Step 1: Understanding the Concept:
This reaction is a classic example of Nucleophilic Aromatic Substitution ($S_NAr$).
Aromatic rings are generally resistant to nucleophilic attack due to electron-rich $\pi$-clouds, but substitution becomes possible if the ring is substituted with strong electron-withdrawing groups (EWGs) like nitro groups ($-NO_2$).
The $S_NAr$ mechanism is most effective when the EWGs are located at ortho or para positions relative to the leaving group (the halogen).
These groups stabilize the negatively charged transition state (Meisenheimer complex) by delocalizing the charge onto the oxygen atoms.
Step 2: Key Formula or Approach:
1. Examine the positions of the Chlorine atoms (leaving groups) relative to the Nitro groups (activating groups).
2. Chlorine at C1 is ortho to $-NO_2$ at C2 and para to $-NO_2$ at C5.
3. Chlorine at C3 is ortho to $-NO_2$ at C2 and para to $-NO_2$ at C5.
4. Both Cl atoms are highly activated for substitution.
Step 3: Detailed Explanation:
The starting material is 1,3-dichloro-2,5-dinitrobenzene.
The methoxide ion ($MeO^-$) is a strong nucleophile. In the presence of methanol and heat, it attacks the ring carbons bearing the chlorine atoms.
Since the nitro groups are positioned perfectly to activate both chlorine atoms, the reaction does not stop at a single substitution if heat and excess nucleophile are provided.
First, one methoxide ion attacks at C1, forming a Meisenheimer intermediate where the negative charge is delocalized into the nitro groups at C2 and C5. The subsequent loss of the chloride ion ($Cl^-$) restores aromaticity, yielding 1-chloro-3-methoxy-2,5-dinitrobenzene.
Because the second chlorine at C3 is also equally activated by the same nitro groups, another methoxide ion attacks C3 in a similar manner.
Under heating conditions, both activated chlorine atoms are replaced by methoxy groups.
The final major product is 1,3-dimethoxy-2,5-dinitrobenzene. This product matches the structure provided in Figure C.
Step 4: Final Answer:
The reaction leads to the replacement of both chlorine atoms by methoxy groups because both positions are ortho/para activated by nitro groups. The correct option is (C).