Question

The plot of log k vs X is linear with a slope = `(-E_a)/(2.303 R)`. What is X?

Answer 1

The variable X in the expression

slope = `(-E_a)/(2.303 R)`

comes from the Arrhenius equation in its logarithmic form

`log k = log A - E_a/(2.303 RT)`

This equation is linear in the form

`log k = -E_a/(2.303 RT) * 1/T + log A`

This is of the form y = mx + cy, where

log⁡k is plotted on the y-axis,

`1/T` is plotted on the x-axis (with temperature T in Kelvin),

slope = `-E_a/(2.303 R)`

∴ `X = 1/T`

So, the plot of log ⁡k vs `1/T` is linear with slope `-E_a/(2.303 R)`