Question

Grignard reagent \( RmgX \) reacts with water and releases a gas \( X \) which has volume 1.4 dm\(^3\)/g at 1 atm, 273 K.
\( X \) reacts with \( I_2 \) and forms \( Y \) which reacts with Na in the presence of dry ether to form \( Z \). Find the molecular mass of \( Z \).

Hint:

Grignard reagents react with water to release hydrogen gas, which can be used to determine the molecular mass of the product formed after subsequent reactions. For methane formation, the reaction with iodine and sodium is important.

Answer 1

Correct Answer: 30

Step 1: Understanding the Concept: 
Grignard reagents (\(RMgX\)) react with any active hydrogen source (water, acids, alcohols) to produce an alkane (\(RH\)). 
The identity of the alkane can be determined from its density or molar volume. 
Subsequently, iodination and the Wurtz reaction are standard organic transformations to identify the chain. 

Step 2: Key Formula or Approach: 
Molar mass of gas \(X = \frac{\text{Molar volume at STP}}{\text{Volume per gram}} = \frac{22.4 \text{ L/mol}}{1.4 \text{ L/g}}\) 
Step 3: Detailed Explanation: 
Step 3.1: Identify Gas X 
Reaction: \(RMgX + H_2O \rightarrow RH(g) + Mg(OH)X\). 
The gas released is an alkane \(RH\). 
Given: 1 g of gas X occupies 1.4 \(dm^3\) at STP (273 K, 1 atm). 
Molar volume at STP = 22.4 L/mol. 
\[ \text{Molar mass of X} = \frac{22.4 \text{ L/mol}}{1.4 \text{ L/g}} = 16 \text{ g/mol} \] 
The alkane with molar mass 16 g/mol is Methane (\(CH_4\)). 
Therefore, \(R = CH_3\), and the Grignard reagent was \(CH_3MgX\). 
Step 3.2: Reaction of X with \(I_2\) to form Y 
\[ CH_4 + I_2 \xrightarrow{h\nu \text{ or heat}} CH_3I + HI \] 
\(Y = CH_3I\) (Iodomethane / Methyl iodide). 
Step 3.3: Wurtz Reaction to form Z 
\[ 2CH_3I + 2Na \xrightarrow{\text{dry ether}} CH_3-CH_3 + 2NaI \] 
\(Z = C_2H_6\) (Ethane). 
Step 3.4: Molecular Mass of Z 
\[ M(C_2H_6) = 2(12) + 6(1) = 24 + 6 = 30 \text{ g/mol} \] 
Step 4: Final Answer: 
The molecular mass of `Z' is 30 g/mol.