# Rate constant or Specific Reaction rate

According to collision theory, the rate of the reaction is proportional to the number of molecular collisions taking place per second. Thus on increasing the concentration of the reactant number of collision increases hence rate of the reaction increases.

Thus for a general reaction:

$A \to \text{Products}$

$r = \dfrac{dx}{dt} = -\dfrac{dC_A}{dt} = kC_A$

Where, r =rate of reaction, $C_A$ =concentration of the reactant A and k =rate constant.

If $C_A = 1$ then r = k

We can say that at a given temperature, rate is equal to the rate constant of reaction when concentration of the reactant in unity. Thus rate constant is also known as specific reaction rate.

In the case of two reactants, the reaction may be written as:

$A + B \to \text{Products}$

$r = \dfrac{dx}{dt} = kC_AC_B$

Where all the terms have usual meaning. If $C_A =C_B = 1$ then r = k

Thus rate constant is equal to rate of the reaction when concentration of each of the reactants is unity.

The value of k depends only upon:

(i) Temperature, (ii) Nature of Reactant, (iii) Presence of catalyst.

• $k \propto C$ Concentration or Pressure

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