A and B react to produce P:
If the initial concentration of the reactant A is much larger than the concentration of B, the concentration of A will not change appreciably during the course of the reaction The concentration of the reactant in excess will remain almost constant. Thus the rate's dependence on B can be isolated and the rate law can be written
Equation
(1) represents the differential form of the rate law. Integration of this equation and evaluation of the integration constant
C produces the corresponding integrated law.
Substituting
[ B ] = c into equation
(1) yields:

Integrating equation
(2) gives:

The constant of integration
C can be evaluated by using boundary conditions. At
t = 0, the concentration of
B is
co.
Therefore

Accordingly is obtained:
If the decrease in concentration of
B is followed by photometric measurement the
Beer' Law must be taken into account.
Combining equation
(4) and
Beer' Law
A = absorbance, e = molar absorbtivity with units of L · mol -1 · cm -1
c = concentration of the compound in solution, expressed in mol · L -1
Po = radiant power for radiation entering; P = radiant power for radiation leaving
gives the relationship between
k' and
lnA:
According to equation
(7), a plot of lnA versus time should lead to a straight line whose slope is the pseudo-first order rate constant
k'. The value of
k' can then be divided by the known, constant concentration of the excess compound to obtain the true constant second order
k:
The
pseudo-first order rate constant k' can be also determined from the
half-life t 1 / 2.
A and B react to produce P:
If the initial concentration of the reactant A is much larger than the concentration of B, the concentration of A will not change appreciably during the course of the reaction The concentration of the reactant in excess will remain almost constant. Thus the rate's dependence on B can be isolated and the rate law can be written
Equation
(1)represents the differential form of the rate law. Integration of this equation and evaluation of the integration constant
Cproduces the corresponding integrated law.
Substituting
[ B ] = cinto equation
(1)yields:
Integrating equation
(2)gives:
The constant of integration
Ccan be evaluated by using boundary conditions. At
t = 0, the concentration of
Bis
co.
Therefore
Accordingly is obtained:
If the decrease in concentration of
Bis followed by photometric measurement the
Beer' Lawmust be taken into account.
Combining equation
(4)and
Beer' Lawc = concentration of the compound in solution, expressed in mol · L -1
Po = radiant power for radiation entering; P = radiant power for radiation leaving
gives the relationship between
k'and
lnA:
According to equation
(7), a plot of lnA versus time should lead to a straight line whose slope is the pseudo-first order rate constant
k'. The value of
k'can then be divided by the known, constant concentration of the excess compound to obtain the true constant second order
k:
The
pseudo-first order rate constant k'can be also determined from the
half-life t 1 / 2.