Answer
42.27 kj
Work Step by Step
using an equation derived from the Arrhenius equation,
ln k= (-Ea/R)x(1/T)
(the natural log of the rate constant is equal to negative activation energy over a gas constant, 8.314, times 1 over temperature in Kelvin)
1) the example gives two separate rate constant, so use each to find the different activation energy and then find the difference between them!
2)ln k= (-Ea/R)x(1/T)
both are at 25℃ so 298 K
k=0.039 s-1 in reaction without catalyst
k=1.0x1000000 s-1 in reaction with a catalyst
ln 0.039 = (-Ea/8.314)x(1/298)
Ea= 8,037.723 J
ln 1.0 x 100000 = (-Ea/8.314)x(1/298)
Ea= -34,228.922 J
3) find the difference! ((((:
(8,037.723 J) -(-34,228.922 J)= 42,266.64543 J
