We consider the transition state of a reaction to be a non accumulating transitory state at a critical point in a reaction. A+B-->X -->P where X is the transition state. X also has the double dagger symbol but I can't make it so I just used x. Also from A+B to X is reversible. K1 is from A+B->X k-1 is from X->A+B. And k2 is from X->P
A) Write d[X]/dT in terms of the concentrations of the relevant species
B) Derive the relationship that the effective rate constant of the reaction K is the same as (d[P]/dT)/([A][B]) takes the form k= k2 exp(-deltaG/RT) Where deltaG(these deltaG are with double dagger )is the standard free energy difference between the free energies of the transition state and reactant states A and B. Please make and state clearly any assumptions that are appropriate in deriving this result.
C) how does the effective rate constant of the reaction (k) depend on the pressure? Derive a relationship for the change in the natural log of the effective rate constant (ln k) vs some small pressure perturbation. Assume that k2 does not change with pressure.
D) if the transition state has a smaller volume than the reactants (deltaV double dagger < 0) does the effectice rate constant of the reactant increase or decrease when the pressure is increased?