What is the activation energy for a reaction that has a rate constant of 0.0883 L mol^-1 s^-1at 333 K and 0.469 L mol^-1 s^-1 at 366 K?

Question

Quizplus · Accepted Answer

The Arrhenius equation states that k=Ae^(-Ea/RT), where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin. Taking the natural logarithm of both sides gives ln(k) = ln(A) - (Ea/RT). We can use this equation to solve for the activation energy by taking the natural logarithm of the ratio of the rate constants and rearranging:

ln(k2/k1) = ln(A) - [(Ea/R)(1/T2 - 1/T1)]
(Equation 1)

Substituting the given values gives:

ln(0.469/0.0883) = ln(A) - [(Ea/R)(1/366 - 1/333)]

Simplifying and solving for Ea gives:

Ea = -R[(1/366 - 1/333)ln(0.469/0.0883)] 
Ea = 51.3 kJ/mol

Therefore, the best choice is C, with an activation energy of 51.3 kJ/mol.

What Is the Activation Energy for a Reaction That Has