CHM 1046
General Chemistry II
Dr. Michael Blaber


Chemical Kinetics

The Change of Concentration with Time


Rate laws tell us what the rate of a reaction is in terms of the concentration(s) of reactant(s)

First Order Reactions

A reaction with a single reactant, where the reaction rate is linearly proportional to the concentration of the reactant (i.e. the 1st power of the reactant) is a first order reaction:

This can be rearranged to relate the effects of a change in time to a change in the concentration of reactant A:

Using calculus, this equation can be transformed (i.e. integrated) to yield an equation that relates the concentration of A at the start of the reaction [A]0, to its concentration at any other time t, [A]t:

Rearranging to solve for [A]t:

y = mx + b

This equation relates the concentration of reactant A after some time t, if given the initial concentration ([A]0) and rate constant k. This equation actually has the form of a linear equation, y = mx + b

Therefore, for a first-order reaction, the plot of ln[A]t (y values) versus time, t, (x values) yields a straight line with a slope of -k and a y-intercept of ln[A]0

 


The conversion of methyl isonitrile (CH3NC) to acetonitrile (CH3CN) is a first order reaction:

CH3NC -> CH3CN

Time
(sec)

Pressure CH3NC
(torr)

ln(Pressure CH3NC)

0

150

5.01064

1250

140

4.94164

2500

130

4.86753

5000

115

4.74493

10000

88

4.47734

15000

68

4.21951

20000

52

3.95124

30000

31

3.43399


For a first order reaction the equation:

can be used to determine:

  1. The concentration of a reactant remaining at any time after reaction has started (i.e. [A]t), if you know k, A0, and t
  2. The time required for a given fraction of a sample to react (i.e. solving for t if you know the ratio of [A]t/[A]0) and k
  3. The time required for a reactant concentration to reach a certain level - as in "half-life" calculations (see below)

 

Half-life

The half-life of a reaction, also known as t1/2, is the amount of time it takes for the concentration to drop to one-half of it's initial level

Note that the half-life is independent of the concentration. This means that if you randomly choose some time to calculate the concentration of reactant, exactly 0.693/k seconds later, the concentration will be 1/2 of what it was

 

Second-Order Reactions

A second order reaction, by definition, can be the result of:

Rate of reaction = k[A]2

Rate of reaction = k[A][B]

Rate = -D[A]/Dt = k [A]2

y = mx + b

 

Note: one way to distinguish between first- and second-order reaction laws is to graph both ln[A]t and 1/[A]t versus time. If the plot is a straight line with ln[A]t, then it is first order; if it is linear with the 1/[A]t values, then it is second order.


© 2000 Dr. Michael Blaber