Question

The rate constant for the synthesis reaction in the presence of a Fe-based catalysts has been determined at various temperatures. The table presents the results: T(C) k (s") 25 100 200 300 400 3.24 x 10° 2.32 x 10° 5.81 x 104 2.11 x 102.64 x 10 11. Use the data provided to determine the activation energy in the presence of the Fe-based catalyst (graphing method, you will need a spreadsheet program: e.g., Excel, google sheets). 12. Estimate how many times faster the reaction is in the presence of catalyst compared to the reaction rate in its absence (E. - 325 kJ/mol) at 500°c.

Answer 1

11. ln K = - Ea/RT

Thus, on ploting ln K vs I/T graph we get a straight line with slope = -Ea/R.

T (K)	1/T	K	ln K
298	0.0034	3.24*10-9	-19.5
373	0.0027	2.32*10-6	-13
473	0.0021	5.81*10-4	-7.5
573	0.0017	2.11*10-2	-3.9
673	0.0015	2.64*10-1	-1.3

1/T 0 0 0.0005 0.001 00015 0.002 0.0025 0.003 0.0035 n -10 In K -15 y = -9416.1x + 12.429 -20 -25

As per the equation-

y = -9416.1 x +12.429

y = ln K

x = 1/T

-Ea/R = -9416.1 K-1

Ea = 9416.1 K-1 * 8.314 J/K mol

= 78.3 kJ/mol