Order, Molecularity & Rate Constant
Theoretical vs Experimental Concepts in Chemical Kinetics
1. Rate Law & Order of Reaction
The Order of Reaction is defined as the sum of the powers of the concentration terms of the reactants in the experimentally determined rate law expression.
For reaction $aA + bB \rightarrow \text{Products}$
Rate Law: $\text{Rate} = k[A]^x [B]^y$
Order ($n$) = $x + y$
Rate Law: $\text{Rate} = k[A]^x [B]^y$
Order ($n$) = $x + y$
Characteristics:
- It is an experimental quantity.
- It can be zero, whole number, or fractional.
- It applies to both elementary and complex reactions.
2. Molecularity of Reaction
Molecularity is the number of reacting species (atoms, ions, or molecules) taking part in an elementary reaction that must collide simultaneously to bring about a chemical reaction.
Characteristics:
- It is a theoretical concept.
- It must be a whole number (1, 2, or 3). It cannot be zero or fractional.
- It is defined only for elementary (single-step) reactions.
3. Difference: Order vs Molecularity
| Parameter | Order of Reaction | Molecularity |
|---|---|---|
| Nature | Experimental Quantity | Theoretical Quantity |
| Value | Can be 0, fractional, or integer | Always a whole number (1, 2, 3) |
| Scope | Applicable to elementary & complex reactions | Applicable only to elementary reactions |
| Mechanism | Does not reveal reaction mechanism directly | derived from the mechanism (slowest step) |
4. Unit of Rate Constant ($k$)
The unit of $k$ depends on the order of the reaction ($n$).
General Formula derivation:
$$ k = \frac{\text{Rate}}{(\text{Conc})^n} = \frac{\text{Conc} \cdot \text{time}^{-1}}{(\text{Conc})^n} = (\text{Conc})^{1-n} \cdot \text{time}^{-1} $$
$$ \text{Unit of } k = (mol \cdot L^{-1})^{1-n} \cdot s^{-1} $$
Common Units:
- Zero Order ($n=0$): $mol \cdot L^{-1} \cdot s^{-1}$
- First Order ($n=1$): $s^{-1}$ (time$^{-1}$)
- Second Order ($n=2$): $L \cdot mol^{-1} \cdot s^{-1}$ (or $M^{-1}s^{-1}$)
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