Chemical Kinetics and Nuclear ChemistryMedium
Question
The overall rate $+ \frac{d\lbrack P\rbrack}{dt}$ for the reaction 2A + C → P from the mechanism
$2A\overset{\quad K\quad}{\leftleftarrows}B\left( \text{fast} \right) $$$B + C\overset{\quad K_{f}\quad}{\rightarrow}P\left( \text{slow} \right)$$
where, K = equilibrium constant and Kf = forward rate constant, is given by
Options
A.$\frac{d\lbrack P\rbrack}{dt} = KK_{f}\lbrack A\rbrack^{2}\lbrack C\rbrack$
B.$\frac{d\lbrack P\rbrack}{dt} = K\lbrack A\rbrack\lbrack B\rbrack$
C.$\frac{d\lbrack P\rbrack}{dt} = K_{f}\lbrack B\rbrack\lbrack C\rbrack$
D.$\frac{d\lbrack P\rbrack}{dt} = KK_{f}\lbrack A\rbrack^{2}\lbrack B\rbrack\lbrack C\rbrack$
Solution
$r = K_{f}\lbrack B\rbrack\lbrack C\rbrack\text{ and }K = \frac{\lbrack B\rbrack}{\lbrack A\rbrack^{2}}$
$\therefore r = K.K_{f}.\lbrack A\rbrack^{2}\lbrack C\rbrack$
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