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Chapter 4: Problem 138

Reaction of a compound having the molecular formula \(\mathrm{C}_{4} \mathrm{H}_{10} \mathrm{O}_{3}\) with acetyl chloride gave a derivative with molar mass \(190 \mathrm{~g} \mathrm{~mol}^{-1} .\) The number of hydroxyl groups in the compound is (a) 1 (b) 2 (c) 3 (d) 0

Short Answer

Expert verified
Answer: 2

Step by step solution

01

Find the molar mass of the given compound

To find the molar mass of the given compound with molecular formula \(\mathrm{C}_{4}\mathrm{H}_{10}\mathrm{O}_{3}\), we must use the atomic masses of the elements (C, H, and O) and calculate their total mass. Molar mass of the compound = \((4\times 12)+(10\times 1)+(3\times 16) = 48 + 10 + 48 = 106\mathrm{~g} \mathrm{~mol}^{-1}\).
02

Calculate the molar mass difference between the given compound and its derivative

The molar mass difference between the two compounds is the difference in their molar mass: Molar mass difference = \((190 - 106) \mathrm{~g} \mathrm{~mol}^{-1} = 84\mathrm{~g} \mathrm{~mol}^{-1}\).
03

Determine the number of hydroxyl groups

Since the acetyl chloride reacts with hydroxyl groups to form acetyl derivatives, the number of hydroxyl groups can be determined from the increase in molar mass. An acetyl group (CH3CO) has a molar mass of \((3\times 12)+(1\times 1)+ (1\times 16)=42\mathrm{~g} \mathrm{~mol}^{-1}\). Now, we need to see how many acetyl groups were added to the compound. In other words, we need to find to how many groups of "42" the difference corresponds: Number of acetyl groups added = \(\frac{84}{42}=2\). Since each hydroxyl group in the compound reacts with one acetyl group, the number of hydroxyl groups in the compound is 2. Therefore, the correct answer is (b) 2.

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