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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).