(a) The gas-phase decomposition of SO 2 Cl 2 , SO 2 Cl 2 (g) → SO 2 (g) + Cl 2 (g), is first order in SO 2 Cl 2 . At 600 K the half-life for this process is 2.3 × 10 5 s. What is the rate constant at this temperature?

Hello everyone. Today, we have the following problem. The thermal cracking of ethane is a first order process and has a half life of 2.11 times 10 to the negative second seconds at 900 degrees Celsius, determine the rate constant at 900 degrees Celsius. So first, what we wanna do is you wanna draw the equation for half life. The equation for half life is going to be the natural log of two divided by some constant K. And so what we wanna do is they want to rearrange this equation. And so that we're solving for K in that K is going to be equal to the natural log of two divided by our half life simply plugging in the values that we have from the problem. We have the natural log if two can be divided by the half life, which was given to us in the question stem as 2.11 times 10 to the negative second seconds. When we plug this into our calculator, this is going to give us a rate constant of 32.9 seconds raised to the -1. And with that, we have the answer to our problem overall, I hope this helped and until next time.

Ch.14 - Chemical Kinetics

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Brown 15th Edition

Ch.14 - Chemical Kinetics

Problem 41a

Chapter 14, Problem 41a

(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?

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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Equilibrium Constant K

Related Practice

Textbook Question

Consider the reaction of peroxydisulfate ion (S₂O₈^2-) with iodide ion (I^-) in aqueous solution:

S₂O₈^2-(aq) + 3 I^-(aq) → 2 SO₄^2-(aq) + I₃^-(aq)

At a particular temperature, the initial rate of disappearance of S₂O₈^2- varies with reactant concentrations in the following manner:

Experiment [S₂O₈^2-] (M) [I^-] (M) Initial Rate (M/s)

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.

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

(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?

(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?

Verified video answer for a similar problem:

Key Concepts

First-Order Reactions

Half-Life of a Reaction

Rate Constant (k)

(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?