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, we need to follow these steps:

### Step 1: Understand the electrolysis process
When electric current is passed through fused anhydrous MgCl₂, magnesium ions (Mg²⁺) are reduced to form magnesium metal (Mg). The overall reaction can be represented as:
\[ \text{Mg}^{2+} + 2e^- \rightarrow \text{Mg} \]

### Step 2: Calculate the number of moles of magnesium produced
To find the number of moles of magnesium produced from the given charge, we use Faraday's laws of electrolysis. According to Faraday's first law, the amount of substance produced at an electrode is directly proportional to the quantity of electricity passed through the electrolyte.

The charge (Q) passed is given as 9.65 C. The Faraday constant (F), which is the charge required to produce one mole of electrons, is approximately 96500 C/mol.

Since 2 moles of electrons are required to produce 1 mole of magnesium, we can set up the following relationship:

\[ \text{Moles of Mg} = \frac{Q}{n \cdot F} \]

where \( n \) is the number of moles of electrons required per mole of magnesium (which is 2 in this case).

### Step 3: Substitute the values into the formula
Substituting the known values into the equation:

\[ \text{Moles of Mg} = \frac{9.65 \, \text{C}}{2 \cdot 96500 \, \text{C/mol}} = \frac{9.65}{193000} \approx 5.00 \times 10^{-5} \, \text{mol} \]

### Step 4: Relate moles of magnesium to moles of Grignard reagent
The magnesium metal produced is completely converted into a Grignard reagent (MgX, where X is a halogen). Therefore, the number of moles of Grignard reagent formed is equal to the number of moles of magnesium produced.

Thus, the moles of Grignard reagent obtained is also \( 5.00 \times 10^{-5} \, \text{mol} \).

### Final Answer
The number of moles of Grignard reagent obtained is \( 5.00 \times 10^{-5} \, \text{mol} \).

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