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Ch.15 - Chemical Equilibrium
All textbooksBrown 15th EditionCh.15 - Chemical EquilibriumProblem 95
Chapter 15, Problem 95

At 800 K, the equilibrium constant for the reaction A2(g) ⇌ 2 A(g) is Kc = 3.1 × 10-4. (d) If the temperature is raised to 1000 K, will the reverse rate constant kr increase or decrease? Will the change in kr be larger or smaller than the change in kf?

Verified step by step guidance
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Step 1: Understand the relationship between temperature and reaction rates. According to the Arrhenius equation, the rate constant k is related to temperature T by the equation k = Ae^(-Ea/RT), where A is the pre-exponential factor, Ea is the activation energy, and R is the gas constant.
Step 2: Analyze how an increase in temperature affects the rate constants. As temperature increases, the exponential factor in the Arrhenius equation increases, leading to an increase in the rate constant k for both the forward and reverse reactions.
Step 3: Consider the effect of temperature on the equilibrium constant Kc. The equilibrium constant is related to the rate constants by the equation Kc = kf/kr, where kf is the forward rate constant and kr is the reverse rate constant.
Step 4: Apply Le Chatelier's principle to predict the effect of temperature on the equilibrium position. If the reaction is endothermic, increasing the temperature will favor the forward reaction, increasing kf more than kr. If exothermic, the reverse is true.
Step 5: Conclude the effect on kr. If the reaction is endothermic, kr will increase, but the increase in kf will be larger, leading to an overall increase in Kc. If exothermic, kr will increase, but the increase in kf will be smaller, leading to a decrease in Kc.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Equilibrium Constant (Kc)

The equilibrium constant (Kc) is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. For the reaction A<sub>2</sub>(g) ⇌ 2 A(g), Kc indicates the extent to which the reaction favors the formation of products (A) over reactants (A<sub>2</sub>). A small Kc value, like 3.1 × 10<sup>-4</sup>, suggests that at equilibrium, the concentration of reactants is much higher than that of products.
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Rate Constants (kf and kr)

Rate constants (kf for the forward reaction and kr for the reverse reaction) are specific to the reaction and depend on temperature. They quantify the speed at which reactants are converted to products and vice versa. The relationship between the rate constants and the equilibrium constant is given by Kc = kf/kr, indicating that changes in temperature can affect both kf and kr, but not necessarily in the same proportion.
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Temperature Dependence of Reaction Rates

The rates of chemical reactions are generally temperature-dependent, often increasing with temperature due to higher kinetic energy of molecules. According to the Arrhenius equation, the rate constants kf and kr are influenced by temperature changes, which can lead to different effects on the forward and reverse reactions. Understanding this relationship helps predict whether kf or kr will increase or decrease with temperature changes, such as raising the temperature from 800 K to 1000 K.
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Related Practice
Textbook Question

Consider the hypothetical reaction A(𝑔) + 2 B(𝑔) ⇌ 2 C(𝑔), for which 𝐾𝑐 = 0.25 at a certain temperature. A 1.00-L reaction vessel is loaded with 1.00 mol of compound C, which is allowed to reach equilibrium. Let the variable x represent the number of mol/L of compound A present at equilibrium.

(d) The equation from part (c) is a cubic equation (one that has the form ax3 + bx2 + cx + d = 0). In general, cubic equations cannot be solved in closed form. However, you can estimate the solution by plotting the cubic equation in the allowed range of x that you specified in part (b). The point at which the cubic equation crosses the x-axis is the solution.

(e) From the plot in part (d), estimate the equilibrium concentrations of A, B, and C. (Hint: You can check the accuracy of your answer by substituting these concentrations into the equilibrium expression.)

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Textbook Question

At a temperature of 700 K, the forward and reverse rate constants for the reaction 2 HI(g) ⇌ H2(g) + I2(g) are kf = 1.8×10−30 M−1s−1 and kr = 0.063 M−1s−1.

(a) What is the value of the equilibrium constant Kc at 700 K?

(b) Is the forward reaction endothermic or exothermic if the rate constants for the same reaction have values of kf = 0.097M−1s−1 and kr = 2.6 M−1s−1 at 800 K?