Physical Chemistry- The following data were obtained for the aqueous phase react

Question

Physical Chemistry-

The following data were obtained for the aqueous phase reaction CO_2 + H_2 O rightarrow HCO_3^- + H^+ The reaction is catalyzed by the enzyme carbonic anhydrase. The following data were obtained for the initial rate of reaction at a temperature T = 1.0 degree C and an enzyme concentration of 2.3 times 10^-9 mol/L. The general model for this type of reaction can be written as follows. Step 1 E + S ES k_1, k_-1 Step 2 ES rightarrow E + P k_2 where E is enzyme, S is free substrate, ES is the enzyme-substrate complex, and P is product. Based on the above model and the experimental data find numerical values for K_m = (k_-1 + k_2)/k_1 (Michalis constant) and k_2 for the reaction (including correct units).

Explanation / Answer

Micheles-menten equation is

V= rate= Vmax [S] / [ KM+S]

KM= (K-1+K2)/K1

1/V= (1/S)* (KM/Vmax)*1/S + 1/Vmax

So a plot of 1/V vs 1/S gives a straight line whose slope is KM/Vmax and intercpet is 1/Vmax

S is CO2 in this case

from the plot 1/Vmax = 4084 , Vmax= 1/4084 = 0.000245 MoL/l.s

KM/Vmax= 39.18, KM= 39.18* 0.000245 M=0.009594 M

the rate V= K2 [Et][S] (KM+S)= Vmax S/ (KM+S)

hence Vmax = K2 [Et] = 0.000245 Mol/L.s

K2 = 0.000245 Mol/l.s / 2.3*10-9 Mol/L=106521.74/s

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