Rate Law
The relationship between the rate of a reaction and the concentration of the reactants is given by rate law. For example, the rate of the decomposition of \(PCl_5\) at high temperature as per the equation \(PCl_5 \rightarrow PCl_3 + Cl_2\) was found to be directly proportional to the concentration of \(PCl_5\).
\[Rate \propto [PCl_5]\]
To equate the left hand side to the right hand side, a proportionality constant \(k\), called the rate constant is introduced.
\[Rate = k[PCl_5]\]
The rate constant is the rate of the reaction if the concentration of the reactant was 1.
As we have seen above the rate of a reaction is directly proportional to the concentration of the reactant and if we have multiple reactants, if will be proportional to the product of the concentrations of the reactants.
As an example, for the reaction given below;
\[aA + bB \rightarrow Products\]
the rate equation can be written as follows;
\[r = k[A]^m[B]^n\]
You would have noticed that the concentrations of A and B have been raised to powers m and n respectively. These powers are also different from the stoichiometric coefficients of A and B in the reaction. These powers to which the concentration terms are raised to in the rate equation is the order of the reaction with respect to that reactant. The sum of these powers is the overall order of the reaction.
\[\text {Order with respect to A} = m\]
\[\text {Order with respect to B} = n\]
\[\text{Overall order of the reaction} = m + n\]
Order of a reaction has to be experimentally found out. The order of a reaction gives us an idea of the times the rate of the reaction will change (increase / decrease) by changing the concentration. The order with respect to the reactants are not the stoichiometric coefficients unless the reaction is an elementary reaction (happens in single step).
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