When 15.0 g of a polyhydroxy compound Q is completely acetylated with acetic anhydride in pyridine, 31.8 g of an acetylated compound is formed. How many grams of a completely methylated product of Q will be formed when, Q is completely methylated with $C H_{3} I / A g_{2} O$ ?

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Solution

Let the molar mass of the polyhydroxy compound be M and it contains n number of $O H$ groups.

Then molar mass of completely acetylated compound will be $(M + 42 \times n)$ and that of the completely methylated compound be $(M + 14 \times n)$ .

Since 15 g of Q is completely acetylated to form 31.8 g of the acetylated compound, the number of moles of both compounds will be the same.
$\frac{15}{M} \times (M + 42 n) = 31.8$
$\Rightarrow n = \frac{16.8 M}{630}$

Hence, mass of completely methylated compound when 30 g of Q is completely methylated.
$= \frac{30}{M} \times (M + 14 n)$
$= \frac{30}{M} \times (M + 14 \times \frac{16.8 M}{630})$
$= 41.2 g$

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