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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

Many reactions involving heterogeneous catalysts are zero order; that is, rate \(=k\). An example is the decomposition of phosphine \(\left(\mathrm{PH}_{3}\right)\) over tungsten (W): $$ 4 \mathrm{PH}_{3}(g) \longrightarrow \mathrm{P}_{4}(g)+6 \mathrm{H}_{2}(g) $$ It is found that the reaction is independent of \(\left[\mathrm{PH}_{3}\right]\) as long as phosphine's pressure is sufficiently high \((\geq 1 \mathrm{~atm}) .\) Explain.

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?

Consider the zero-order reaction \(\mathrm{A} \longrightarrow \mathrm{B}\). Sketch the following plots: (a) rate versus [A] and (b) [A] versus \(t\).

Consider the reaction $$ X+Y \longrightarrow Z $$ These data are obtained at \(360 \mathrm{~K}\): $$ \begin{aligned} &\text { Initial Rate of }\\\ &\begin{array}{ccc} \text { Disappearance of } \mathrm{X}(\mathrm{M} / \mathrm{s}) & {[\mathrm{X}]} & {[\mathrm{Y}]} \\ \hline 0.147 & 0.10 & 0.50 \\ 0.127 & 0.20 & 0.30 \\ 4.064 & 0.40 & 0.60 \\ 1.016 & 0.20 & 0.60 \\ 0.508 & 0.40 & 0.30 \end{array} \end{aligned} $$ (a) Determine the order of the reaction. (b) Determine the initial rate of disappearance of \(X\) when the concentration of \(\mathrm{X}\) is \(0.30 \mathrm{M}\) and that of \(\mathrm{Y}\) is \(0.40 \mathrm{M}\)
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