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?

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Step 1: Understand that the problem is asking for the time it will take for the partial pressure of SO2Cl2 to decline to one-tenth its initial value. This is a first-order reaction, which means the rate of the reaction depends on the concentration of one reactant. The rate constant for the reaction is given.

Step 2: Recall the first-order reaction formula, which is ln([A]0/[A]) = kt, where [A]0 is the initial concentration, [A] is the final concentration, k is the rate constant, and t is the time.

Step 3: In this case, we are looking for the time when the concentration of SO2Cl2 is one-tenth its initial value. So, [A]0/[A] = 10. Substitute this into the first-order reaction formula: ln(10) = kt.

Step 4: We know the rate constant k is 4.5 * 10^-2 s^-1. Substitute this into the equation: ln(10) = (4.5 * 10^-2 s^-1) * t.

Step 5: Solve the equation for t to find the time it will take for the partial pressure of SO2Cl2 to decline to one-tenth its initial value.

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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 processes where the rate of reaction is directly proportional to the concentration of one reactant. This means that as the concentration decreases, the rate of reaction also decreases. The mathematical representation involves a natural logarithm, allowing for the calculation of time required for a specific change in concentration.

Rate Constant (k)

The rate constant (k) is a proportionality factor in the rate equation that is specific to a given reaction at a particular temperature. For first-order reactions, the rate constant has units of s^-1 and indicates how quickly the reaction proceeds. A higher rate constant signifies a faster reaction, which is crucial for determining the time it takes for the concentration to change.

Half-Life and Time Calculations

In first-order reactions, the half-life is the time required for the concentration of a reactant to decrease to half its initial value and remains constant regardless of concentration. To find the time for a reactant to decline to a specific fraction of its initial value, such as one-tenth, one can use the integrated rate law, which relates concentration and time, allowing for precise calculations.

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First-Order Half-Life

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Textbook Question

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

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

The first-order rate constant for the decomposition of N₂O₅, 2 N₂O₅(g) → 4 NO₂(g) + O₂(g), at 70°C is 6.82×10^-3 s^-1. Suppose we start with 0.0250 mol of N₂O₅(g) in a volume of 2.0 L. (a) How many moles of N₂O₅ will remain after 5.0 min?

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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. (b) At what time will the partial pressure of SO2Cl2 decline to one-tenth its initial value?

Verified video answer for a similar problem:

Key Concepts

First-Order Reactions

Rate Constant (k)

Half-Life and Time Calculations

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?