SO2 Cl2 decomposes in a first-order process with a half life of 4.88 ×10^3 s. If the original c

step 1 So here we're given an example of a first order reaction. And first order reactions, as we know,

SO2 Cl2 decomposes in a first-order process with a half life...

$\mathrm{SO}_{2} \mathrm{Cl}_{2}$ decomposes in a first-order process with a half life of $4.88 \times 10^{3} \mathrm{~s}$. If the original concentration of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ is $0.012 \mathrm{M}$, how many seconds will it take for the $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ to reach $0.0020 \mathrm{M}$ ?

Key Concepts

First_Order_Kinetics

This concept refers to reactions whose rate is directly proportional to the concentration of one reactant. The reaction follows an exponential decay pattern, meaning that the amount of reactant decreases at a rate proportional to its current value.

Half_Life

The half-life of a reaction is defined as the time required for the concentration of a reactant to fall to half of its initial value. In first-order kinetics, this value is constant and independent of the starting concentration, and it is related to the rate constant.

Integrated_Rate_Law

The integrated rate law for a first-order reaction relates the concentrations of the reactant at two different times using the formula ln([A]?/[A]) = kt. This equation is key for determining the elapsed time or the rate constant when the initial and final concentrations are known.

Exponential_Decay

Exponential decay describes a process where the quantity decreases at a rate that is directly proportional to its current value. In the context of first-order reactions, this concept underlies the mathematical modeling of reactant concentration over time.

Natural_Logarithm

The natural logarithm is used to linearize the exponential decay equation found in first-order kinetics. By taking the logarithm of concentration ratios, the integrated rate law becomes linear in time, facilitating the calculation of reaction kinetics parameters.

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