How many times the rate of reaction increases at 200C for a reaction having the activation energies in the presence and absence of catalyst as 50 kJ/mol and 75 kJ/mol?
K = Ae^(-Ea/RT)
Taking ln on both sides
lnk = lnA + (-Ea/R) x 1/T
Now ATQ: lnk1 = lnA + (-Ea1/R) x 1/T
lnk2 = lnA + (-Ea2/R) x 1/T
Subtracting the two equations
ln(k2/k1) = (Ea1 - Ea2)/RT
ln(k2/k1) = (75 - 50) x 1000 / 8.314 x 293
K2/K1 = e (25000 / 8.314 x 293)
K2/K1 = e10.26
This is approximately equal to 30000.
Hence C is correct.
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