One function of organometallic reagents in chemical synthesis is the catalysis of hydrogen transfer reactions that would be very difficult in isolated organic compounds. For example, a chemical complex of rhodium and an alkyne is believed to form an intermediate of the form HMCCH (where the M represents the Rh and some additional ligands). This intermediate then transfers the metal-bound H atom to the other end of the alkyne, forming the alkene complex MCCH2 . This elementary step was proposed to be bimolecular, with two complexes meeting to form a square-bridged dimer so that H atoms were traded from one complex to the next. To test this, the reaction was carried out with an equimolar mixture of normal reagent and deuterium and 13C doubly-isotopically-labeled reagent, leading to the following possible reactions:

Assume that the initial concentration of both reactants is 0.020 M, and that the isotopic masses do not influence the reaction rate.

a. Predict the Final concentrations of the four products, without solving the integrated rate laws.

b. Now solve for the integrated rate laws that predict the concentrations of the four products as functions of time, and predict the Final concentrations of each product in the long-time limit. (Note that without reverse reactions the Final concentrations need not be the equilibrium concentrations.)

If your two answers for the Final product yields do not agree, Find the incorrect assumption.