An alcohol X (C4H10O3) is chiral and absorbs two moles of HIO4 per mol...
X satisfying the given criteria is

Hence, X has four optically active isomers.
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An alcohol X (C4H10O3) is chiral and absorbs two moles of HIO4 per mol...
Explanation:
Chiral alcohol X: Chiral molecules are those molecules that cannot be superimposed on their mirror images. Alcohol X is chiral, which means it has a non-superimposable mirror image.
HIO4 reaction: Alcohol X reacts with two moles of HIO4 per mole of X. This reaction is used to determine the number of stereoisomers present in the molecule.
Number of stereoisomers: The number of stereoisomers for alcohol X can be determined by the number of possible arrangements of its substituents. The number of stereoisomers is given by 2^n, where n is the number of chiral centers.
Formula: Number of stereoisomers = 2^n
Calculations:
- Alcohol X has 4 carbon atoms and 1 oxygen atom, making a total of 5 atoms.
- Out of these 5 atoms, 3 atoms are unique (1 oxygen atom and 2 methyl groups).
- Each of these 3 atoms can have two different arrangements in space, giving a total of 2^3 = 8 possible stereoisomers.
- However, alcohol X has a plane of symmetry perpendicular to the carbon chain. This means that the mirror image of one half of the molecule is identical to the other half.
- Therefore, half of the stereoisomers are identical to the other half, and the actual number of stereoisomers is 8/2 = 4.
Hence, the correct answer is '4'.