Concept:The equilibrium constants \( K_p \) and \( K_c \) are mathematically identical only when there is no net change in the total number of gaseous moles during the reaction.
Formula:$$ K_p = K_c(RT)^{\Delta n} $$
Solution:- We must find the reaction where \( \Delta n = (\text{Moles of Products}) - (\text{Moles of Reactants}) = 0 \).
- For Option A: \( \Delta n = 2 - 4 = -2 \).
- For Option B: \( \Delta n = (1+1) - 1 = +1 \).
- For Option C: \( \text{H}_2 + \text{I}_2 \rightarrow 2\text{HI} \). Reactants = 1 + 1 = 2. Products = 2. Therefore, \( \Delta n = 2 - 2 = 0 \).
- Because \( \Delta n = 0 \), \( (RT)^0 = 1 \), making \( K_p = K_c \).
Why other options are incorrect:Options A, B, and D all feature a change in the total moles of gas, meaning the \( (RT)^{\Delta n} \) factor will alter the value between \( K_p \) and \( K_c \).
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