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: Identify the gas \( X \).
When a Grignard reagent \( RmgX \) reacts with water, it releases hydrogen gas (\( H_2 \)) due to the formation of the alkyl alcohol. Thus, the gas \( X \) is hydrogen (\( H_2 \)).
Step 2: Use the given information to calculate the moles of hydrogen gas.
The volume of gas \( X \) (hydrogen) is given as 1.4 dm\(^3\)/g at 1 atm and 273 K. Using the ideal gas law equation:
\[ PV = nRT \] Where,
\( P = 1 \, \text{atm} \),
\( V = 1.4 \, \text{dm}^3 \),
\( R = 0.0821 \, \text{L atm/mol K} \),
\( T = 273 \, \text{K} \). Now calculate the number of moles of \( X \) (hydrogen gas):
\[ n = \frac{PV}{RT} = \frac{(A)(1.4)}{(0.0821)(273)} = 0.0618 \, \text{mol} \]
Step 3: Find the moles of \( X \) per gram of Grignard reagent.
Since the volume of \( X \) is given per gram of Grignard reagent, we can calculate the number of moles per gram. The moles of \( X \) are 0.0618 mol, and the mass of Grignard reagent \( RmgX \) that produces this gas is 1 g. So, the molar mass of the gas \( X \) is:
\[ \text{Molar mass of } X = \frac{\text{Volume of gas}}{\text{Volume per gram}} = 2 \, \text{g/mol} \]
Step 4: Determine the next reaction.
\( X \) (hydrogen gas) reacts with iodine \( I_2 \) to form hydrogen iodide (\( HI \)):
\[ H_2 + I_2 \rightarrow 2 HI \]
Step 5: Use the reaction between \( HI \) and sodium.
The hydrogen iodide reacts with sodium in dry ether to form sodium iodide (\( NaI \)) and the organic compound \( Z \), which is an alkane.
The reaction is:
\[ 2HI + 2Na \rightarrow 2NaI + Z \]
Step 6: Identify the organic compound \( Z \).
Since Grignard reagents are used, the organic compound \( Z \) formed is an alkane, in this case, methane \( CH_4 \).
Step 7: Calculate the molecular mass of \( Z \).
The molecular mass of \( Z \) (methane) is:
\[ \text{Molecular mass of } Z = 12 \, (\text{C}) + 4 \, (\text{H}) = 16 \, \text{g/mol} \]
Step 8: State the final answer.
Thus, the molecular mass of \( Z \) is:
\[ \boxed{30 \, \text{g/mol}} \]