The basic theory of Arrhenius equation is that:
(1) Activation energy and pre-exponential factors are always temperature independent
(2) The number of effective collisions is proportional to the number of molecules above a certain threshold energy.
(3) As the temperature increases, the number of molecules with energies exceeding the threshold energy increases.
(4) The rate constant is a function of temperature

1, 2, 3 and 4

The correct answer is option 1. 1, 2, 3 and 4.

Arrhenius equation is used to determine the relationship between the temperature and the rate at which the reaction will proceed. The expression gives us a relationship between the rates constant, the absolute temperature, and the A factor which is also called the pre-exponential factor. It gives us a clearer picture of the dependency of the rate of reaction on temperatures. As you know at higher temperatures, the chances of collisions of two molecules are higher. This high rate of collision results in higher kinetic energy, which further affects the activation energy of the reaction. The Arrhenius equation is given by the expression:

\(k = Ae^{−E_a/RT}\)−−−−−−−(1)

Where, k= the rate constant of the reaction,

A= The pre-exponential factor, according to the collision theory, is the frequency of successful collisions between the reacting molecules.

E_a=The activation energy of the chemical reaction (energy per mole).

R=Universal gas constant,

T= absolute temperature (in Kelvin)

The activation energy required by the molecule comes from the surrounding and the Pre-exponential factor is always constant for every reaction. Hence, both of these factors are independent of temperature. Therefore, we can say that rate is a function of temperature as it depends on temperature only.

If we take \(ln\) on both side, we get this equation and now we can plot a graph between \(ln k\) verses \(\frac{1}{T}\),

\(lnk = lnA − \frac{E_a}{RT}\)

The graph can be seen as we get a straight line

We get the equation as above, the slope is given as \(\frac{E_a}{R}\) and intercept as \(lnA\)

Hence, all the given statements are correct.