Question

RMgI when treated with ice cold water liberated a gas which occupied 1.4 dm$^3$/g at STP. The gas produced is further reacted with iodine in presence of $HIO_3$ to give compound (X). Compound (X) in presence of Na and dry ether produced compound (Y). Molar mass of compound (Y) is ______ g mol$^{-1}$. (Nearest integer)}

Answer 1

Correct Answer: 30

Step 1: Understanding the Concept:
Grignard reagents react with compounds containing active hydrogen (like water) to produce alkanes. The molar mass of the liberated gas identifies the alkyl group R. Subsequent reactions include the iodination of alkanes and the Wurtz reaction.
: Key Formula or Approach:
1. Reaction: $RMgI + H_2O \to RH + Mg(OH)I$.
2. Molar mass $M = \frac{\text{Molar Volume at STP}}{\text{Specific Volume}}$.
3. Wurtz Reaction: $2R-X + 2Na \xrightarrow{\text{ether}} R-R + 2NaX$.
Step 2: Detailed Explanation:
1. Identification of the gas:
Molar volume at STP = 22.4 L/mol = 22.4 dm$^3$/mol.
Specific volume of the gas = 1.4 dm$^3$/g.
Molar mass of the gas ($RH$) = $\frac{22.4 \text{ dm}^3/\text{mol}}{1.4 \text{ dm}^3/\text{g}} = 16 \text{ g/mol}$.
The alkane with molar mass 16 is Methane ($CH_4$). Thus, the alkyl group $R$ is Methyl ($-CH_3$).
2. Formation of Compound (X):
Methane reacts with $I_2$ in the presence of $HIO_3$ (which removes $HI$ to prevent the reversible reaction):
$CH_4 + I_2 \xrightarrow{HIO_3} CH_3I + HI$.
So, Compound (X) is Methyl iodide ($CH_3I$).
3. Formation of Compound (Y):
Methyl iodide undergoes the Wurtz reaction with Sodium in dry ether:
$2CH_3I + 2Na \xrightarrow{\text{ether}} CH_3-CH_3 + 2NaI$.
So, Compound (Y) is Ethane ($C_2H_6$).
4. Molar mass of (Y):
Molar mass of $C_2H_6 = 2(12) + 6(1) = 30 \text{ g/mol}$.
Step 3: Final Answer:
The molar mass of compound (Y) is 30 g mol$^{-1}$.