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Ch.14 - Chemical Kinetics
All textbooksBrown 15th EditionCh.14 - Chemical KineticsProblem 41b
Chapter 14, Problem 41b

(b) At 320°C the rate constant is 2.2 × 10-5 s-1. What is the half-life at this temperature?

Verified step by step guidance
1
Identify the type of reaction. Since the rate constant is given in s-1, this suggests a first-order reaction.
Recall the formula for the half-life of a first-order reaction: t1/2=0.693k, where k is the rate constant.
Substitute the given rate constant value into the formula: t1/2=0.6932.2×10-5.
Perform the division to calculate the half-life: divide 0.693 by the rate constant value.
The result from the division will give you the half-life of the reaction at 320°C.

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Key Concepts

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

Rate Constant

The rate constant (k) is a proportionality factor in the rate equation of a chemical reaction, indicating the speed of the reaction at a given temperature. It is specific to the reaction and varies with temperature, reflecting how the frequency of effective collisions between reactants changes. In this case, the rate constant is given as 2.2 × 10<sup>-5</sup> s<sup>-1</sup>, which is essential for calculating the half-life.
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Rate Constant Units

Half-Life

Half-life 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 inversely proportional to the rate constant, allowing for straightforward calculations. The formula for half-life (t<sub>1/2</sub>) in first-order kinetics is t<sub>1/2</sub> = 0.693/k, where k is the rate constant.
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Zero-Order Half-life

First-Order Kinetics

First-order kinetics describes a reaction where the rate is directly proportional to the concentration of one reactant. This means that as the concentration decreases, the rate of reaction also decreases. The relationship between the rate constant and half-life in first-order reactions simplifies calculations, making it easier to determine how long it takes for a substance to reduce to half its amount.
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Related Practice
Textbook Question

(a) For the generic reaction A → B what quantity, when graphed versus time, will yield a straight line for a first-order reaction?

Textbook Question

(b) How can you calculate the rate constant for a first-order reaction from the graph you made in part (a)?

Textbook Question

(a) The gas-phase decomposition of SO2Cl2, SO2Cl2(g) → SO2(g) + Cl2(g), 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?

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Textbook Question

As described in Exercise 14.41, the decomposition of sulfuryl chloride (SO2Cl2) is a first-order process. The rate constant for the decomposition at 660 K is 4.5 × 10-2 s-1. (a) If we begin with an initial SO2Cl2 pressure of 450 torr, what is the partial pressure of this substance after 60 s?

Textbook Question

As described in Exercise 14.41, the decomposition of sulfuryl chloride (SO2Cl2) 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?