At a temperature of 700 K, the forward and reverse rate constants for the reaction 2 HI(g) ⇌ H₂(g) + I₂(g) are k_f = 1.8×10⁻³⁰ M⁻¹s⁻¹ and k_r = 0.063 M⁻¹s⁻¹.
(a) What is the value of the equilibrium constant K_c at 700 K?
(b) Is the forward reaction endothermic or exothermic if the rate constants for the same reaction have values of k_f= 0.097M⁻¹s⁻¹ and k_r= 2.6 M⁻¹s⁻¹ at 800 K?

Verified step by step guidance

First, recall that the equilibrium constant (K) for a reaction is given by the ratio of the forward rate constant (kf) to the reverse rate constant (kr). So, K = kf/kr.

Calculate the equilibrium constant at 700 K using the given rate constants. K1 = kf1/kr1.

Next, calculate the equilibrium constant at 800 K using the given rate constants. K2 = kf2/kr2.

Compare the two equilibrium constants. If K2 > K1, the reaction shifts to the right (towards the products) as the temperature increases, indicating that the reaction is endothermic. If K2 < K1, the reaction shifts to the left (towards the reactants) as the temperature increases, indicating that the reaction is exothermic.

Remember, an endothermic reaction absorbs heat from its surroundings (ΔH > 0), while an exothermic reaction releases heat to its surroundings (ΔH < 0).

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Key Concepts

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

Rate Constants and Temperature

Rate constants (k) are values that indicate the speed of a reaction at a given temperature. They are influenced by temperature changes, typically increasing with higher temperatures due to increased molecular energy and collision frequency. Understanding how rate constants vary with temperature is crucial for analyzing reaction kinetics and determining the nature of the reaction.

Equilibrium and Le Chatelier's Principle

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products. Le Chatelier's Principle states that if a system at equilibrium is disturbed, it will shift in a direction that counteracts the disturbance. This principle helps predict how changes in temperature or concentration affect the position of equilibrium.

Endothermic vs. Exothermic Reactions

Endothermic reactions absorb heat from their surroundings, leading to a decrease in temperature, while exothermic reactions release heat, increasing the temperature. The nature of a reaction can be inferred from the temperature dependence of the rate constants; if increasing temperature increases the rate of the endothermic forward reaction more than the reverse, it suggests the forward reaction is endothermic.

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Endothermic & Exothermic Reactions

Related Practice

Textbook Question

At 700 K, the equilibrium constant for the reaction CCl₄(𝑔) ⇌ C(𝑠) + 2 Cl₂(𝑔) is 𝐾_𝑝= 0.76. A flask is charged with 2.00 atm of CCl₄, which then reaches equilibrium at 700 K. (b) What are the partial pressures of CCl₄ and Cl₂ at equilibrium?

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Textbook Question

Consider the hypothetical reaction A(𝑔) + 2 B(𝑔) ⇌ 2 C(𝑔), for which 𝐾_𝑐= 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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