Reaction Rates
I. Reaction Rates
A. The area of chemistry that concerns reaction rates is called chemical kinetics. The reaction rate of a chemical
reaction is defined as the change in concentration of a reactant or product per unit time. The rate of a reaction
is not constant but changes over time because of the change in concentration. The instantaneous rate for a reaction
is the slope of a line tangent to a point on the curve.
II. Rate Laws
A. If the reverse reaction is neglected, the reaction rate will depend only on the concentrations of the reactants.
Therefore rate = k[A]n where n is an integer usually being 0,1,2, or 3. The value of n must be determined by
experiment; it cannot be written from the balanced equation. A rate law that expresses how the rate depends on
concentration is technically called the differential rat law. The overall reaction order is the sum of the exponents
in the rate law.
B. The integrated rate law expresses how the concentrations depend on time. The rate law for a reaction of the
first order is ln[A] = -kt + ln[A]0. A plot of ln[A] versus t will give a straight line. A second order rate
law has the form 1/[A] = kt + 1/[A]-0. A plot of 1/[A] versus t will produce a straight line. The rate law for
a zero order reaction is [A] = -kt + [A]0. A plot of [A] versus t will give a straight line.
C. Half-life is the time required for a reactant to reach half its original concentration. The half-life of a
first-order reaction is t1/2 = 0.693/k. The half-life of a first order reaction does not depend on concentration.
The expression for the half-life of a second-order reaction is t1/2 = 1/(k[A]0). The half-life for a zero-order
rate law is given as t1/2 = [A]0/2k.
III. A model for Chemical Kinetics
A. The collision model states the molecules must collide to react. The kinetic molecular theory of gases predicts
that an increase in temperature raises molecular velocities and so increases the frequency of collisions between
molecules. But there is an uneven distribution of these velocities so only a fraction of the molecules have enough
energy to react.
B. Activation energy is the energy that must be overcome to produce a chemical reaction. The activated complex
is the unstable molecule at the top of the energy "hill." DE has no effect on the rate of reaction.
The rate depends on the size of the Ea.
C. Another factor in the production of a chemical reaction is the steric factor. This involves the orientations
of the molecules. With all the factors counted a formula can be written as k = Ae-Ea/RT where A is a combination
of the collision frequency and the steric factor. The logarithmic form of this equation is ln(k) = -Ea/R * (1/T)
+ ln(A) where -Ea/R is the slope, y is ln(k) and x is 1/T. Another form of this equation is ln(k2/k1) = Ea/R *
(1/T1 - 1/T2).