Question

# The activation energy for a reaction is changed from 184 kJ/mol to 59.5 kJ/mol at 600....

The activation energy for a reaction is changed from 184 kJ/mol to 59.5 kJ/mol at 600. K by the introduction of a catalyst. If the uncatalyzed reaction takes about 2627 years to occur, about how long will the catalyzed reaction take? Assume the frequency factor A is constant and assume the initial concentrations are the same.

From the arrhenius equation

Rate constant = frequency factor x exp(-Activation energy /gas constant x Temperature)

k = A exp(-Ea/RT)

Take natural logarithm to both sides

ln k = ln A -Ea/RT

Without catalyst

ln k = ln A - (184 *1000 J/mol /8.314 J/mol·K x 600 K)

ln k = ln A - (36.88)......... Eq1

With catalyst

ln k = ln A - (59.5*1000 J/mol /8.314 J/mol·K x 600 K)

ln k' = ln A - (11.93).......... Eq2

Eq 1 - eq2

ln k - ln k' = (ln A - 36.88) - (ln A - 11.93)

ln k/k' = -24.95

k/k' = exp (-24.95) = 1.459 x 10^-11

Rate constant is inversely proportional to Time taken by the reaction

T = time taken by uncatalyzed reaction = 2627 years

T' = time taken by catalyzed reaction

T'/T = 1.459 x 10^-11

T' = 1.459 x 10^-11 x 2627

= 3.84 x 10^-8 years x 31536000s/year

= 1.21 s

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