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Chapter 15: Problem 30

Consider the equilibrium $\mathrm{Na}_{2} \mathrm{O}(s)+\mathrm{SO}_{2}(g) \rightleftharpoons\( \)\mathrm{Na}_{2} \mathrm{SO}_{3}(s) .(\mathbf{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
In terms of partial pressures, the equilibrium constant expression for the given reaction is \(K_p = \frac{1}{P_{\mathrm{SO}_{2}}}\). When all compounds are dissolved in water, the equilibrium constant expression in terms of molarities is \(K_c = \frac{[\mathrm{Na}_2\mathrm{SO}_{3}]}{[\mathrm{Na}_2\mathrm{O}][\mathrm{SO}_{2}]}\).

Step by step solution

01

Write the balanced equilibrium reaction

The balanced chemical equation for the given reaction is: \[ \mathrm{Na}_2\mathrm{O}(s) + \mathrm{SO}_{2}(g) \rightleftharpoons \mathrm{Na}_2\mathrm{SO}_{3}(s) \]
02

Write the equilibrium constant expression in terms of partial pressures

For any reaction, the equilibrium constant expression in terms of partial pressures is given by: \[ K_p = \frac{(\text{partial pressures of products})^{coefficients}}{(\text{partial pressures of reactants})^{coefficients}} \] In the balanced chemical equation, only one reactant \(\mathrm{SO}_{2}\) is in the gaseous state. All the other reactants and products are solids. Thus, the equilibrium constant in terms of partial pressure is given by: \[ K_p = \frac{1}{P_{\mathrm{SO}_{2}}} \] #b. Writing the equilibrium constant expression in terms of molarities for the aqueous reaction#
03

Write the balanced aqueous reaction

When all compounds are dissolved in water, the balanced chemical equation for the given reaction is: \[ \mathrm{Na}_2\mathrm{O}(aq) + \mathrm{SO}_{2}(aq) \rightleftharpoons \mathrm{Na}_2\mathrm{SO}_{3}(aq) \]
04

Write the equilibrium constant expression in terms of molarities

For any reaction, the equilibrium constant expression in terms of molarities is given by: \[ K_c = \frac{(\text{concentrations of products})^{coefficients}}{(\text{concentrations of reactants})^{coefficients}} \] In the balanced aqueous chemical equation, all reactants and products are in the aqueous state. Thus, the equilibrium constant in terms of molarities is given by: \[ K_c = \frac{[\mathrm{Na}_2\mathrm{SO}_{3}]}{[\mathrm{Na}_2\mathrm{O}][\mathrm{SO}_{2}]} \]

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Most popular questions from this chapter

Consider the following exothermic equilibrium (Boudouard reaction) $$2 \mathrm{CO}(g) \rightleftharpoons \mathrm{C}(s)+\mathrm{CO}_{2}(g)$$ How will each of the following changes affect an equilibrium mixture of the three gases: (a) a catalyst is added to the mixture; $(\mathbf{b}) \mathrm{CO}_{2}(g)\( is added to the system; \)(\mathbf{c}) \mathrm{CO}(g)$ is added from the system; \((\mathbf{d})\) the reaction mixture is heated; (e) the volume of the reaction vessel is doubled; \((\mathbf{f})\) the total pressure of the system is increased by adding a noble gas?

At \(700 \mathrm{~K}\), the equilibrium constant for the reaction $$\mathrm{CCl}_{4}(g) \rightleftharpoons \mathrm{C}(s)+2 \mathrm{Cl}_{2}(g)$$ is \(K_{p}=77\). A flask is charged with \(202.7 \mathrm{kPa}\) of \(\mathrm{CCl}_{4}\), which then reaches equilibrium at \(700 \mathrm{~K}\). (a) What fraction of the \(\mathrm{CCl}_{4}\) is converted into \(\mathrm{C}\) and \(\mathrm{Cl}_{2} ?\) (b) What are the partial pressures of \(\mathrm{CCl}_{4}\) and \(\mathrm{Cl}_{2}\) at equilibrium?

As shown in Table \(15.2,\) the equilibrium constant for the reaction $\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)\( is \)K_{p}=4.23 \times 10^{-7}\( at \)300^{\circ} \mathrm{C}\(. Pure \)\mathrm{NH}_{3}$ is placed in a 1.00-L flask and allowed to reach equilibrium at this temperature. There are $1.05 \mathrm{~g} \mathrm{NH}_{3}$ in the equilibrium mixture. (a) What are the masses of \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\) in the equilibrium mixture? (b) What was the initial mass of ammonia placed in the vessel? (c) What is the total pressure in the vessel?

If \(K_{c}=1\) for the equilibrium $3 \mathrm{~A}(g) \rightleftharpoons 2 \mathrm{~B}(g)$, what is the relationship between [A] and [B] at equilibrium?

At \(2000^{\circ} \mathrm{C}\), the equilibrium constant for the reaction $2 \mathrm{NO}(g) \rightleftharpoons \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g)$ is \(K_{c}=2.4 \times 10^{3} .\) If the initial concentration of NO is \(0.250 \mathrm{M}\), what are the equilibrium concentrations of \(\mathrm{NO}, \mathrm{N}_{2}\), and \(\mathrm{O}_{2}\) ?
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