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To what temperature would the reaction below need to be heated to have a rate constant...

To what temperature would the reaction below need to be heated to have a rate constant of 2.299e9 M-1s-1 if the rate constant was 1.0800e9 M-1s-1 at -78.00°C and the activation energy was 11.900 kJ/mol?

NO(g) + O3(g) ↔ NO2(g) + O2(g)

Answer Choices:

-23.64°C

-55.58°C

-68.86°C

204.29°C
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Homework Answers

Answer #1

To Solve this problem we use Arrhenius equation which is K=K0 x e-Ea/RT

K = Rate constant

Ea = Activation energy

R = universal Gas constant = 8.314 J/mol.K

T= Temperature

For the same gas K0 will be same so the equation can be written as

lnK1 = lnK0 - Ea/RT1 &    lnK2 = lnK0 - Ea/RT2 Subtracting these two equations

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

K1 = 2.299e9 M-1s-1 K2= 1.0800e9 M-1s-1 T2 = -78.00°C = 273-78 = 195 K Ea = 11.9 KJ/mol

2.299e9/1.08e9 = 11900/8.314 (1/195 - 1/T1)

2.128 = 1431.32 (0.00512 - 1/T1)

1/T1 = 0.00512 -0.00148 = 0.00364

T1 = 274.725 K

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