D32.1 Reaction Rate

The rate of a chemical reaction is usually defined as the change in concentration of a reactant or a product per unit time. Rates can be experimentally determined by measuring the concentration of a reactant or a product at a series of fixed time intervals after the reaction has started.

Often, it is easier to measure some property related to a substance’s concentration. For example, for a reaction involving a colored reactant, light absorption can be measured at different times after the start of the reaction. Then the reactant’s concentration at a given time can be calculated from the proportionality between light absorption and concentration.

Consider the decomposition reaction of cyclobutane in the gas phase:

C4H8(g) ⟶ 2 C2H4(g)

The rate at which cylcobutane decomposes can be expressed in terms of the rate of change of its concentration:

 \begin{array}{rcl} \text{rate of decomposition of C}_4\text{H}_8 &= & - \dfrac{\text{change in concentration of reactant}}{\text{time interval}} \\[1em] &= & - \dfrac{[\text{C}_4\text{H}_8]_{t_2}\;-\;[\text{C}_4\text{H}_8]_{t_1}}{t_2\;-\;t_1} \\[1em] &= & - \dfrac{{\Delta}[\text{C}_4\text{H}_8]}{{\Delta}t} \end{array}

In this equation, Δ[C4H8] represents the change in concentration of cyclobutane during the time interval Δt. The minus sign in front of the fraction is there because reaction rate is defined to be positive. The reactant concentration decreases as the reaction proceeds, making Δ[C4H8] a negative quantity, so a negative sign is needed to make the calculated rate positive.

The table below provides an example of data collected during the decomposition of C4H8. Notice that the reaction rate varies with time, decreasing as [C4H8] decreases.

Table: Concentrations of cyclobutane measured at 40 °C
Time (s) [C4H8] (M) Δ[C4H8] (M) Δt (s) Rate of decomposition (M/s)
0.0 0.240
20.0 0.120 -0.120 20.0 0.00600
40.0 0.060 -0.060 20.0 0.0030
60.0 0.030 -0.030 20.0 0.0015
80.0 0.015 -0.015 20.0 0.00075

An average rate over a given time period can be calculated using the concentrations at the beginning and the end of the period. For example, the average rate for the first and last 20-second period are:

 \text{rate =} \dfrac{-{\Delta}[\text{C}_4\text{H}_8]}{{\Delta}t} = \dfrac{-(0.120\;\text{M}\;-\;0.240\;\text{M})}{(20.0\;\text{s}\;-\;0.00\;\text{s})} = 0.00600\;\dfrac{\text{M}}{\text{s}}
 \text{rate =} \dfrac{-{\Delta}[\text{C}_4\text{H}_8]}{{\Delta}t} = \dfrac{-(0.015\;\text{M}\;-\;0.030\;\text{M})}{(80.0\;\text{s}\;-\;60.0\;\text{s})} = 0.00075\;\dfrac{\text{M}}{\text{s}}

The rate of reaction at any specific time is known as the instantaneous rate. The instantaneous rate when the reaction starts (at t0), is the initial rate. The instantaneous rate of a reaction may be determined one of two ways:

  • If concentration changes can be measured at very short time intervals, then average rates over these very short time intervals provide reasonably good approximations of instantaneous rates.
  • If we plot reactant concentration vs. time, the instantaneous rate at any time t is given by the negative of the slope of a straight line that is tangent to the curve at that time.
Figure: Instantaneous rate. Graph of [C4H8] versus time. The reaction rate at any instant is equal to the negative of the slope of a line tangent to this curve at that time. Tangents are shown at t = 0 s (magenta; initial rate) and at t = 40 s (orange); click on “+” signs for more information.

Exercise: Reaction Rates from Concentration Graph

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Chemistry 109 Fall 2021 Copyright © by John Moore; Jia Zhou; and Etienne Garand is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.