Relative Rf Value of Alcohol Product from Hydration

To determine the $R_f$ value of the major organic product $(X)$, we analyze the chemical reaction and the fundamental principles of thin-layer chromatography (TLC).

Step 1: Identification of Product $(X)$

When 2-methylpropene is treated with dilute $\text{H}_2\text{SO}_4$, it undergoes acid-catalyzed hydration via Markovnikov's addition:

$\text{(CH}_3)_2\text{C=CH}_2 + \text{H}_2\text{O} \xrightarrow{\text{dil. H}_2\text{SO}_4} \text{(CH}_3)_3\text{C-OH}$

The major organic product $(X)$ is 2-methylpropan-2-ol ($tert$-butyl alcohol).

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Step 2: Principle of Retardation Factor ($R_f$) in Chromatography

The retardation factor ($R_f$) is given by:

$R_f = \frac{\text{Distance travelled by the compound}}{\text{Distance travelled by the solvent front}}$

In standard thin-layer chromatography:

1. The stationary phase (e.g., silica gel) is highly polar.
2. The mobile phase carries the compounds up the adsorbent layer.
3. Polarity Relationship:
   • More polar compounds adsorb more strongly onto the polar stationary phase, moving a shorter distance, which results in a lower $R_f$ value.
   • Less polar compounds adsorb weakly, moving a larger distance with the solvent front, which results in a higher $R_f$ value.

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Step 3: Comparison of Polarities and $R_f$ Values

• 2-methylpropene: An alkene, which is non-polar / weakly polar. Its given $R_f$ value is $0.42$.
• 2-methylpropan-2-ol $(X)$: An alcohol with a hydroxyl ($-\text{OH}$) group, which is highly polar and forms strong hydrogen bonds with the stationary phase.

Since product $(X)$ is significantly more polar than 2-methylpropene:

$\text{Polarity: } \text{2-methylpropan-2-ol } (X) > \text{2-methylpropene}$

Consequently, product $(X)$ moves slower and has a smaller $R_f$ value than 2-methylpropene:

$R_f(X) < R_f(\text{2-methylpropene}) = 0.42$

Among the given options ($0.42$, $0.82$, $0.62$, and $0.12$), the only value less than $0.42$ is $0.12$.

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Conclusion

The $R_f$ value for product $(X)$ under identical conditions is $0.12$.

Correct Option: D