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Question

Explain Rate law and Rate constant with an example.

Vidyadip · Accepted Answer

→ Rate of a reaction depends upon the concentration of reactants.
→ Consider a general reaction
$
→ aA + bB \rightarrow cC + dD
$
where $a , b , c$ and d are the stoichiometric coefficients of reactants and products.
→ The rate expression for this reaction is Rate $\alpha[ A ]^{ x }[ B ]^{ y }$
where exponents x and y may or may not be equal to the stoichiometric coefficients (a and b) of the reactants. Above equation can also be written as
$\begin{array}{l}\text { Rate }= k [ A ]^{ x }[ B ]^{ y } \\ -\frac{ d [ A ]}{ dt }= k [ A ]^{ x }[ B ]^{ y }\end{array}$
→ This form of equation is known as differential rate equation,
→ where k is proportionality constant called rate constant.
→ The equation which relates the rate of reaction to concentration of reactants is called rate law or rate expression.
→ "Thus, rate law is the expression in which reaction rate is given in terms of molar concentration of reactants with each term raised to some power, which may or may not be same as stoichiometric coefficient of the reacting species in a balanced equation."
→ For example : $2 NO ( g )+ O _2(g) \rightarrow 2 NO _2(g)$ the rate equation for this reaction will be
$
\text { Rate }= k [ NO ]^2\left[ O _2\right]
$
→ This differential form of this rate expression is given as
$
-\frac{ d [ R ]}{ dt }= k [ NO ]^2\left[ O _2\right]
$
→ Some other examples are given below :
Reaction
1. $CHCl _3+ Cl _2 \rightarrow CCl _4+ HCl$
2. $CH _3 COOC _2 H _5+ H _2 O \rightarrow CH _3 COOH +$ $C _2 H _5 OH$
Experimental rate expression
$
\begin{array}{l}
\text { Rate }= k \left[ CHCl _3\right] \cdot\left[ Cl _2\right]^{\frac{1}{2}} \\
\text { Rate }= k \left[ CH _3 COOC _2 H _5\right]\left[ H _2 O \right]^0
\end{array}
$
→ In these reactions, the exponents of the concentration terms are not the same as their stoichiometric coefficients. Thus, we can say that:
→ Rate law for any reaction cannot be predicted by merely looking at the balanced chemical equation. i.e. theoretically but must be determined experimentally.

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