Question

The slope of the line formed from ln(k) vs 1/T represents which of the following? A. Ea B. Ea/R C. -Ea D. -Ea/R

Answer 1

The slope of the line formed from ln(k) vs 1/T represents
`-\left((E_(a))/(R)\right)`

Answer: Option D

Step-by-step explanation:

Based on the Arrhenius equation, we can calculate the activation energies if rate constant is well-known, or vice versa. It also expresses mathematically the relationship: as the activation energy component
`E_(a)` increases, the rate constant k decreases, so the reaction rate decreases.

The Arrhenius equation is
`k=A e^(-E a / R T)`

Taking logarithm on both the sides we will have
`\ln k=-(E_(a))/(R T)+\ln A`

We know the equation y=mx+c where ‘ m ‘ is the slope and c is the Intercept

Equating y=mx+c to the logarithmic equation

we have y= ln k

`m=-(E_(a))/(R)`

x=1/T and

c =ln A

so, slope
`m=(-E_(a))/(R)` that is the answer