The temperature dependence of a reaction rate can be represented by the Arrhenius equation

\[K =Ae^{-E_a/RT}\]

The pre-exponential factor \(A\) is called the frequency factor and \(E_a\) is the energy of activation. The unit of \(E_a\) is J/mol or Kcal/mol.

The rate constants at two different temperatures are related as

\[log\frac{K_2}{K_1} = \frac{E_a}{2.303R}\left[\frac{T_2 – T_3}{T_1T_2}\right]\]

Log K versus 1/T gives a linear graph with negative slope. The reactant molecules collide with each other to cross over an energy barrier existing between the reactants and products. If the value of the difference in the internal energies of reactants and product is positive, the reaction is exothermic and if it is negative, the reaction is endothermic. If the temperature is raised the kinetic energy of the molecules increases which causes increase in (i) number of collisions (ii) number of molecules halving higher energy than threshold energy. For every 10°C rise in temperature, the increase in kinetic energy is about 3.3%. So the increase in number of collisions is about \(\sqrt{3.3}\) . , i.e., 1.8%. Hence the rate of reaction must increase only by about 1.8%. For every 10°C rise in temperature, the rate of reaction increases by 100%, i.e., two times If the rate of reaction is doubled for every rise of 10 K temperature, the rate of reaction increased for rise of temperature from 30°C to 80°C is 32 times. The activation energy does not depend on the concentration. The ratio of the rate constants at two different temperatures (preferably 35°C and 25°C) is known as temperature coefficient. If the activation energy is zero, then all the collisions will be fruitful and the reaction is 100% complete.

Identify the false statement from the following:

A reaction with high activation energy proceeds rapidly when temperature is lowered

The correct answer is option 4. A reaction with high activation energy proceeds rapidly when temperature is lowered.

Here are the explanations for the statements:

• Threshold energy: It is the minimum energy that the colliding molecules must have in order to react and form products. If the colliding molecules do not have enough energy, they will not be able to react and the reaction will not occur.
• Activation energy: It is the difference between the threshold energy and the average kinetic energy of the reactants. The activation energy is the energy that must be supplied to the reactants in order for them to react.
• Nature of the reactants: The activation energy for a specific reaction depends primarily on the nature of the reactants. This is because the activation energy is determined by the strength of the bonds that must be broken in order for the reaction to occur.
• Temperature: The temperature of a reaction affects the rate of the reaction by affecting the kinetic energy of the reactants. As the temperature increases, the kinetic energy of the reactants increases. This means that more of the reactants have enough energy to react, which increases the rate of the reaction.

Therefore, a reaction with high activation energy proceeds slowly when the temperature is lowered.