9.65 C of electric current is passed through fused anhydrous `MgCl_(2)` . The magnesium metal thus obtained is completely converted into a Grignard reagent. The number of moles of Grignard reagent obtained is :

Options

A. `5xx10^(-4)`
B. `1xx10^(-4)`
C. `5xx10^(-5)`
D. `1xx10^(-5)`

Explanation

To solve the problem step by step, we need to determine how many moles of Grignard reagent are produced when 9.65 C of electric current is passed through fused anhydrous MgCl₂.

### Step 1: Understand the electrolysis of MgCl₂
When an electric current is passed through molten MgCl₂, magnesium ions (Mg²⁺) are reduced to magnesium metal (Mg) at the cathode. The half-reaction for the reduction of magnesium ions is:
\[ \text{Mg}^{2+} + 2e^- \rightarrow \text{Mg} \]

This indicates that 2 moles of electrons are required to produce 1 mole of magnesium.

### Step 2: Calculate the number of moles of electrons used
To find out how many moles of electrons correspond to the charge passed (9.65 C), we can use Faraday's constant (F), which is approximately 96500 C/mol. The number of moles of electrons (n) can be calculated using the formula:
\[ n = \frac{Q}{F} \]
where \( Q \) is the charge in coulombs.

Substituting the values:
\[ n = \frac{9.65 \, \text{C}}{96500 \, \text{C/mol}} \]

### Step 3: Perform the calculation
Calculating the moles of electrons:
\[ n = \frac{9.65}{96500} \approx 0.0001 \, \text{mol} \]

### Step 4: Calculate the moles of magnesium produced
Since 2 moles of electrons produce 1 mole of magnesium, we can find the moles of magnesium produced using the relationship:
\[ \text{Moles of Mg} = \frac{\text{Moles of electrons}}{2} \]
Substituting the value we calculated:
\[ \text{Moles of Mg} = \frac{0.0001}{2} = 0.00005 \, \text{mol} \]

### Step 5: Determine the moles of Grignard reagent produced
Since the problem states that all the magnesium produced is converted into Grignard reagent, the moles of Grignard reagent produced will be equal to the moles of magnesium produced:
\[ \text{Moles of Grignard reagent} = \text{Moles of Mg} = 0.00005 \, \text{mol} \]

### Final Answer
The number of moles of Grignard reagent obtained is:
\[ \text{0.00005 mol} \]