Concept:The generic formula to find the units of a rate constant (\( k \)) for an \( n \)-th order reaction is derived from equating rate units with concentration units.
Formula:$$ \text{Unit of } k = (\text{mol dm}^{-3})^{1-n} \text{s}^{-1} $$
Solution:- We are given the unit: \( \text{dm}^{3}\text{mol}^{-1}\text{s}^{-1} \).
- This can be rewritten as \( (\text{mol dm}^{-3})^{-1} \text{s}^{-1} \).
- Comparing this to the generic formula, we set the exponents equal: \( 1 - n = -1 \).
- Solving for \( n \): \( n = 2 \).
- Therefore, it is a second-order reaction.
Why other options are incorrect:First order gives \( \text{s}^{-1} \). Zero order gives \( \text{mol dm}^{-3}\text{s}^{-1} \). Third order gives \( \text{dm}^{6}\text{mol}^{-2}\text{s}^{-1} \).
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