[Lisa_JO]

 The reversible reaction, A(aq) + H2O(l)---> P(aq)
is first-order in A(aq) and P(aq), and pseudo-zero order in H2O(l). What must be
the most appropriate expression for the relaxation time, τ, when the reaction
returns to its equilibrium after a sudden increase in temperature?

the key answer is: relation time=1/kf+kr but my question is why not 1/kf( [A]+kr [p] since only water will be eliminated?

[mjc123]

For a start, you can see your proposed answer is wrong, because for a first order reaction the rate constant has the dimensions 1/time.
For a more thorough answer, let the equilibrium be displaced slightly so that the concentrations are [A]_e + δ and [P]_e - δ. Set up a differential equation for the rate of change of δ and solve it.

[Lisa_JO]

Thank you for the explanation, but I still don't get it when I followed these steps I didn't get the key answer "1/Kr+Kf "because the reactant didn't got cancel out with the product that's what am confused about

[mjc123]

Can you show your working?