A rule of thumb is that a reaction rate roughly doubles for every 10 °C increase in temperature. What is the activation energy of a reaction whose rate exactly doubles between 25.0 °C and 35.0 °C

FOR EVERY 10 DEGREE CELSIUS INCREASE IN TEMPERATURE, THE ACTIVATION ENERGY THAT SHOWS THIS IS 52.4 KJ/MOL

Explanation:

From Arrhenius equation, the relationship between the rate constant and the temperature is as shown below:

k = Ae^ -Ea/RT

At initial temperature T1, the initial rate constant is (k1)

At final temperature T2, the final rate constant is k2

For the reaction rate to be doubled, we must double the rate constant which shows that the ratio of k2 / k1 must be equal to 2.

That is, k2 / k1 = 2 (rate is doubled)

Equating this into the Arrhenius equation, we have:

k2 / k1 = Ae^ (-Ea / R ) (1/ T2 - 1/T1)

2 = e^ (-Ea / R) (1 / T2 = 1 / T1)

Taking the natural logarithm of both sides:

ln 2 = - (Ea / R) (1 / T2 - 1 / T1)

Making Ea the subject of the formula, we obtain:

Ea = - (ln 2 R / (1 / T2- 1 / T1))

Let T1 = 25 C = 25 + 273 K = 298 K

T2 = 35 C = 35 + 273 K = 308 K

R = 8.314

So,

Ea = - (ln 2 * 8.314 / ( 1/308 - 1 / 298))

Ea = - (0.693 * 8.314 / 0.00324 - 0.00335)

Ea = - 5.7616 / -0.00011

Ea = 52 378,18 J / mol

So therefore, the activation energy Ea is 52.4 kJ/mol.

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