Chemistry

Problem

In a kinetics lecture, a generalized relationship between the overall reaction order

n

and the units of the rate constant

k

(assuming rate is measured in

\text{mol}\,\text{L}^{-1}\,\text{s}^{-1}

) was stated without proof. (a) Starting from the definition of reaction rate, derive an expression that gives the units of

k

explicitly as a function of

n

. (b) Use your derived expression to predict the units of

k

for a hypothetical one-half-order reaction. (c) A researcher reports a rate constant value of

k=3.1\times10^{-5}\;\text{mol}^{3/2}\,\text{L}^{-3/2}\,\text{s}^{-1}

. Based on your result from part (b), evaluate whether the researcher’s units are self-consistent for a one-half-order reaction. Provide quantitative reasoning. (a) Derive the general unit expression for

k

as a function of overall order

n

. (b) Apply the expression to predict units for a one-half-order reaction. (c) Evaluate the consistency of the reported units for

k

with

n=\tfrac12

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