Ch.14 - Chemical Kinetics

Problem 41a

Chapter 14, Problem 41a

(a) The gas-phase decomposition of SO2Cl2, SO2Cl21g2 ¡SO21g2 + Cl21g2, is first order in SO2Cl2. At 600 K the half-life for this process is 2.3 * 105 s. What is the rate constant at this temperature?

Verified step by step guidance

Step 1: Understand the problem. We are given that the reaction is first order and we are given the half-life. We need to find the rate constant (k).

Step 2: Recall the formula for the rate constant in a first order reaction. The formula is k = ln(2) / t1/2, where t1/2 is the half-life of the reaction.

Step 3: Substitute the given half-life into the formula. The half-life is given as 2.3 * 10^5 s.

Step 4: Calculate the rate constant. Remember that ln(2) is approximately 0.693.

Step 5: The rate constant k is then the result of the calculation from step 4. This is the final answer.

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Key Concepts

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

First-Order Reactions

First-order reactions are chemical reactions where the rate is directly proportional to the concentration of one reactant. This means that as the concentration of the reactant decreases, the rate of the reaction also decreases. The rate law for a first-order reaction can be expressed as rate = k[A], where k is the rate constant and [A] is the concentration of the reactant.

Half-Life of a Reaction

The half-life of a reaction is the time required for the concentration of a reactant to decrease to half of its initial value. For first-order reactions, the half-life is constant and independent of the initial concentration, calculated using the formula t1/2 = 0.693/k, where k is the rate constant. This relationship is crucial for determining the rate constant from the given half-life.

Rate Constant (k)

The rate constant (k) is a proportionality factor in the rate law that quantifies the speed of a reaction at a given temperature. It is specific to each reaction and varies with temperature. For first-order reactions, the rate constant can be derived from the half-life using the equation k = 0.693/t1/2, allowing us to calculate k when the half-life is known.

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Consider the reaction of peroxydisulfate ion 1S2O82-2 with iodide ion 1I - 2 in aqueous solution: S2O8 2 - 1aq2 + 3 I - 1aq2¡2 SO42 - 1aq2 + I3- 1aq2 At a particular temperature, the initial rate of disappearance of S2O82 - varies with reactant concentrations in the following manner: Experiment 3S2o8 24 1M 2 3I4 1M 2 Initial Rate 1M,s2 1 0.018 0.036 2.6 * 10-6 2 0.027 0.036 3.9 * 10-6 3 0.036 0.054 7.8 * 10-6 4 0.050 0.072 1.4 * 10-5 (a) Determine the rate law for the reaction and state the units of the rate constant.

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Open Question

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As described in Exercise 14.41, the decomposition of sulfuryl chloride 1SO2Cl22 is a first-order process. The rate constant for the decomposition at 660 K is 4.5 * 10-2 s-1. (b) At what time will the partial pressure of SO2Cl2 decline to one-tenth its initial value?

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