## CHEMICAL KINETICS

**The branch of physical chemistry is associated with the study of the rate of reaction (how fast or slow a reaction occurs) and also the mechanism of chemical reactions.**

Unlike thermodynamics, it also gives us insight into the actual pathway of reaction to convert a reactant into a product.

### RATE OF REACTION:

**The rate of a reaction is defined as the change in the concentration of reacting species (reactant) or change in the concentration of product per unit time.**

Mathematically,

\[Rate\; =\; \frac{Change\; in\; the\; concentration\; of\; product/reactant}{Time\; taken}\]

\[Rate\; =\; \frac{\Delta x}{\Delta t}\]

### Instantaneous rate of reaction:

We know that the slope of the concentration-time graph is not a straight line so to measure the slope of this graph we have to first divide the path into infinitesimally small intervals in such a way that the slope of each interval is a straight line.When we measure rate for extremely small intervals of time we call that rate an instantaneous rate of reaction.

\[Instantaneous\; rate\; =\; \frac{dx}{dt}\]

To calculate the overall rate of reaction, we add up slopes of all the intervals of time or by applying integration over it. If there are 'n' number of intervals then the overall rate of reaction will be

\[Rate\; of\; reaction =\; \int\limits_{1}^{n} \frac{dx}{dt}\]

**The rate of reaction w.r.t reactant will be**

**The rate of reaction w.r.t product will be**

### UNIQUE RATE:

**Unique rate is defined as the rate of increase in the concentration of product or decrease in the concentration of reactant divided by the coefficient of that species in a balanced chemical equation.**

It is the same for each species in a chemical reaction while on the other hand, the average rate may be different. Therefore average rate may not be equal to the unique rate.

Unique rate is positive for products and negative for reactants as the concentration of product increases and concentration of reactant decreases.

Consider a hypothetical reaction,

\[aA\; +bB\; \rightarrow \;cC\; +\;dD\]

The unique rate for the reaction is

\[Unique\; Rate\; =\; -\frac{1}{a}.\frac{d[A]}{dt}\; =\; -\frac{1}{b}.\frac{d[B]}{dt}\; =\; +\frac{1}{c}.\frac{d[C]}{dt}\; =\; -\frac{1}{d}.\frac{d[D]}{dt}\]

#### For example,

\[N_{2}\; +\; 3H_{2}\; \rightleftharpoons\; 2NH_{3}\]In this reaction, the rate of reaction of the nitrogen molecule, the hydrogen molecule, and the ammonia are not same because all these molecules have different number of moles(coefficient) in the balanced chemical equation. The rate of reaction hydrogen is three times the rate of reaction of nitrogen.

The unique rate of the given reaction will be:

\[Unique\; Rate\; =\; -\frac{1}{1}.\frac{d[N_{2}]}{dt}\; =\; -\frac{1}{3}.\frac{d[H_{2}]}{dt}\; =\; +\frac{1}{2}.\frac{d[NH_{3}]}{dt}\]