Question

Show that the reaction A - B + C, which is first-order forward (rate constant k) and second-order reverse (rate constant k), relaxes exponentially for small displacements from equilibrium. Find an expression for the relaxation time in terms of k, and k. (Hint: Let x be a small displacement from equilibrium. For such a displacement, xº is negligible.)

Answer 1

show that the reaction A B+c. which is first order forward (rate constant ki and second order reverse (rate constant K₂), relaxes exponentially for small displacements from equilibrio find an expression for the relaxation time in terms of k, and K₂. Hing: leta be the small displa from equilibrium, for such displa negligible As the given reaction :- bre Suppose :- b initial concentration ar initial 0 0 at timet 1-2 a 2 Bao I rate of o displacementen forward reaction - KCAL = kilion - first orden Backward reaction: akz [B][ - second onder Rate of - herefore, - Knaar - k₂22 Rase of reaction = Rate of forever Reactions - Rate of Back word Reaction

Page No. Date da = Rate of Reaction? dt da du As = k11-2) - Rza? is so small displacement, s treat a? as negligible u dat Now! donc K, (1-2) - da kidt in integrating both sides 12 many thanks to Relaxation time (t) = Leln(n.