Reaction Rates and Rate Laws
Reaction Rates
Introduction to Reaction Rates
Chemical kinetics studies reaction rates.
The rate of reaction can be expressed in terms of the change in concentration of reactants or products over time.
Stoichiometry affects the rate
All rates are physically valid.
Convention for Expressing Rates
Rates are expressed in terms of reactants.
Rates are positive.
Units for rate are typically M/s (molarity per second).
Disappearing refers to reactants, and appearing refers to products.
Most reaction rates change with concentration over time.
Instantaneous Rate
We don't use average rates; instead, we use instantaneous rates.
Rate = -\frac{d[NO_2]}{dt}, which is the instantaneous rate.
Initial rate is the instantaneous rate at t = 0.
The instantaneous rate is the slope of the line tangent to the concentration curve.
Rate Law
The rate law is a mathematical expression that relates reaction rates to reactant concentrations.
Two types of rate laws:
Differential rate law: Rate depends on concentration.
where k is the rate constant and n is the reaction order.
Integral rate law: Obtained by integrating the differential rate law; concentration depends on time.
All rate laws must be obtained from experimental rate data; you cannot use equation stoichiometry.
The reaction mechanism is reflected in the rate law.
Reaction Orders
Differential rate law: Rate = -\frac{d[A]}{dt} = k[A]^m[B]^n
The exponents m and n give the order of the reaction with respect to reactants A and B.
Exponents can be whole or fractional numbers, or even zero.
The overall order of the reaction is given by the sum of the exponents (m + n).
Differential Rate Law by Method of Initial Rates
Method to determine the differential rate law from experimental data.
Steps:
Write the general differential rate law
Take ratios of sets of data to cancel out k and a reactant.
Repeat.
Solve for k (including units!).
Integrated Rate Laws
Obtained by integration of the differential rate law.