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Chapter 15: Problem 27

Define reaction quotient. How does it differ from equilibrium constant?

Short Answer

Expert verified
The reaction quotient (\(Q_c\)) is the ratio of the concentrations of the products of a reaction to the concentrations of the reactants at any given moments during a reaction, each raised to their stoichiometrically appropriate powers. The equilibrium constant (\(K_c\)) is the value of \(Q_c\) when the reaction has reached equilibrium. The key difference between them is that \(Q_c\) can be calculated at any point during a reaction, while \(K_c\) is only calculated when the reaction has reached equilibrium.

Step by step solution

01

Definition of Reaction Quotient

The Reaction Quotient, \(Q_c\), for a reaction is a ratio that is equal to the concentrations of the products of a reaction, raised to the respective stoichiometric coefficients, divided by the concentrations of the reactants, also raised to their stoichiometric coefficients, at any given moments during a reaction. The subscript \(c\) indicates that the concentrations are used to define \(Q\). For a general reaction, \(aA + bB \rightarrow cC + dD\), the reaction quotient is given by: \(Q_c = \frac{[C]^c [D]^d}{[A]^a [B]^b}\)
02

Definition of Equilibrium Constant

The equilibrium constant is a special case of the reaction quotient. It is defined as the value of the reaction quotient when the reaction has reached equilibrium (when the forward and reverse reactions occur at the same rate, resulting in constant concentrations of reactants and products). The equilibrium constant, \(K_c\), is given by: \(K_c = \frac{[C]^c_{eq} [D]^d_{eq}}{[A]^a_{eq} [B]^b_{eq}}\)
03

Distinguishing between Reaction Quotient and Equilibrium Constant

While the reaction quotient and the equilibrium constant may seem similar in form, the key difference between them lies in when they are used. The reaction quotient can be calculated at any point during a reaction, while the equilibrium constant is calculated only when the reaction has reached equilibrium. Also, while the equilibrium constant \(K_c\) remains constant for a given reaction at a specific temperature, regardless of the initial concentrations of reactants and products, \(Q_c\) varies with the concentrations of reactants and products at any given point in time during the reaction.

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Most popular questions from this chapter

The equilibrium constant \(K_{\mathrm{c}}\) for the reaction $$ \mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}(g) $$ is 4.2 at \(1650^{\circ} \mathrm{C}\). Initially \(0.80 \mathrm{~mol} \mathrm{H}_{2}\) and \(0.80 \mathrm{~mol}\) \(\mathrm{CO}_{2}\) are injected into a \(5.0-\mathrm{L}\) flask. Calculate the concentration of each species at equilibrium.

The equilibrium constant \(K_{P}\) for the reaction $$ 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g) $$ is \(5.60 \times 10^{4}\) at \(350^{\circ} \mathrm{C} . \mathrm{SO}_{2}\) and \(\mathrm{O}_{2}\) are mixed initially at 0.350 atm and 0.762 atm, respectively, at \(350^{\circ} \mathrm{C}\). When the mixture equilibrates, is the total pressure less than or greater than the sum of the initial pressures, 1.112 atm?

Baking soda (sodium bicarbonate) undergoes thermal decomposition as $$ 2 \mathrm{NaHCO}_{3}(s) \rightleftharpoons \mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g) $$ Would we obtain more \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) by adding extra baking soda to the reaction mixture in (a) a closed vessel or (b) an open vessel?

The equilibrium constant \(K_{\mathrm{c}}\) for the reaction \(2 \mathrm{NH}_{3}(g) \rightleftharpoons \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g)\) is 0.83 at \(375^{\circ} \mathrm{C} . \mathrm{A}\) 14.6-g sample of ammonia is placed in a 4.00 -L flask and heated to \(375^{\circ} \mathrm{C}\). Calculate the concentrations of all the gases when equilibrium is reached.

A 2.50 -mol quantity of \(\mathrm{NOCl}\) was initially placed in a 1.50-L reaction chamber at \(400^{\circ} \mathrm{C}\). After equilibrium was established, it was found that 28.0 percent of the NOCl had dissociated: $$ 2 \mathrm{NOCl}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) $$ Calculate the equilibrium constant \(K_{c}\) for the reaction.
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