Arrhenius equation

The Arrhenius equation is $k = A e^{-E_a/(RT)}$ where:

• $k$ = rate constant
• $A$ = frequency factor
• $E_a$ = activation energy
• $R$ = gas constant
• $T$ = absolute temperature

How does $k$ vary with $T$?

Since $k = A e^{-E_a/(RT)},$ as $T$ increases, the factor $\dfrac{E_a}{RT}$ decreases, so the exponential term increases.

Therefore, $k$ increases with increase in $T$.

Shape of the graph of $k$ vs $T$

The increase is not linear. Because of the exponential dependence, the $k$ vs $T$ graph is a rising curve.

More precisely:

• At low $T$, $k$ changes slowly.
• At higher $T$, $k$ increases more rapidly.

So the correct plot should show an increasing, upward-curving (nonlinear) graph.

Useful transformed form

Taking logarithm: $\ln k = \ln A - \frac{E_a}{R}\cdot \frac{1}{T}$

This means:

• $\ln k$ vs $1/T$ is a straight line with negative slope.
• But $k$ vs $T$ itself is an increasing exponential-type curve.

Selecting the correct option

Among the given plots, the one that represents this Arrhenius behavior is Option A.

Comparison with stored answer

Derived answer: A

Stored correct answer: A

Hence, they agree.