All the compounds in this reaction are soluble in water. Rewrite the equilibrium-constant expression in terms of molarities for the aqueous reaction.

Short Answer

Expert verified
(a) The equilibrium constant expression in terms of partial pressures (K_p) for the given reaction is: \[K_p = \frac{P_{\mathrm{Na}_2\mathrm{SO}_3}}{P_{\mathrm{SO}_2}}\] (b) For the aqueous reaction, the equilibrium constant expression based on molarities (K_c) is: \[K_c = \frac{[\mathrm{Na}_2\mathrm{SO}_3]}{[\mathrm{SO}_2]}\]

Step by step solution

01

Write the chemical equation

Write the given equilibrium reaction: \(\mathrm{Na}_2 \mathrm{O}(s) + \mathrm{SO}_2(g) \rightleftharpoons \mathrm{Na}_2 \mathrm{SO}_3(s)\)
02

Write equilibrium constant expression based on partial pressures

For the given reaction, the equilibrium constant expression in terms of partial pressures (K_p) can be written as: \[K_p = \frac{P_{\mathrm{Na}_2\mathrm{SO}_3}}{P_{\mathrm{SO}_2}}\] Notice that we didn't include the solid reactant, \(\mathrm{Na}_2 \mathrm{O}\), in the expression because its concentration does not affect the equilibrium constant.
03

Write the equilibrium constant expression based on molarities

As all compounds are soluble in water, we can rewrite the equilibrium constant expression based on molarities (K_c) instead of partial pressures for the aqueous reaction: \[K_c = \frac{[\mathrm{Na}_2\mathrm{SO}_3]}{[\mathrm{SO}_2]}\] Now, we have the equilibrium constant expression based on molarities for the given reaction.

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Most popular questions from this chapter

The equilibrium \(2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{NOCl}(g)\) is estab- lished at \(500 \mathrm{~K}\). An equilibrium mixture of the three gases has partial pressures of 0.095 atm, 0.171 atm, and 0.28 atm for \(\mathrm{NO}, \mathrm{Cl}_{2},\) and \(\mathrm{NOCl}\), respectively. (a) Calculate \(K_{p}\) for this reaction at \(500.0 \mathrm{~K}\). (b) If the vessel has a volume of \(5.00 \mathrm{~L}\) calculate \(K_{c}\) at this temperature.

Nitric oxide (NO) reacts readily with chlorine gas as follows: $$ 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{NOCl}(g) $$ At \(700 \mathrm{~K}\) the equilibrium constant \(K_{p}\) for this reaction is \(0.26 .\) Predict the behavior of each of the following mixtures at this temperature and indicate whether or not the mixtures are at equilibrium. If not, state whether the mixture will need to produce more products or reactants to reach equilibrium. (a) \(P_{\mathrm{NO}}=0.15 \mathrm{~atm}, P_{\mathrm{Cl}_{2}}=0.31 \mathrm{~atm},\) and \(P_{\mathrm{NOCl}}=0.11 \mathrm{~atm} ;\) (b) \(P_{\mathrm{NO}}=0.12 \mathrm{~atm}, P_{\mathrm{Cl}_{2}}=0.10 \mathrm{~atm},\) and \(P_{\mathrm{NOCl}}=0.050 \mathrm{~atm} ;\) (c) \(P_{\mathrm{NO}}=0.15 \mathrm{~atm}, P_{\mathrm{Cl}_{2}}=0.20 \mathrm{~atm},\) and \(P_{\mathrm{NOCl}}=5.10 \times\) \(10^{-3}\) atm.

When \(1.50 \mathrm{~mol} \mathrm{CO}_{2}\) and \(1.50 \mathrm{~mol} \mathrm{H}_{2}\) are placed in a 3.00-L container at \(395^{\circ} \mathrm{C},\) the following reaction occurs: \(\mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) . \quad\) If \(\quad K_{c}=0.802\) what are the concentrations of each substance in the equilibrium mixture?

Both the forward reaction and the reverse reaction in the following equilibrium are believed to be elementary steps: $$ \mathrm{CO}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{COCl}(g)+\mathrm{Cl}(g) $$ At \(25^{\circ} \mathrm{C}\) the rate constants for the forward and reverse reactions are \(1.4 \times 10^{-28} \mathrm{M}^{-1} \mathrm{~s}^{-1}\) and \(9.3 \times 10^{10} \mathrm{M}^{-1} \mathrm{~s}^{-1}\), respectively. (a) What is the value for the equilibrium constant at \(25^{\circ} \mathrm{C} ?\) (b) Are reactants or products more plentiful at equilibrium? (c) What additional information would you need in order to decide whether the reaction as written is endothermic or exothermic?

For the equilibrium $$2 \mathrm{IBr}(g) \rightleftharpoons \mathrm{I}_{2}(g)+\mathrm{Br}_{2}(g)$$ \(K_{p}=8.5 \times 10^{-3}\) at \(150^{\circ} \mathrm{C}\). If 0.025 atm of IBr is placed in a 2.0-L container, what is the partial pressure of all substances after equilibrium is reached?
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