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Chapter 15: Problem 42

(a) If \(Q_{c}>K_{c}\), how must the reaction proceed to reach equilibrium? (b) At the start of a certain reaction, only reactants are present; no products have been formed. What is the value of \(Q_{c}\) at this point in the reaction?

Short Answer

Expert verified
(a) If \(Q_c > K_c\), the reaction must proceed in the reverse direction to reach equilibrium, converting some products back into reactants until \(Q_c = K_c\). (b) At the start of a reaction with only reactants present and no products formed, the value of \(Q_c\) is 0.

Step by step solution

01

(a) Analyzing the reaction when \(Q_c > K_c\)

To determine how a reaction will proceed when \(Q_c > K_c\), we need to examine the definition of the reaction quotient, which is given by: $$Q_c = \frac{[\text{Products}]}{[\text{Reactants}]}$$ When \(Q_c > K_c\), it means that the concentration of the products is greater than their concentration at equilibrium. To reach equilibrium, the reaction needs to proceed in the reverse direction, converting some of the products back into reactants. This will decrease the product concentration and increase the reactant concentration until \(Q_c = K_c\).
02

(b) Calculating \(Q_c\) at the start of a reaction with only reactants present

At the beginning of a reaction, when only reactants are present and no products have been formed, the concentration of products is essentially zero. Therefore, using the definition of the reaction quotient, we have: $$Q_c = \frac{[\text{Products}]}{[\text{Reactants}]} = \frac{0}{[\text{Reactants}]} = 0$$ So, at the start of the reaction with only reactants present and no products formed, the value of \(Q_c\) is 0.

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Most popular questions from this chapter

The following equilibria were attained at \(298 \mathrm{~K}:\) $$\begin{array}{c} \mathrm{Ag}^{+}(a q)+\mathrm{Cl}^{-}(a q) \rightleftharpoons \mathrm{AgCl}(s) \quad K_{c}=5.6 \times 10^{9} \\ \mathrm{Ag}^{+}(a q)+2 \mathrm{NH}_{3}(a q) \rightleftharpoons\left[\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}\right]^{+}(a q) \\ K_{c}=1.6 \times 10^{7}\end{array}$$ Based on these equilibria, calculate the equilibrium constant $\text { for } \mathrm{AgCl}(s)+2 \mathrm{NH}_{3}(a q) \rightleftharpoons \mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}(a q)+\mathrm{Cl}^{-}(a q)$ at \(298 \mathrm{~K}\).

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?

Assume that the equilibrium constant for the dissociation of molecular bromine, \(\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{Br}(g)\), at 800 \(\mathrm{K}\) is \(K_{c}=5.4 \times 10^{-3}\). (a) Which species predominates at equilibrium, \(\mathrm{Br}_{2}\) or Br, assuming that the concentration of \(\mathrm{Br}_{2}\) is larger than $5.4 \times 10^{-3} \mathrm{~mol} / \mathrm{L} ?$ (b) Assuming both forward and reverse reactions are elementary processes, which reaction has the larger numeric value of the rate constant, the forward or the reverse reaction?

When \(2.00 \mathrm{~mol}\) of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) is placed in a 5.00 -Lflaskat \(310 \mathrm{~K}\), \(40 \%\) of the $\mathrm{SO}_{2} \mathrm{Cl}_{2}\( decomposes to \)\mathrm{SO}_{2}\( and \)\mathrm{Cl}_{2}$ : $$\mathrm{SO}_{2} \mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{SO}_{2}(g)+\mathrm{Cl}_{2}(g)$$ (a) Calculate \(K_{c}\) for this reaction at this temperature. (b) Calculate \(K_{P}\) for this reaction at \(310 \mathrm{~K}\). (c) According to Le Châtelier's principle, would the percent of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) that decomposes increase, decrease or stay the same if the mixture was transferred to a 1.00 -L vessel? (d) Use the equilibrium constant you calculated above to determine the percentage of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) that decomposes when 2.00 mol of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) is placed in a \(1.00-\mathrm{L}\) vessel at \(310 \mathrm{~K}\).

Which of the following statements are true and which are false? (a) For the reaction $2 \mathrm{~A}(g)+\mathrm{B}(g) \rightleftharpoons \mathrm{A}_{2} \mathrm{~B}(g) K_{c}$ and \(K_{p}\) are numerically the same. (b) It is possible to distinguish \(K_{c}\) from \(K_{p}\) by comparing the units used to express the equilibrium constant. \((\mathbf{c})\) For the equilibrium in (a), the value of \(K_{c}\) increases with increasing pressure.
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