See image — Isomerism and Stereochemistry Chemistry Question

💡 Solution & Explanation

Concept: In a Fischer projection, the molecule is drawn with the carbon chain vertical. For a molecule with one chiral center like lactic acid (2-hydroxypropanoic acid), we need to count all possible Fischer projection representations by considering all allowed rotations and permutations of the four substituents. Step 1: Identify the molecule. Lactic acid has one chiral center (C2) with four different substituents: CO2H, OH, H, and CH3. It exists as two enantiomers: d (R or S, one configuration) and l (the other configuration). Step 2: Count representations per enantiomer. In a Fischer projection, the vertical bonds go back (into the page) and horizontal bonds come forward (out of the page). For a given configuration (say l-lactic acid), we can place any of the 4 substituents at the top of the vertical chain. However, in standard Fischer projections, the chain must be vertical, so we fix which groups are on the vertical axis (the carbon chain: CO2H and CH3) vs. horizontal. Step 3: More precisely, for a tetrahedral carbon in a Fischer projection, there are 4! = 24 ways to arrange 4 substituents in the four positions (top, bottom, left, right). However, certain rotations of the Fischer projection by 180° in the plane give the same configuration (valid operations), while 90° rotations or flipping give the enantiomer. For each enantiomer, the number of distinct Fischer projection representations (considering all possible assignments of groups to the four positions of a cross) is 4!/2 = 12 per enantiomer, but we must also consider that in a Fischer projection the top and bottom are on the vertical (chain) and left/right are horizontal. Step 4: For each enantiomer, the number of valid Fischer projections: We have 4 substituents to place in 4 positions. The total arrangements = 4! = 24. Each unique 3D configuration corresponds to 4!/2 = 12 Fischer projections (since half the 24 permutations give one enantiomer and half give the other). So for d-lactic acid: 12 representations, for l-lactic acid: 12 representations. Step 5: Total representations for both d and l = 12 + 12 = 24. Why other options fail: - (a) 8: Undercounts; does not account for all permutations of substituents in the cross. - (b) 12: This would be the count for only one enantiomer (d or l), not both. - (d) 36: Overcounts; there is no valid combinatorial basis for 36. Therefore, the correct answer is C.