Pseudo First-Order Kinetics Kinetic measurements of second-order reactions, using an excess of one reactant (pseudo fint-order reactions) can yield more accurate rate data than is generally realized, even if only a twofold excess is employed. Consider a reaction in which a is the initial concentration of reactant in excess; b, the initial concentration of the other reactant; z,the instantaneous concentration of the product; t, the time elapsed; k, the specific second-order rate constant; and k', the pseudo first-order rate constant. Improved accuracy, of the value of k , is achieved using a least squares treatment t o deduce the slope of the In (b - 2 ) against t plot (a computer facilitates this) and using eqn. (1) t o calculate k from the derived value of k'. I n eqn. (I), m is the mean value of z aver the range of conversion far which experimental data is available.
k = k'/(a
- m)
Percent reaction
Time (min)
k' (min-I)
10 20 30 40 50 60 70 80 90
1.059 2.255 3.625 5.222 , 7.132 9.505 12.57 16.95 24.54
0.09949 0.09895 0.09839 0.09782 0.09640 0.09640 0.09578 0.09495 0.09383
QQ
fin ni
n
nqznx
(1)
Specific 2nd-order constant (k) Eqn. (1) Eqn. (2) 99.49 98.95 98.39 97.82 96.19 96.40 95.78 94.95 93.83 92 .OR
100 100 100 100 100 100 100 99.7 99.3 97.8
- -
M, b = lo-&M, and k = loP1 The table was derived from hypothetical data for a reaction where a = mole-' mi".-1 From the data given in the first two columns, values of k were calculated, a t succeesive stages, using the above treatment, and d s o the usually reeommended'eqn. (2). k = k'/a
(2)
It can be seen that, employing eqn. (I), the error in the value of k is less than 0.1% up to 70% conversion and less than 1% up to 90% conversion. Similar caloulations, for a reaction where a / b = 5 show an error of
