The reaction orders in a rate law describe the mathematical dependence of the rate on reactant concentrations. Referring to the generic rate law above, the reaction is m order with respect to A and n order with respect to B. For example, if m = 1 and n = 2, the reaction is first order in A and second order in B. The overall reaction order is simply the sum of orders for each reactant. For the example rate law here, the reaction is third order overall (1 + 2 = 3). A few specific examples are shown below to further illustrate this concept.
The rate law:
$$rate=k[H_2O_2]$$describes a reaction that is first order in hydrogen peroxide and first order overall. The rate law:
$$rate=k[C_4H_6]^2$$describes a reaction that is second order in C4H6 and second order overall. The rate law:
$$rate=k[H^+][OH^-]$$describes a reaction that is first order in H+, first order in OH−, and second order overall.
Writing Rate Laws from Reaction OrdersAn experiment shows that the reaction of nitrogen dioxide with carbon monoxide:
$$NO_2(g)+CO(g)⟶NO(g)+CO_2(g)$$is second order in NO2 and zero order in CO at 100 °C. What is the rate law for the reaction?
Solution
The reaction will have the form: $$rate=k[NO_2]^m[CO]^n$$ We are told the reaction is second order in NO2; thus m = 2. The reaction is zero order in CO; thus n = 0. The rate law is: $$rate=k[NO_2]^2[CO]^0=k[NO_2]^2$$ Remember that any number raised to the zero power is equal to 1, thus [CO]0 = 1, which is why the CO concentration term may be omitted from the rate law: The concentration of CO has no effect on the rate (that term is always 1) so the rate of reaction is solely dependent on the concentration of NO2. A later chapter section on reaction mechanisms will explain how a reactant’s concentration can have no effect on a reaction rate despite being involved in the reaction.
Check Your Learning
The rate law for the reaction:
has been determined to be rate = k[NO]2[H2]. What are the orders with respect to each reactant, and what is the overall order of the reaction?
Solution
Since the power on [NO] in the rate law is 2, order in NO = 2. Since the power on H2 in the rate law is 1 (implied since no value is written), order in H2 = 1. This means the overall order = (2 + 1) = 3.
Check Your Learning
In a transesterification reaction, a triglyceride reacts with an alcohol to form an ester and glycerol. Many students learn about the reaction between methanol (CH3OH) and ethyl acetate (CH3CH2OCOCH3) as a sample reaction before studying the chemical reactions that produce biodiesel:
The rate law for the reaction between methanol and ethyl acetate is, under certain conditions, determined to be:
$$rate=k[CH_3OH]$$What is the order of reaction with respect to methanol and ethyl acetate, and what is the overall order of reaction?
Solution
From the rate law, the order in CH3OH = 1 and the order in CH3CH2OCOCH3 = 0. Overall order is (1 + 0) = 1.