Step 1: Understanding Equivalent Weight Formula
Equivalent weight \( E \) is given by:
\[
E = \frac{\text{Molar mass} (M)}{\text{n-factor}}
\]
where \( n \)-factor is the number of replaceable hydrogen or electrons involved in the reaction.
Step 2: Calculating Equivalent Weights
- \( Na_2CO_3 \) (Sodium Carbonate):
- Acts as a dibasic salt (providing 2 \( Na^+ \)), so \( n = 2 \).
- Equivalent weight = \( \frac{M}{2} \).
- (A - III).
- \( KMnO_4 | H^+ \) (Acidic Medium):
- In acidic medium, Mn changes from +7 to +2, i.e., 5-electron transfer.
- Equivalent weight = \( \frac{M}{5} \).
- (B - I).
- \( K_2Cr_2O_7 | H^+ \) (Acidic Medium):
- In acidic medium, Cr changes from +6 to +3, meaning a total 6-electron transfer.
- Equivalent weight = \( \frac{M}{6} \).
- (C - IV).
- \( KMnO_4 | H_2O \) (Neutral/Basic Medium):
- In neutral or basic medium, Mn changes from +7 to +4, i.e., 3-electron transfer.
- Equivalent weight = \( \frac{M}{3} \).
- (D - II).
Thus, the correct matching is A - III; B - I; C - IV; D - II.
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