Question

The Arrhenius equation is k = A*e -\Delta G Δ G ‡/RT in units of sec-1. Let’s assume A= 1 and RT = 1. The NEW Arrhenius equation is k = e -\Delta G Δ G ‡ (also in units of sec-1). For the uncatalyzed reaction (A -> P), the free energy barrier is \Delta G Δ G ‡ = 5. Fraction of total product at time t = 1 - e-kt Now you add a catalyst which breaks this reaction down into 2 steps A -> B -> P with free energy barriers\Delta G Δ G ‡1 = 3 and \Delta G Δ G ‡2 = 2 (rate for step 1 (AB) is k1, rate for step 2 (BP) is k2). Fraction of total product at time t = 1- [ ( k2e-k1*t – k1e-k2*t ) / (k2-k1) ] What fraction of A is P after t=5 seconds in the uncatalyzed case? (PU) What fraction of A is P after t=5 seconds in the catalyzed case? (PC) How many times faster is catalyzed versus uncatalyzed? PC/PU (This will be your answer to this question) Use at least 2 decimal places