Question

Fill up the following with suitable terms
(i) Activation energy=threshold energy-________.
(ii) Half-life period of zero order reaction=_____.
(iii) Average rate of the reaction=.
(iv) Instantaneous rate of reaction=.
(a) Potential energy, $\dfrac{0.693}{k}$,$\dfrac{dx}{dt}$,$\dfrac{\Delta [A]}{\Delta t}$
(b) Energy of the reactants, $\dfrac{1}{k}$,$\dfrac{\Delta [A]}{\Delta t}$,$\dfrac{dx}{dt}$
(c) Energy of reaction, $\dfrac{\log k}{t}$,$\dfrac{\Delta [A]}{\Delta t}$,$\dfrac{dx}{dt}$
(d) Average kinetic energy of reactant, $\dfrac{a}{2k}$,$\dfrac{\Delta [A]}{\Delta t}$,$\dfrac{dx}{dt}$

Answer 1

Hint: All the terms above are related to chemical kinetics. It describes the rate of the reaction and how it depends on certain factors such as time, temperature, pressure and volume of the reactants and products in a reaction.

Complete step-by-step answer:
The activation energy is the excess energy required to break the bonds in reactants and then convert it to products. Threshold energy is energy required to break the bonds of reactant. Therefore, Activation energy=threshold energy –average kinetic energy of reactant.
Half life of a reaction is the time required for the reaction to complete half of the initial concentration of the reactant. For a zero order reaction the half life = ${{t}_{\dfrac{1}{2}}}=\dfrac{a}{2k}$
Average rate of a reaction is the change in concentration of any of the reactants or any product per unit time in a specific interval of time. It is given by r. It is a change in concentration divided by the time interval.
Average rate of the reaction=$\dfrac{\Delta [A]}{\Delta t}$
Instantaneous rate of reaction is the rate of change of any reactant or any of the products at a particular time for that particular reaction. dx is the change in concentration of product in infinitesimally small intervals of time dt , then instantaneous rate of reaction will be $\dfrac{dx}{dt}$.
Thus, Instantaneous rate of reaction =$\dfrac{dx}{dt}$
Therefore the correct order of the answers is option (d).
Average kinetic energy of reactant, $\dfrac{a}{2k}$,$\dfrac{\Delta [A]}{\Delta t}$,$\dfrac{dx}{dt}$

Note: Average rate of reaction and instantaneous rate of reaction are different. Average rate of reaction is over a large period of time, while the instantaneous rate of reaction is over an infinitesimally small period of time.