Question

The data below shows the production of CO₂ from carbonic aanhydrase. The zero-order rate constant was measured at different temperatures. Calculate E_A , Delta H⁺ , the Arrhenius Constant, and Delta S⁺.

T(K)	289	293.5	298.1	303.2	308	113.5
k (10-6)	1.04	1.34	1.53	1.89	2.29	2.84

Answer 1

Solution:

Zero order reaction is said in the problem so the rate expression for zero order reaction is given as,

-rA = K

Arhenius equation is,

K = Ae^-EA/RT

take log on both side

lnK = lnA + lne^-EA/RT

lnK = -EA/RT + lnA

we have Temperature and K data so draw graph of lnK vs 1/T then the slope of the line will be, -EA/R

from the above table,

T (K)	1/T	K*10-6	lnK
289	0.00346	1.04	13.85
293.5	0.003407	1.34	14.10
298.1	0.003354	1.53	14.24
303.2	0.003298	1.89	14.45
308	0.003246	2.29	14.64
113.5	0.00881	2.84	14.85

Draw a graph if you want and slope of that line will be,

Slope = -EA/R = Y/X

= (14.24 - 14.10)/(0.003354 - 0.003407)

= 0.14/-0.000053

-EA/R = -2641.5

EA/R = 2641.5

EA = 2641.* 8.314

EA = 21961 KJ/Kmol

2.Hcan be calculated by formula we have,

EA = H + RT

H = EA - RT

and Arhenius constant A can be calculated by

K = e-EA/RT

lnK = lnA - EA/RT

lnA = lnK + EA/RT

T	K*10-6	EA	H	lnA	A
289	1.04	21961	19558	9.17	9693
293.5	1.34	21961	19520	9.29	10856
298.1	1.53	21961	19482	9.28	10788
303.2	1.89	21961	19440	9.34	11481
308	2.29	21961	19400	9.40	12145
113.5	2.84	21961	21017	24.31	3.64*1010