Ratio of rate constants of a uncatalyzed reaction to that of uncatalyzed reaction is 10 . If the activation energy for thecatalyzed reaction is 400kcal at 1000k then activation energy for uncatalyzed reaction at same temperature will be?
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The natural log of the Arrhenius Equation-
ln(k) = ln(A) - Ea/RT
rearrange to get-
ln(A) = ln(k) + Ea/RT
A is the same for both reactions so ln(A) is a constant
ln(k1) + 14.0kJ/RT = ln(k2) + 11.9 kJ/RT
ln(k1) - ln(k2) = (11900 J - 14000 J)/RT
RT = 8.314 x (273+25) = 2478
ln(k1) - ln(k2) = -2100/2478 = -0.8475
ln(k1/k2) = -0.8475
k1/k2 = 0.4285
k2 : k1 = 2.33 : 1
ln(k) = ln(A) - Ea/RT
rearrange to get-
ln(A) = ln(k) + Ea/RT
A is the same for both reactions so ln(A) is a constant
ln(k1) + 14.0kJ/RT = ln(k2) + 11.9 kJ/RT
ln(k1) - ln(k2) = (11900 J - 14000 J)/RT
RT = 8.314 x (273+25) = 2478
ln(k1) - ln(k2) = -2100/2478 = -0.8475
ln(k1/k2) = -0.8475
k1/k2 = 0.4285
k2 : k1 = 2.33 : 1
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