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Problem: 03-02-2

Question

The rate law for a particular reaction is rate =k[\mathrm{XY}]^2. In an experiment, the initial rate of the reaction is determined to be 0.16 \mathrm{~mol} /(\mathrm{L} \cdot \mathrm{s}) when the initial concentration of \mathrm{XY} is 0.40 \mathrm{~mol} / \mathrm{L}.

  • What is the value of the rate constant, k, for the reaction?
    • 0.10 \mathrm{~L} /(\mathrm{mol} \cdot \mathrm{s})
    • 0.40 \mathrm{~L} /(\mathrm{mol} \cdot \mathrm{s})
    • 1.0 \mathrm{~L} /(\mathrm{mol} \cdot \mathrm{s})
    • 2.5 \mathrm{~L} /(\mathrm{mol} \cdot \mathrm{s})

Solution

lo tind the value of the rate constant for the reaction, let's first solve the rate law for k :


k=\frac{\text { rate }}{[\mathrm{XY}]^2}

Next, let's plug in the initial rate and concentration given in the text:


\begin{aligned}
k & =\frac{0.16 \mathrm{~mol} /(\mathrm{L} \cdot \mathrm{s})}{(0.40 \mathrm{~mol} / \mathrm{L})^2} \\
& =\frac{0.16 \mathrm{~mol} /(\mathrm{L} \cdot \mathrm{s})}{0.16 \mathrm{~mol}^2 / \mathrm{L}^2} \\
& =1.0 \mathrm{~L} /(\mathrm{mol} \cdot \mathrm{s})
\end{aligned}

So, the value of the rate constant for the reaction is 1.0 \mathrm{~L} /(\mathrm{mol} \cdot \mathrm{s})