Question

1) A first order reaction has an activation energy of 66.6 kJ/mol and a frequency factor (Arrhenius constant) of 8.78 x 10¹⁰ sec ^-1. Calculate the rate constant at 19 ^oC. Use 4 decimal places for your answer.

2) A first order reaction has a rate constant of 0.988 at 25 ^oC and 9.6 at 33 ^oC. Calculate the value of the activation energy in KILOJOULES (enter answer to one decimal place)

Answer 1

Arhenius equation is lnK= lnKo-Ea/RT

where Ea= activation energy= 66.6 Kj/mole= 66.6*1000J/mole, R= gas constant= 8.314 J/mole.K, T= 19+273= 292K

K0= frequency factor= 8.78*10¹⁰/sec

lnK= ln(8.78*10¹⁰)- 66.6*1000/(8.314*292)

K=0.1069/sec

when Arheius equation is written for two diffeent temperatures T1, T2 where rate constants are K1 and K2

ln (K2/K1)= (Ea/R)*(1/T1-1/T2)

T1= 25+273= 298K, K1= 0.988, T2= 33+273= 306K, K2= 9.6

hecne ln(9.6/0.988)= (Ea/8.314)*(1/298-1/306)

Ea= 215485 Joules= 215.48 KJ