Chemical thermodynamics tells us whether a reaction is capable of occurring spontaneously, but it does not tell us how fast the reaction will proceed. The study of reaction rates is called chemical kinetics.
The reaction rate describes how quickly the concentrations of reactants and products change as a reaction proceeds. For a general reaction
\[ aA+bB\rightarrow cC+dD \]the reaction rate can be expressed using the rate of disappearance of any reactant or the rate of appearance of any product:
\[ \text{Rate} = -\frac{1}{a}\frac{d[A]}{dt} = -\frac{1}{b}\frac{d[B]}{dt} = \frac{1}{c}\frac{d[C]}{dt} = \frac{1}{d}\frac{d[D]}{dt} \]The stoichiometric coefficients ensure that each expression gives the same overall reaction rate, regardless of which chemical species is monitored experimentally.
Experimental measurements show that reaction rates often depend on the concentrations of one or more reactants. This relationship is described by the reaction rate law. A common form is
\[ \text{Rate} = k[A]^{\alpha}[B]^{\beta} \]where the exponents must be determined experimentally. The rate law can then be used to predict how the reaction rate changes as reactant concentrations change.
The exponents in a rate law are called the orders of reaction. The exponent associated with each reactant gives the order with respect to that reactant, while the sum of all exponents gives the overall reaction order.
| Rate law | Order in A | Order in B | Overall order |
|---|---|---|---|
| \(\text{Rate}=k[A]\) | 1 | — | 1 |
| \(\text{Rate}=k[A]^2\) | 2 | — | 2 |
| \(\text{Rate}=k[A][B]\) | 1 | 1 | 2 |
| \(\text{Rate}=k[A]^2[B]\) | 2 | 1 | 3 |
| \(\text{Rate}=k[A]^{1/2}[B]\) | 1/2 | 1 | 3/2 |
Unlike the coefficients in a balanced chemical equation, reaction orders generally cannot be predicted from stoichiometry. Instead, they must be determined experimentally from kinetic data.
| Term | Meaning |
|---|---|
| Reaction rate | How rapidly the concentrations of reactants or products change with time. The reaction rate usually changes during a reaction as concentrations change. |
| Reaction rate law | The mathematical equation that relates the reaction rate to the concentrations of reactants (and sometimes products or catalysts). |
| Rate constant (\(k\)) | The proportionality constant in the rate law. For a given reaction, \(k\) is independent of concentration but depends strongly on temperature. |
Big picture: The reaction rate tells us how fast a reaction is occurring at a particular instant, the reaction rate law tells us how the rate depends on concentration, and the rate constant measures the intrinsic speed of the reaction under a given set of conditions.
A reaction is found experimentally to obey the rate law
\[ \text{Rate}=k[A]^2[B] \]where
\[ k=0.850\ \mathrm{M^{-2}\,s^{-1}} \]Calculate the reaction rate when
\[ [A]=0.250\ \mathrm{M} \]and
\[ [B]=0.400\ \mathrm{M}. \]Begin by writing the rate law.
\[ \text{Rate}=k[A]^2[B] \]Substitute the known values.
\[ \text{Rate} = (0.850\ \mathrm{M^{-2}\,s^{-1}}) (0.250\ \mathrm{M})^2 (0.400\ \mathrm{M}) \]First evaluate the squared concentration.
\[ (0.250)^2=0.0625 \]Now calculate the reaction rate.
\[ \text{Rate} = (0.850)(0.0625)(0.400) = 0.0213 \]The concentration units combine as
\[ \mathrm{M^{-2}\times M^2\times M=M\,s^{-1}} \]Therefore,
\[ \boxed{\text{Rate}=2.13\times10^{-2}\ \mathrm{M\,s^{-1}}} \]Physical interpretation: The reaction is second order in A and first order in B. As a result, doubling the concentration of A would increase the reaction rate by a factor of four, while doubling the concentration of B would only double the reaction rate.
For the rate law shown below, determine the overall reaction order and the units of the rate constant \(k\).
1. What is the overall reaction order?
2. What are the units of the rate constant \(k\)?
Use the rate law and the information provided to calculate the missing quantity.
Big picture: The reaction rate tells us how fast a reaction is occurring, the rate law tells us how that rate depends on concentration, and the rate constant characterizes the speed of the reaction under a particular set of conditions. Together, these quantities provide a mathematical description of reaction kinetics and allow reaction rates to be predicted from experimental conditions.