a hydrogen molecule consists of two hydrogen atoms covalently bonded t

Question

A hydrogen molecule consists of two hydrogen atoms covalently bonded together. Gaseous molecular hydrogen can occur in two isometric forms, due to the magnetic moment associated with the spin of the proton nucleus. In the orthoisomer (o-H2) the two nuclear spins are parallel while the para isomer (p-H2) has antiparallel nuclear spins. The gas phase reaction to convert p-H2 to o-H2 has the following time-independent stoichiometry: p-\mathrm{H}_{2}(\mathrm{~g})=o-\mathrm{H}_{2}(\mathrm{~g}) Under certain conditions, the reaction is found to have an experimental rateequation of the following form: J=k_{\mathrm{R}}\left[p-\mathrm{H}_{2}\right]^{3 / 2} p-\mathrm{H}_{2}+\mathrm{M} \longleftarrow \frac{k_{1}}{k_{1}} \mathrm{H}^{*}+p-\mathrm{H}_{2}-\frac{k_{2}}{\rightarrow} \mathrm{H}^{\bullet}+o-\mathrm{H}_{2} where M is an inert 'third body' involved with the collision processes in the mechanism. (a) Explain why the experimental rate equation (Equation 2.2) indicates that Reaction 2.1 cannot be a simple elementary reaction. (b) State the form of the experimental rate equation predicted by the proposed mechanism assuming that the first step (Reaction 2.3) is rate-limiting.Explain, in these circumstances, why the mechanism effectively reduces to' two irreversible consecutive steps'. (i) With reference to the two-step mechanism and assuming that the second step (Reaction 2.4) is rate-limiting, show that the concentration of the radical intermediate [H•] can be expressed as follows: \left[\mathbf{H}^{\cdot}\right]=\left(\frac{k_{1}}{k_{-1}}\right)^{1 / 2}\left[p-\mathbf{H}_{2}\right]^{1 / 2} (ii) Write an expression for the rate of change of concentration of p-H2 with time (that is d[p-H/dt) as predicted by the proposed mechanism. Show that this leads to a chemical rate equation that is consistent with the experimental rate equation given in Equation 2.2.