A currrent of 5.0 A flows for 4.0 h through an electrlytic cell containing a molten salt of metalM. This results in deposition of 0.25 mol of the metal M at the cathode. The oxidation state of M in the molten salt is : (1 Faraday=`96485 C "mol"^(-1)`)

Answer

To determine the oxidation state of metal M in the molten salt, we will follow these steps:

### Step 1: Calculate the total charge (Q) passed through the electrolytic cell.
We know that current (I) is given as 5.0 A and the time (t) is 4.0 hours. First, we need to convert the time from hours to seconds.

\[ t = 4.0 \text{ hours} \times 60 \text{ minutes/hour} \times 60 \text{ seconds/minute} = 14400 \text{ seconds} \]

Now, we can calculate the total charge using the formula:

\[ Q = I \times t \]

Substituting the values:

\[ Q = 5.0 \, \text{A} \times 14400 \, \text{s} = 72000 \, \text{C} \]

### Step 2: Use the relationship between charge, moles of metal deposited, and the number of electrons involved.
We know that the number of moles of metal M deposited (n) is 0.25 mol. The relationship between charge (Q), number of moles (n), number of electrons transferred (N), and Faraday's constant (F) is given by:

\[ n = \frac{Q}{N \times F} \]

Where:
- \(F = 96485 \, \text{C/mol}\) (Faraday's constant)

Rearranging the formula to find N:

\[ N = \frac{Q}{n \times F} \]

### Step 3: Substitute the known values into the equation.
Substituting the values we have:

\[ N = \frac{72000 \, \text{C}}{0.25 \, \text{mol} \times 96485 \, \text{C/mol}} \]

Calculating the denominator:

\[ 0.25 \times 96485 = 24121.25 \, \text{C} \]

Now substituting back into the equation for N:

\[ N = \frac{72000}{24121.25} \approx 2.99 \approx 3 \]

### Step 4: Determine the oxidation state of metal M.
The number of electrons (N) corresponds to the oxidation state of the metal. Since we found that \(N \approx 3\), the oxidation state of metal M in the molten salt is:

\[ \text{Oxidation state of M} = +3 \]

Thus, metal M is present as \(M^{3+}\).

### Final Answer:
The oxidation state of metal M in the molten salt is +3.

---