1.
The reaction mechanism for the reaction P→R\text{P} \rightarrow \text{R} is as follows:

P⇌2Q(fast equilibrium; k1/k2)\text{P} \rightleftharpoons 2\text{Q} \quad \text{(fast equilibrium; } k_1/k_2\text{)}


2Q+P→k3R(slow)2\text{Q} + \text{P} \xrightarrow{k_3} \text{R} \quad \text{(slow)}


The rate law for the main reaction (P→R\text{P} \rightarrow \text{R}) is: