Concept:The overall unit for the equilibrium constant \( K_c \) is derived from the difference in the stoichiometric coefficients of gaseous products and reactants.
Formula:$$ \text{Units} = (\text{mol/dm}^3)^{\Delta n} $$
Solution:- First, calculate \( \Delta n = \text{Moles of Products} - \text{Moles of Reactants} \).
- The balanced equation is \( \text{PCl}_5 \rightleftharpoons \text{PCl}_3 + \text{Cl}_2 \).
- Moles of Reactants = 1 (from \( \text{PCl}_5 \)).
- Moles of Products = 1 + 1 = 2 (from \( \text{PCl}_3 \) and \( \text{Cl}_2 \)).
- \( \Delta n = 2 - 1 = 1 \).
- Therefore, the unit is \( (\text{mol/dm}^3)^1 = \text{mol/dm}^3 \).
Why other options are incorrect:Option A is the unit if \( \Delta n = -1 \). Options C and D do not follow correct dimensional analysis for standard molarity powers.
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