The constant

k

for a certain reaction is measured at two different temperatures:

temperature

k

142.0

o

C

8.3

*

10

8

67.0

o

C

6.9

*

10

6

Assuming the rate constant obeys the Arrhenius equation, calculate the activation energy

E

a

for this reaction. Round your answer to 2 significant digits.

75 kJ/mol

Explanation:

The reactions occur at a rate, which means that the concentration of the reagents decays at a time. The rate law is a function of the concentrations and of the rate constant (k) which depends on the temperature of the reaction.

The activation energy (Ea) is the minimum energy that the reagents must have so the reaction will happen. The rate constant is related to the activation energy by the Arrhenius equation:

ln (k) = ln (A) - Ea/RT

Where A is a constant of the reaction, which doesn't depend on the temperature, R is the gas constant (8.314 J/mol. K), and T is the temperature. So, for two different temperatures, if we make the difference between the two equations:

ln (k1) - ln (k2) = ln (A) - Ea/RT1 - ln (A) + Ea/RT2

ln (k1/k2) = (Ea/R) * (1/T2 - 1/T1)

k1 = 8.3x10⁸, T1 = 142.0°C = 415 K

k2 = 6.9x10⁶, T2 = 67.0°C = 340 K

ln (8.3x10⁸/6.9x10⁶) = (Ea/8.314) * (1/340 - 1/415)

4.8 = 6.39x10⁻⁵Ea

Ea = 75078 J/mol

Ea = 75 kJ/mol