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calculate the activation energy of a first order reaction whose temperature coefficient is 2 obtained by studying the reaction between 25 degrees centigrade and 35 degrees centigrade


Doma Swapna 22nd Jul, 2020
Answer (1)
Ankita Grover 30th Jul, 2020

Hello,

The activation energy can be calculated using the Arrhenius Equation which is:

Ln(k2/k1) = - (Ea/R) * ((1/t2) – (1/t1)) (Equation 1)

where   k2 = rate constant at temperature t2

k1 = rate constant at temperature t1

Ea = activation energy in J/mol

R = gas constant = 8.314 J/mol-K

t1 = reaction temperature 1 in Kelvin

t2 = reaction temperature 2 in Kelvin

Now, temperature coefficient = 2 (given)

We know that temperature coefficient = ratio of rate of the reaction

Therefore, k2/k1 = 2

Also, T1 = 25C = 298.15 K (given)

and T2 = 35C = 308.15 K (given)

Now substituting the values of k2/k1, R, t1 and t2 in equation 1, we get

ln(2) = - (Ea/8.314) * ((1/308.15) - (1/298.15))

Rearranging and solving the above equation, we get Ea = 5.29 * 10^4 J/mol (Answer)

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