Preferred Label : kinetic equivalence;
IUPAC definition : Two reaction schemes are kinetically equivalent if they imply the same rate law. For
example, consider the two schemes (i) and (ii) for the formation of C from A: \[{(i)}\qquad
{A}\overset{k_{1},{OH} {-}}{\underset{k_{-1},{OH} {-}}\rightleftarrows }{B}\overset{k_{2}}{\rightarrow
}{C}\] Providing that B does not accumulate as a reaction intermediate. \[\frac{{d}[{C}]}{{d}t}
\frac{k_{1}\ k_{2}\ [{A}]\ [{OH} {-}]}{k_{2}\, \,k_{-1}\ [{OH} {-}]}\] \[{(ii)}\qquad
{A}\overset{k_{1}}{\underset{k_{-1}}\rightleftarrows }{B}\overset{k_{2}}{\underset{{OH}
{-}}\rightarrow }{C}\] Providing that B does not accumulate as a reaction intermediate:
\[\frac{{d}[{C}]}{{d}t} \frac{k_{1}\ k_{2}\ [{A}]\ [{OH} {-}]}{k_{-1}\, \,k_{2}\
[{OH} {-}]}\] Both equations for d[C]/dt are of the form: \[\frac{{d}[{C}]}{{d}t}
\frac{r\ [{A}]\ [{OH} {-}]}{1\, \,s\ [{OH} {-}]}\] where r and s are constants (sometimes
called 'coefficients in the rate equation'). The equations are identical in their
dependence on concentrations and do not distinguish whether OH sup class minus /sup
catalyses the formation of B, and necessarily also its reversion to A, or is involved
in its further transformation to C. The two schemes are therefore kinetically equivalent
under conditions to which the stated provisos apply.;
Origin ID : K03403;
See also
Two reaction schemes are kinetically equivalent if they imply the same rate law. For
example, consider the two schemes (i) and (ii) for the formation of C from A: \[{(i)}\qquad
{A}\overset{k_{1},{OH} {-}}{\underset{k_{-1},{OH} {-}}\rightleftarrows }{B}\overset{k_{2}}{\rightarrow
}{C}\] Providing that B does not accumulate as a reaction intermediate. \[\frac{{d}[{C}]}{{d}t}
\frac{k_{1}\ k_{2}\ [{A}]\ [{OH} {-}]}{k_{2}\, \,k_{-1}\ [{OH} {-}]}\] \[{(ii)}\qquad
{A}\overset{k_{1}}{\underset{k_{-1}}\rightleftarrows }{B}\overset{k_{2}}{\underset{{OH}
{-}}\rightarrow }{C}\] Providing that B does not accumulate as a reaction intermediate:
\[\frac{{d}[{C}]}{{d}t} \frac{k_{1}\ k_{2}\ [{A}]\ [{OH} {-}]}{k_{-1}\, \,k_{2}\
[{OH} {-}]}\] Both equations for d[C]/dt are of the form: \[\frac{{d}[{C}]}{{d}t}
\frac{r\ [{A}]\ [{OH} {-}]}{1\, \,s\ [{OH} {-}]}\] where r and s are constants (sometimes
called 'coefficients in the rate equation'). The equations are identical in their
dependence on concentrations and do not distinguish whether OH sup class minus /sup
catalyses the formation of B, and necessarily also its reversion to A, or is involved
in its further transformation to C. The two schemes are therefore kinetically equivalent
under conditions to which the stated provisos apply.