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

step 1 In this question, we know the decomposition of SO2 CL2 is first order, and we are provided the r

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. a. What is the half-life for this reaction? b. How long will it take for the concentration of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ to decrease to $25 \%$ of its initial concentration? c. If the initial concentration of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ is $1.00 \mathrm{M}$, how long will it take for the concentration to decrease to $0.78 \mathrm{M} ?$ d. If the initial concentration of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ is $0.150 \mathrm{M},$ what is the concentration of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ after $2.00 \times 10^{2} \mathrm{~s}$ ? After $5.00 \times 10^{2} \mathrm{~s} ?$

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.
a. What is the half-life for this reaction?
b. How long will it take for the concentration of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ to decrease to $25 \%$ of its initial concentration?
c. If the initial concentration of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ is $1.00 \mathrm{M}$, how long will it take for the concentration to decrease to $0.78 \mathrm{M} ?$
d. If the initial concentration of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ is $0.150 \mathrm{M},$ what is the concentration of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ after $2.00 \times 10^{2} \mathrm{~s}$ ? After $5.00 \times 10^{2} \mathrm{~s} ?$

Key Concepts

First-Order Kinetics

In first-order kinetics, the rate of a chemical reaction is directly proportional to the concentration of one reactant. This means that the rate law has the form rate = k[A], where k is the rate constant and [A] is the concentration of the reactant. Such reactions exhibit exponential decay of reactant concentration over time.

Half-Life in First-Order Reactions

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

Integrated Rate Law

The integrated rate law for a first-order reaction provides a relationship between the concentration of the reactant and time. It is expressed as ln([A]_t/[A]_0) = -kt, where [A]_0 is the initial concentration, [A]_t is the concentration at time t, and k is the rate constant. This equation allows for the determination of reactant concentration at any time or the time required to reach a certain conversion.

Exponential Decay

Exponential decay describes the behavior of first-order reactions where the reactant concentration decreases exponentially over time. This concept is mathematically characterized by the exponential function derived from the integrated rate law, reflecting the continuous decrease of the reactant as a function of time.

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