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Ch.15 - Chemical Equilibrium
Chapter 15, Problem 141

Forward and reverse rate constants for the reaction CO2(g) + N2(g) ⇌ CO(g) + N2O(g) exhibit the following temperature dependence: Temperature (K), kf (M-1 s-1), kr (M-1 s-1): 1200 K: kf = 9.1 * 10^-11, kr = 1.5 * 10^5; 1300 K: kf = 2.7 * 10^-9, kr = 2.6 * 10^5. Is the reaction endothermic or exothermic? Explain in terms of kinetics.

Verified step by step guidance
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Step 1: Understand the relationship between temperature and reaction rates. In general, an increase in temperature will increase the rate constants for both the forward and reverse reactions due to increased molecular collisions.
Step 2: Calculate the equilibrium constant (K) at each temperature using the formula K = kf / kr, where kf is the forward rate constant and kr is the reverse rate constant.
Step 3: Compare the equilibrium constants at the two different temperatures. If the equilibrium constant increases with temperature, the reaction is endothermic. If it decreases, the reaction is exothermic.
Step 4: Analyze the change in equilibrium constant with temperature. An endothermic reaction absorbs heat, shifting the equilibrium towards the products as temperature increases, thus increasing K. Conversely, an exothermic reaction releases heat, shifting the equilibrium towards the reactants, thus decreasing K.
Step 5: Conclude whether the reaction is endothermic or exothermic based on the trend observed in the equilibrium constants calculated in Step 3.

Key Concepts

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

Rate Constants and Temperature Dependence

Rate constants (kf for the forward reaction and kr for the reverse reaction) are crucial in determining the speed of a chemical reaction. They are temperature-dependent, often described by the Arrhenius equation, which shows that as temperature increases, the rate constants typically increase. This relationship helps in understanding how reaction rates change with temperature, which is essential for analyzing the given data.
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Kw Temperature Dependence

Equilibrium and Reaction Direction

In a reversible reaction, the equilibrium position can shift based on the relative magnitudes of the forward and reverse rate constants. If kf is significantly smaller than kr, the reaction favors the products at equilibrium. Conversely, if kf increases relative to kr with temperature, it suggests that the reaction may favor the formation of products, indicating the nature of the reaction (endothermic or exothermic) based on energy changes.
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Equilibrium Constant K

Endothermic vs. Exothermic Reactions

Endothermic reactions absorb heat from the surroundings, leading to an increase in the rate of the forward reaction with temperature, while exothermic reactions release heat, often resulting in a decrease in the forward rate with increasing temperature. By analyzing the temperature dependence of the rate constants, one can infer the heat exchange associated with the reaction, thus determining whether it is endothermic or exothermic.
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Related Practice
Textbook Question
Which of the following relative values of kf and kr results in an equilibrium mixture that contains large amounts of reactants and small amounts of products? (a) kf 7 kr (b) kf = kr (c) kf 6 kr
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Textbook Question
Consider the reaction of chloromethane with OH- in aque- ous solution: CH Cl1aq2 + OH-1aq2 ∆kf CH OH1aq2 + Cl-1aq2 At 25 °C, the rate constant for the forward reaction is 6 * 10-6 M-1 s-1, and the equilibrium constant Kc is 1 * 1016. Calculate the rate constant for the reverse reac- tion at 25 °C.
Textbook Question
In automobile catalytic converters, the air pollutant nitric oxide is converted to nitrogen and oxygen. Listed in the table are forward and reverse rate constants for the reac- tion 2 NO1g2 ∆ N21g2 + O21g2. Temperature (K) kf1M — 1 s-12 kr1M-1 s — 121400 0.29 1.1 * 10-61500 1.3 1.4 * 10-5Is the reaction endothermic or exothermic? Explain in terms of kinetics.
Textbook Question
Given the Arrhenius equation, k = Ae-Ea>RT, and the rela- tion between the equilibrium constant and the forward and reverse rate constants, Kc = kf>kr, explain why Kc for an exothermic reaction decreases with increasing temperature.
Textbook Question
Vinegar contains acetic acid, a weak acid that is partially dissociated in aqueous solution:CH3CO2H1aq2 ∆ H+ 1aq2 + CH3CO-1aq2 (b) What is the value of Kc if the extent of dissociation in1.0 M CH3CO2H is 0.42%?
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Textbook Question
Heavy water, symbolized D2O 1D = 2H2 finds use as a neutron moderator in nuclear reactors. In a mixture with ordinary water, exchange of isotopes occurs according to the following equation: H2O + D2O ∆ 2 HDO Kc = 3.86 at 298 K When 1.00 mol of H2O is combined with 1.00 mol of D2O, what are the equilibrium amounts of H2O, D2O, and HDO (in moles) at 298 K? Assume the density of the mixture is constant at 1.05 g>cm3.
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