The decomposition of SO2 Cl2 is a first-order reaction: SO2 Cl2(g) ⟶SO2(g)+Cl2(g) The rate const

step 1 So we're told for this reaction that this is first order. And so in order to solve something lik

The decomposition of SO2 Cl2 is a first-order reaction: SO2...

The decomposition of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ is a first-order reaction: $$\mathrm{SO}_{2} \mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow \mathrm{SO}_{2}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g})$$ The rate constant for the reaction is $2.8 \times 10^{-3} \mathrm{min}^{-1}$ at $600 \mathrm{K} .$ If the initial concentration of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ is $1.24 \times 10^{-3}$ mol/L, how long will it take for the concentration to drop to $0.31 \times 10^{-3} \mathrm{mol} / \mathrm{L} ?$

The decomposition of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ is a first-order reaction:
$$\mathrm{SO}_{2} \mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow \mathrm{SO}_{2}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g})$$
The rate constant for the reaction is $2.8 \times 10^{-3} \mathrm{min}^{-1}$ at $600 \mathrm{K} .$ If the initial concentration of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ is $1.24 \times 10^{-3}$ mol/L, how long will it take for the concentration to drop to $0.31 \times 10^{-3} \mathrm{mol} / \mathrm{L} ?$

Key Concepts

First-Order Reaction

A first-order reaction is one whose rate is directly proportional to the concentration of a single reactant. This means that as the concentration changes, the reaction rate changes linearly, and the time taken for the reaction to progress depends on the intrinsic rate constant of the reaction.

Integrated Rate Law

The integrated rate law for a first-order reaction relates the concentration of the reactant to time through an exponential decay function. It is expressed mathematically as ln([A]_0/[A]) = kt, where [A]_0 is the initial concentration, [A] is the concentration at time t, and k is the rate constant. This equation allows for direct calculation of time based on concentration changes.

Rate Constant

The rate constant in kinetics is a proportionality factor that quantifies the speed of a reaction under given conditions. In a first-order reaction, it is expressed in inverse time units and is a critical parameter in the integrated rate law, determining how quickly the concentration of the reactant decreases.

Logarithmic Analysis

Logarithmic analysis in reaction kinetics involves using natural logarithms to linearize the exponential decay of reactant concentration over time. This approach simplifies the process of solving for variables such as time or rate constant in the integrated rate law, making it an essential tool for understanding and predicting reaction behavior.

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