Some chemical reactions occur instantly while others take much more time. The production of NaCl from solid sodium and chlorine gas happens in an instant. Digestion can take hours to a few days while rusting of metal can take months. Diamond will convert to the more stable allotrope of carbon, graphite, but it will take about two million years.
Kinetics is the study of reaction rates and the predicted mechanisms for chemical reactions.
The rate of a reaction is measured in terms of changes in the concentrations of reactants or products per unit time. For the general reaction,
we measure the concentration of A at some time t1 and at some time t2.
\(\displaystyle \mathrm{Rate}\;=\;\frac{\mathrm{change\;in\;concentration\;of\;A}}{\mathrm{change\;in\;time}}\;=\;-\frac{\mathrm{[A_2]\;-\;[A_1]}}{t_2\;-\;t_1}\;=\;-\frac{\Delta [A]}{\Delta t}\)
The square brackets, [A], indicate the concentration of A in moles/L (M). The negative sign is to show that the concentration of reactant is decreasing as the reaction proceeds. The rate has units of molarity per unit time. Time can be in milliseconds, seconds, minutes, years, etc.
Below is concentration/time data for the reaction, A → P.
The data was plotted as concentration of A, [A], vs time. It can be seen the data is not linear.
The rate of reaction, M/s, changes as the reaction proceeds. The average rate of reaction can be determined for the time interval, 0 – 100 s — the blue line, labeled a, on the plot below.
The average rate of reaction from 0 – 100 s is calculated as:
\(\displaystyle \frac{[A]_{100\;s}\;-[A]_{0\;s}}{100\;s\;-\;0;s}\;=\;\frac{0.31\;M\;-\;0.64\;M}{100\;s\;-\;0\;s}-3.3\times 10^{-3}\;M/s\)
The average rate of reaction from 40 – 60 s is calculated as:
\(\displaystyle \frac{[A]_{60\;s}\;-[A]_{40\;s}}{100\;s\;-\;0;s}\;=\;\frac{0.41\;M\;-\;0.47\;M}{60\;s\;-\;40\;s}-3.0\times 10^{-3}\;M/s\)
The rate of the reaction decreases as the concentration of [A] decreases. The instantaneous rate can be determined from any point on the plot by drawing a line tangent to the curve at that point and taking the slope of the tangent line.
The instantaneous rate at 40 s is 3.5 x 10-3 M/s. Still another way to determine the rate is by calculating the initial rate of reaction, the rate when the reactants are first mixed at, t = 0. This would be determined from the plot of the tangent line drawn at t = 0. We will discuss initial rates of reaction in a later study guide.
For the general reaction,
aA + bB → cC + dD
the reaction rate is given by:
\(\displaystyle -\frac{\Delta[A]}{a\;\Delta t}\;=\;-\frac{\Delta [B]}{b\Delta t}\;=\;\frac{\Delta [C]}{c\Delta t}\;=\;\frac{\Delta [D]}{d\Delta t}\)
The negative signs are used to show the reactants are decreasing in concentration as the reaction proceeds. The products do not include a negative sign because the concentration of products increases as the reaction proceeds. Note, the reciprocals of the stoichiometric coefficients are used to write the rate.
For the reaction, 2 NO (g) + 2 H2 (g) → N2 (g) + H2O (g), we write the rate expression in terms of the disappearance of each reactant and appearance of each product as:
\(\displaystyle -\frac{\Delta [NO]}{2\Delta t}\;=\;-\frac{\Delta [H_2]}{2\Delta t}\;=\;\frac{\Delta [N_2]}{\Delta t}\;=\;\frac{\Delta[H_2O]}{\Delta t}\)
If the rate of appearance of water vapor is 6.2 x 10-4 M/s, what is the rate of disappearance of NO?
\(\displaystyle -\frac{\Delta [NO]}{2\Delta t}\;=\;\frac{\Delta[H_2O]}{\Delta t}\)
\(\displaystyle \frac{\Delta [NO]}{\Delta t}\;=\;-2\times\;(6.2\times 10^{-4})\;M/s\;=\;-1.2\times 10^{-3}\;M/s\)
The negative sign just indicates the disappearance of the reactant. There are no negative rates of reaction.
Exercises
Exercise 1. Consider the plot below. What is the average rate for the disappearance of CO2 over the first 40 minutes of the reaction? What is the average rate between 60 and 80 minutes?
Exercise 2. Consider the table below for the disappearance of C4H9Cl.
Calculate the average rate in the time interval 100 – 400 seconds.
Exercise 3. Write the rate expression in terms of products and reactants for the following reaction:
Exercise 4. Consider the following chemical reaction:
4 NH3 (g) + 5 O2 (g) → 4 NO (g) + 6 H2O (g)
What is the rate of disappearance of NH3 if the rate of formation of NO is 2.6 x 10-5 M/s? What is the rate of the disappearance of O2 in the same time interval?
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