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Chapter 14: Problem 68

What are the units of the rate constant for a thirdorder reaction?

Short Answer

Expert verified
The units of the rate constant for a thirdorder reaction are \(M^{-2}T^{-1}\).

Step by step solution

01

Understanding reaction rates

Reaction rate can also be expressed in terms of the decrease in the concentration of one of the reactants or the increase in the concentration of one of the products during a unit of time.
02

Expressing reaction rates in terms of reactant concentration and rate constant

The rate of reaction can be expressed as the change in molar concentration of the reactant in a unit time and mathematically, Rate = \(-\frac{d[\text{{Reactant}}]}{dt}\) where \([\text{{Reactant}}]\) is the molar concentration of the reactant. For a third order reaction, Rate = \(k[\text{{Reactant}}]^3\) where k is the rate constant.
03

Determining units of the third order rate constant

From the equation in Step 2, we infer that the dimensions of the rate constant 'k' can be determined by using the dimensional analysis. The dimension of 'Rate' is \([M T^{-1}]\), 'M' being the molar concentration and 'T' being the time. So, the unit of 'k' for third order reactions should be \(M^{-2}T^{-1}\)

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Most popular questions from this chapter

What are the units of the rate of a reaction?

The rate constant of a first-order reaction is \(66 \mathrm{~s}^{-1}\) What is the rate constant in units of minutes?

Explain why termolecular reactions are rare.

The bromination of acetone is acid-catalyzed: \(\mathrm{CH}_{3} \mathrm{COCH}_{3}+\mathrm{Br}_{2} \frac{\mathrm{H}^{+}}{\text {catalyst }} \mathrm{CH}_{3} \mathrm{COCH}_{2} \mathrm{Br}+\mathrm{H}^{+}+\mathrm{Br}\) The rate of disappearance of bromine was measured for several different concentrations of acetone, bromine, and \(\mathrm{H}^{+}\) ions at a certain temperature: $$ \begin{array}{lcllc} & & & & {\text { Rate of }} \\ & & & & \text { Disappearance } \\ & {\left[\mathrm{CH}_{3} \mathrm{COCH}_{3}\right]} & {\left[\mathrm{Br}_{2}\right]} & {\left[\mathrm{H}^{+}\right]} & \text {of } \mathrm{Br}_{2}(\mathrm{M} / \mathrm{s}) \\ \hline \text { (a) } & 0.30 & 0.050 & 0.050 & 5.7 \times 10^{-5} \\ \text {(b) } & 0.30 & 0.10 & 0.050 & 5.7 \times 10^{-5} \\ \text {(c) } & 0.30 & 0.050 & 0.10 & 1.2 \times 10^{-4} \\ \text {(d) } & 0.40 & 0.050 & 0.20 & 3.1 \times 10^{-4} \\ \text {(e) } & 0.40 & 0.050 & 0.050 & 7.6 \times 10^{-5} \end{array} $$ (a) What is the rate law for the reaction? (b) Determine the rate constant.

Consider the following elementary steps for a consecutive reaction $$ \mathrm{A} \stackrel{k_{1}}{\longrightarrow} \mathrm{B} \stackrel{k_{2}}{\longrightarrow} \mathrm{C} $$ (a) Write an expression for the rate of change of \(\mathrm{B}\). (b) Derive an expression for the concentration of \(\mathrm{B}\) under steady- state conditions; that is, when \(\mathrm{B}\) is decomposing to \(\mathrm{C}\) at the same rate as it is formed from \(\mathrm{A}\).
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