[charco]

can someone check please:

The first-order reaction:
2N2(g) ---> 2N2(g) + O2(g)

has a rate constant of 1.3 x 10-11 s-1 at 270°C and 4.5 x 10-10 s-1 at 350°C. What is the activation energy for this reaction?

(A) 15 kJ
(B) 30 kJ
(C) 68 kJ
(D) 120 kJ

I get a different answer using:

k = Ae^-(Ea/RT)

lnk = lnA – Ea/RT

ln(1.3 x 10-11) = lnA – Ea/(8.314 x 543)

and

ln(4.5 x 10-10) = lnA – Ea/(8.314 x 623)

subtract one from the other

ln(4.5 x 10-10) - ln(1.3 x 10-11) = – Ea/(8.314 x 623) + Ea/(8.314 x 543)
 
8.314[ln(4.5 x 10-10) - ln(1.3 x 10-11)] = Ea/543  - Ea/623

8.314[ln(4.5 x 10-10) - ln(1.3 x 10-11)] = (623Ea – 543Ea)/ (623 x 543)

8.314 x 623 x 543 [ln(4.5 x 10-10) - ln(1.3 x 10-11)] = 80Ea

2812534.7[-21.52 + 25.07] = 80Ea

(2812534.7 x 3.5449)/80 = Ea

Ea = 124806

Ea = 124.8kJ mol-1

[Donaldson Tan]

your working is correct.

in fact, the quantities quoted in your question are in 2 significant figures, so your final answer must be given in 2 significant figures, therefore your answer is correct.


Ea = 124.8kJ mol-1 = 120 kJ mol-1 (2s.f)

[charco]

Thanks geo - although I feel that it's somewhat inappropriate to not have it pointed out in the question!

[Donaldson Tan]

this is a MCQ. How much stuff do you think will be pointed out?