2.24 ml of a gas 'X' is produced at STP by the action of 4.6 mg of a alcohol (ROH) with methyl magnesium iodide the molecular mass of alcohol and the gas 'X' are respectively

Options

A. 0,46, `CH_4`
B. 4,6,`C_2H_6`
C. 46,`CH_4`
D. 46,`C_2H_4`

Answer

To solve the problem, we need to determine the molecular mass of the alcohol (ROH) and the gas (X) produced during the reaction. The gas produced is methane (CH₄), and we will follow these steps:

### Step 1: Understand the Reaction
The reaction involves an alcohol (ROH) reacting with methyl magnesium iodide (CH₃MgI) to produce methane (CH₄) and a magnesium salt.

### Step 2: Use the Volume of Gas at STP
We know that 2.24 mL of gas (CH₄) is produced at Standard Temperature and Pressure (STP). At STP, 1 mole of gas occupies 22,400 mL.

### Step 3: Calculate Moles of Gas Produced
To find the moles of CH₄ produced:
\[ \text{Moles of CH₄} = \frac{\text{Volume of gas (mL)}}{22,400 \text{ mL/mol}} = \frac{2.24 \text{ mL}}{22,400 \text{ mL/mol}} = 1 \times 10^{-4} \text{ mol} \]

### Step 4: Determine Moles of Alcohol (ROH) Required
From the stoichiometry of the reaction, we can assume that 1 mole of ROH produces 1 mole of CH₄. Therefore, the moles of ROH required to produce \(1 \times 10^{-4}\) moles of CH₄ is also \(1 \times 10^{-4}\) moles.

### Step 5: Convert Mass of Alcohol to Moles
We are given that the mass of alcohol (ROH) is 4.6 mg. We need to convert this mass into grams:
\[ 4.6 \text{ mg} = 4.6 \times 10^{-3} \text{ g} \]

### Step 6: Use the Formula for Moles
The formula for moles is:
\[ \text{Moles} = \frac{\text{Mass (g)}}{\text{Molecular Weight (g/mol)}} \]
Substituting the known values:
\[ 1 \times 10^{-4} = \frac{4.6 \times 10^{-3}}{M} \]
Where \(M\) is the molecular weight of ROH.

### Step 7: Solve for Molecular Weight of Alcohol (ROH)
Rearranging the equation to find \(M\):
\[ M = \frac{4.6 \times 10^{-3}}{1 \times 10^{-4}} = 46 \text{ g/mol} \]

### Step 8: Identify the Molecular Mass of Gas X
The gas produced (X) is methane (CH₄), which has a molecular mass of:
\[ \text{C} (12 \text{ g/mol}) + 4 \times \text{H} (1 \text{ g/mol}) = 12 + 4 = 16 \text{ g/mol} \]

### Final Answer
The molecular mass of the alcohol (ROH) is 46 g/mol, and the molecular mass of the gas (X, which is CH₄) is 16 g/mol.

### Summary
- Molecular mass of alcohol (ROH): **46 g/mol**
- Molecular mass of gas (X, CH₄): **16 g/mol**

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