Q.Among the following graphs showing variation of rate constant with temperature (T) for a reaction, the one that exhibits Arrhenius behavior over the entire temperature range is

Reaction (II) is faster than reaction (I) because its potential-energy diagram shows a smaller activation energy, and rate increases as activation energy decreases.

The activation energy $E_a$ is the minimum extra energy that reactant molecules must acquire (over and above their average energy) in order to cross the energy barrier (the 'threshold energy' hump) and be converted into products. The Arrhenius equation relates the rate constant $k$ of a reaction to its activation energy:

$k = A\,e^{-E_a/RT}$

where $A$ is the frequency (pre-exponential) factor, $R$ the gas constant, and $T$ the absolute temperature.

From this equation, $k$ depends exponentially and inversely on $E_a$: the smaller the activation energy, the larger the value of $e^{-E_a/RT}$, and hence the larger the rate constant $k$. Physically, this is because, at a given temperature, the fraction of molecules in a Maxwell-Boltzmann energy distribution that possess energy equal to or greater than $E_a$ increases sharply as $E_a$ decreases - so more collisions become 'effective' (successful) collisions leading to product formation per unit time.

In the given diagrams, reaction (I) has a taller energy hump (larger $E_a$) than reaction (II), whose hump/activation energy is drawn distinctly lower. Since reaction (II)'s molecules need to cross a smaller energy barrier, a larger proportion of its reactant molecules can do so at any given temperature, making it the faster of the two reactions - regardless of whether the two reactions are exothermic or endothermic overall, since rate is governed by the height of the barrier, not by the net energy change.