Question

The rate constant of a reaction is measured at different temperatures. A plot of the natural log of the rate constant as a function of the inverse of the temperature (in kelvins) yields a straight line with a slope of −8.55×103 K−1. What is the activation energy (Ea) for the reaction?

Answer 1

The activation energy is 7.11 × 10⁴ J/mol.

Step-by-step explanation:

Let's consider the Arrhenius equation.

`lnk=lnA-(Ea)/(R) .(1)/(T)`

where,

k is the rate constant

A is a collision factor

Ea is the activation energy

R is the ideal gas constant

T is the absolute temperature

The plot of ln k vs 1/T is a straight line with lnA as intercept and -Ea/R as slope. Then,

`(-Ea)/(R) =-8.55 * 10^(3) K^(-1) \\Ea= 8.55 * 10^(3) K^(-1) * 8.314 (J)/(K.mol) =7.11 * 10^(4) J/mol`