Question

The rate constants for the first-order decomposition of a compound are 5.22× 10–4 s–1 at 43°C and 2.91 × 10–3 s–1 at 62°C. What is the value of the activation energy for this reaction? (R = 8.31 J/(mol · K)) a. 79.5 kJ/mol b. 34.5 kJ/mol c. 0.751 kJ/mol d. 0.87104 kJ/mol e. 2 kJ/mol

Answer 1

Answer:

Activation energy of the reaction is 79.5 kJ/mol

Explanation:

According to Arrhenius equation for a reaction-

                     $k=Ae^{(\frac{-E_{a}}{RT})}$

where k is the rate constant, A is the Arrhenius constant, $E_{a}$ is the activation energy and T is temperature in kelvin

For the given two different set of condition, we can write-

at $43^{0}\textrm{C}$, $5.22\times 10^{-4}=Ae^{(\frac{-E_{a}}{8.31\times 316})}$............(1)

at $62^{0}\textrm{C}$, $2.91\times 10^{-3}=Ae^{(\frac{-E_{a}}{8.31\times 335})}$............(2)

$Eq-(1)\div Eq-(2)$ gives-

$\frac{5.22\times 10^{-4}}{2.91\times 10^{-3}}=e^{\frac{E_{a}}{8.31}(\frac{1}{335}-\frac{1}{316})}$

Solving this equation we get $E_{a}=79.5 kJ/mol$

So activation energy of the reaction is 79.5 kJ/mol