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

Answer:

The activation energy is 7.11 × 10⁴ J/mol.

Explanation:

Let's consider the Arrhenius equation.

$lnk=lnA-\frac{Ea}{R} .\frac{1}{T}$

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,

$\frac{-Ea}{R} =-8.55 \times 10^{3} K^{-1} \\Ea= 8.55 \times 10^{3} K^{-1} \times 8.314 \frac{J}{K.mol} =7.11 \times 10^{4} J/mol$