Cyclopropane, C3 H6, is a gas used as a general anesthetic....

Cyclopropane, $\mathrm{C}_{3} \mathrm{H}_{6}$, is a gas used as a general anesthetic. It undergoes a slow molecular rearrangement to propylene. At a certain temperature, the following data were obtained relating concentration and rate: $$\begin{array}{cc}\text { Initial Concentration of } & \text { Initial Rate of Formation } \\\text { Cyclopropane }\left(\mathrm{mol} \mathrm{L}^{-1}\right) & \text {of Propylene }\left(\mathrm{mol} \mathrm{L}^{-1} \mathrm{~s}^{-1}\right) \\0.050 & 2.95 \times 10^{-5} \\0.100 & 5.90 \times 10^{-5} \\0.150 & 8.85 \times 10^{-5}\end{array}$$ What is the rate law for the reaction? What is the value of the rate constant, with correct units?

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Key Concepts

Rate Constant Units

The units of the rate constant (k) depend on the overall reaction order to ensure that the rate has consistent units (typically mol L^-1 s^-1). For a first?order reaction, k has units of s^-1, while for a second-order reaction, k typically has units of L mol^-1 s^-1.

Initial Rate Method

The initial rate method involves measuring the rate of reaction at the very beginning when concentrations are known and comparing changes in rate as the initial concentration of a reactant is varied. This is a common approach to deducing the reaction order by isolating the effect of one reactant at a time.

Rate Law

The rate law is an equation that relates the rate of a chemical reaction to the concentration of its reactants, typically written as rate = k[Reactant1]^m[Reactant2]^n. It summarizes how the concentration of each species influences the overall reaction rate and includes the rate constant k.

Reaction Order

The reaction order defines how the rate of reaction depends on the concentration(s) of reactants. It is determined by the exponent applied to the concentration in the rate law. In experiments, observing a proportional change in rate with the change in concentration often indicates the reaction order with respect to that reactant.

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