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Ch.16 - Acid-Base Equilibria
All textbooksBrown 14th EditionCh.16 - Acid-Base EquilibriaProblem 125
Chapter 16, Problem 125

The iodate ion is reduced by sulfite according to the following reaction: IO3^- (aq) + 3 SO3^2- (aq) -> I^- (aq) + 3 SO4^2- (aq). The rate of this reaction is found to be first order in IO3^-, first order in SO3^2-, and first order in H+. (b) By what factor will the rate of the reaction change if the pH is lowered from 5.00 to 3.50? Does the reaction proceed more quickly or more slowly at the lower pH? (c) By using the concepts discussed in Section 14.6, explain how the reaction can be pH-dependent even though H+ does not appear in the overall reaction.

Verified step by step guidance
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Step 1: Understand the rate law for the reaction. Since the reaction is first order in IO3^-, first order in SO3^2-, and first order in H+, the rate law can be expressed as: rate = k[IO3^-][SO3^2-][H+].
Step 2: Determine the change in [H+] when the pH changes. Use the formula [H+] = 10^(-pH) to calculate the hydrogen ion concentration at pH 5.00 and pH 3.50.
Step 3: Calculate the factor by which [H+] changes. Divide the [H+] at pH 3.50 by the [H+] at pH 5.00 to find the factor by which the concentration of H+ increases.
Step 4: Relate the change in [H+] to the change in reaction rate. Since the reaction is first order in H+, the rate of the reaction will change by the same factor as the change in [H+].
Step 5: Explain the pH-dependence of the reaction. Even though H+ does not appear in the overall reaction, it affects the rate because it is part of the rate law. This suggests that H+ is involved in the mechanism of the reaction, possibly in a fast pre-equilibrium step or as a catalyst.

Key Concepts

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

Reaction Order

Reaction order refers to the power to which the concentration of a reactant is raised in the rate law of a chemical reaction. In this case, the reaction is first order in IO3^-, SO3^2-, and H+, meaning that the rate of reaction is directly proportional to the concentration of each of these species. Understanding reaction order is crucial for predicting how changes in concentration affect the reaction rate.
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pH and Hydrogen Ion Concentration

pH is a measure of the hydrogen ion concentration in a solution, with lower pH values indicating higher concentrations of H+. In this reaction, lowering the pH from 5.00 to 3.50 increases the concentration of H+, which is first order in the rate law. This change can significantly affect the reaction rate, as the presence of H+ can influence the reaction mechanism even if it does not appear in the overall balanced equation.
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pH-Dependent Reaction Mechanism

A pH-dependent reaction mechanism indicates that the rate of a reaction can be influenced by the concentration of H+ ions, even if H+ does not appear in the overall stoichiometry. This can occur if H+ participates in an intermediate step or alters the stability of reactants or products. Understanding this concept helps explain why the reaction rate can change with pH, highlighting the importance of reaction pathways in determining kinetics.
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Related Practice
Textbook Question

At 50 °C, the ion-product constant for H2O has the value Kw = 5.48 * 10-14. (a) What is the pH of pure water at 50 °C? (b) Based on the change in Kw with temperature, predict whether ΔH is positive, negative, or zero for the autoionization reaction of water: 2 H2O1l2 Δ H3O+1aq2 + OH-1aq2

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Textbook Question
Using dissociation constants from Appendix D, determine the value for the equilibrium constant for each of the following reactions.(i) HCO3-1aq2 + OH-1aq2 ΔCO32-1aq2 + H2O1l2(ii) NH4+1aq2 + CO32-1aq2 ΔNH31aq2 + HCO3-1aq2
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