•Expresses the reactant concentrations as a function of time.

aA → products

•Kinetics are first order in [A], and the rate law isRate = k[A]

•Integrated first-order rate law isln[A] = -kt + ln[A]0

1.Equation shows how concentration of A depends on time. If the initial concentration of A and the rate constant k are known, the concentration of A can be calculated at any time.

ln[A] = -kt + ln[A]0

2. Equation is of the form y = mx + b, where a plot of y versus x is a straight line with slope m and intercept b.

y = ln[A] x = t m = -k b = ln[A]0

Thus, for a first-order reaction, plotting the natural logarithm of concentration vs. time always gives a straight line. For the reaction,

aA → productsthe reaction is first order in A if a plot of ln[A] vs. t is a straight line.

ln[A] = -kt + ln[A]0

3. The integrated rate law for a first-order reaction also can be expressed in terms of a ratio of [A] and [A]0 as follows:

kt

]A[]A[ln 0

2N2O5(g) → 4NO2(g) + O2(g)

Since the plot of ln[N2O5] vs. time is a straight line, it confirms that the reaction is first order in N2O5, since it follows the equation ln[N2O5] = -kt + ln[N2O5]0.

•Half-life = the time required for a reactant to reach half its original concentration.•Designated by the symbol t1/2.

•General equation for the half-life of a first order reaction is (derivation in textbook (p. 542):

•Note for a first-order reaction, the half-life does not depend on concentration.

kt 693.0

2/1

•General reaction:aA → products

•That is second order in A, the rate law is:Rate = k[A]2

•The integrated second-order rate law has the form

1.A plot of 1/[A] vs. t will produce a straight line with a slope equal to k.

0]A[1

]A[1 kt

0]A[1

]A[1 kt

02/1 ]A[

1k

t

•The rate law for a zero-order reaction is:Rate = k[A]0 = k(1) = k

•For a zero-order reaction, the rate is constant. •It does not change with concentration as it does for first-order or second-order reactions.

•Integrated rate law for a zero-order reaction is:[A] = -kt + [A]0 Plot of [A] vs. t gives a straight line.

Half-Life equation:

kt

2]A[ 0

2/1