The decomposition of SO2 Cl2 is first order in SO2 Cl2 and has a rate constant of 1.42 ×10^-4 s^

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The decomposition of SO2 Cl2 is first order in SO2 Cl2 and...

The decomposition of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ is first order in $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ and has a rate constant of $1.42 \times 10^{-4} \mathrm{s}^{-1}$ at a certain temperature. \begin{equation}\begin{array}{l}{\text { a. What is the half-life for this reaction? }} \\ {\text { b. How long will it take for the concentration of } S \mathrm{O}_{2} \mathrm{Cl}_{2} \text { to }} \\ {\text { decrease to } 25 \% \text { of its initial concentration? }}\\{\text { c. If the initial concentration of } \mathrm{SO}_{2} \mathrm{Cl}_{2} \text { is } 1.00 \mathrm{M}, \text { how long will }} \\ {\text { it take for the concentration to decrease to } 0.78 \mathrm{M} ?}\\{\text { d. If the initial concentration of } \mathrm{SO}_{2} \mathrm{Cl}_{2} \text { is } 0.150 \mathrm{M}, \text { what is }} \\ {\text { the concentration of } \mathrm{SO}_{2} \mathrm{Cl}_{2} \text { after } 2.00 \times 10^{2} \mathrm{s} ? \text { After }} \\ {5.00 \times 10^{2} \mathrm{s} ?}\end{array}\end{equation}

The decomposition of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ is first order in $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ and has a rate constant of $1.42 \times 10^{-4} \mathrm{s}^{-1}$ at a certain temperature.
\begin{equation}\begin{array}{l}{\text { a. What is the half-life for this reaction? }} \\ {\text { b. How long will it take for the concentration of } S \mathrm{O}_{2} \mathrm{Cl}_{2} \text { to }} \\ {\text { decrease to } 25 \% \text { of its initial concentration? }}\\{\text { c. If the initial concentration of } \mathrm{SO}_{2} \mathrm{Cl}_{2} \text { is } 1.00 \mathrm{M}, \text { how long will }} \\ {\text { it take for the concentration to decrease to } 0.78 \mathrm{M} ?}\\{\text { d. If the initial concentration of } \mathrm{SO}_{2} \mathrm{Cl}_{2} \text { is } 0.150 \mathrm{M}, \text { what is }} \\ {\text { the concentration of } \mathrm{SO}_{2} \mathrm{Cl}_{2} \text { after } 2.00 \times 10^{2} \mathrm{s} ? \text { After }} \\ {5.00 \times 10^{2} \mathrm{s} ?}\end{array}\end{equation}

Key Concepts

Integrated Rate Law

The integrated rate law for a first order reaction relates the concentration of the reactant to time. It is given by ln([A]/[A]?) = -kt, where [A]? is the initial concentration, [A] is the concentration at time t, and k is the rate constant. This equation is commonly used to calculate the time required for the concentration to drop to a certain level or to find the concentration at a given time.

Exponential Decay

Exponential decay describes the process by which the concentration of a reactant decreases over time in a predictable manner according to the exponential function. In the context of first order kinetics, the decay follows an exponential pattern, reflecting that the rate at which the concentration decreases is proportional to the current concentration. This concept is directly related to the integrated rate law for first order reactions.

First Order Kinetics

First order kinetics refers to a reaction in which the rate of reaction is directly proportional to the concentration of a single reactant raised to the first power. This means that if the reactant concentration is doubled, the rate of the reaction will also double. In mathematical terms, the rate law can be written as Rate = k[A].

Half-Life

The half-life of a reaction is the time required for the concentration of a reactant to decrease to half of its initial value. In first order reactions, the half-life is constant and is independent of the initial concentration. It can be calculated using the formula t1/2 = 0.693/k, where k is the rate constant.

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