Concept:The units of the rate constant (\( k \)) depend strictly on the overall reaction order to balance the rate equation.
Formula:$$ \text{Unit of } k = (\text{mol dm}^{-3})^{1-n} \text{s}^{-1} $$
Solution:- For a first-order reaction (\( n = 1 \)):
- Substitute \( n=1 \) into the formula: \( (\text{mol dm}^{-3})^{1-1} \text{s}^{-1} \).
- This simplifies to \( (\text{mol dm}^{-3})^{0} \text{s}^{-1} \).
- Since any value to the power of 0 is 1, the concentration units completely cancel out.
- The final unit for \( k \) is simply \( \text{s}^{-1} \) (or sec\(^{-1}\)).
Why other options are incorrect:Zero order yields \( \text{mol dm}^{-3}\text{s}^{-1} \). Second order yields \( \text{mol}^{-1}\text{dm}^3\text{s}^{-1} \). Third order yields \( \text{mol}^{-2}\text{dm}^6\text{s}^{-1} \).
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