The decomposition of SO2 Cl2 described in Problem 13.53 has a first-order rate constant, k=2.2 ×

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The decomposition of SO2 Cl2 described in Problem 13.53 has...

The decomposition of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ described in Problem 13.53 has a first-order rate constant, $k=2.2 \times 10^{-5} \mathrm{~s}^{-1}$ at $320^{\circ} \mathrm{C}$. If the initial $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ concentration in a container is $0.0040 \mathrm{M}$, what will its concentration be (a) after 1.00 hour and $(\mathbf{b})$ after 1.00 day?

Key Concepts

First-Order Reaction Kinetics

A first-order reaction is one in which the reaction rate is directly proportional to the concentration of a single reactant. This means the rate at which the reactant is consumed decreases exponentially over time, with the proportionality constant k expressing the intrinsic rate of the process.

Integrated Rate Law for First-Order Reactions

The integrated rate law for a first-order reaction, given by ln([A]t/[A]0) = -kt, allows one to relate the concentration of the reactant at any time to its initial concentration, the rate constant, and the elapsed time. This law is essential for calculating the concentration of a reactant at a future point when the reaction follows first-order kinetics.

Exponential Decay

Exponential decay is a characteristic behavior of first-order processes, where the quantity being measured decreases at a rate proportional to its current value. In the context of chemical kinetics, this explains how the concentration of a reactant declines over time during a first-order reaction.

Time Unit Conversion in Kinetics

Accurate kinetic calculations require consistency in time units. Often, the rate constant is expressed in seconds, so when time is given in other units such as minutes or days, proper conversion is necessary to maintain the precision of the calculations and ensure the integrated rate law is applied correctly.

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