A current strength of `1.0A` is passed for `96.5 s` through `100mL` of a solution of `0.05 M KCl`. The concentration of the final solution with respect to `overset(c-)(O)H` ions is

Options

A. `0.005M`
B. `0.05M`
C. `0.01M`
D. `0.001M`

Explanation

To solve the problem step by step, we will follow the electrolysis process and calculate the concentration of hydroxide ions (OH⁻) produced.

### Step 1: Calculate the total charge (Q) passed through the solution
The total charge can be calculated using the formula:
\[ Q = I \times t \]
where:
- \( I \) is the current in amperes (A)
- \( t \) is the time in seconds (s)

Given:
- \( I = 1.0 \, A \)
- \( t = 96.5 \, s \)

Calculating \( Q \):
\[ Q = 1.0 \, A \times 96.5 \, s = 96.5 \, C \]

**Hint**: Remember that the charge is the product of current and time.

### Step 2: Calculate the number of moles of electrons (n)
To find the number of moles of electrons, we use Faraday's constant:
\[ n = \frac{Q}{F} \]
where:
- \( F \) (Faraday's constant) = 96500 C/mol

Calculating \( n \):
\[ n = \frac{96.5 \, C}{96500 \, C/mol} \approx 0.001 \, mol \]

**Hint**: Faraday's constant relates the charge to the amount of substance in moles.

### Step 3: Determine the equivalents of OH⁻ produced
In the electrolysis of KCl solution, water is reduced at the cathode to produce hydrogen gas and hydroxide ions (OH⁻). The generation of 1 mole of OH⁻ requires 1 mole of electrons. Therefore, the number of equivalents of OH⁻ produced is equal to the number of moles of electrons.

Thus, the equivalents of OH⁻ produced:
\[ \text{Equivalents of OH⁻} = n = 0.001 \, eq \]

**Hint**: Each mole of electrons corresponds to one equivalent of hydroxide ions produced.

### Step 4: Calculate the concentration of OH⁻ in the final solution
To find the concentration of OH⁻ ions in molarity (M), we use the formula:
\[ \text{Concentration (M)} = \frac{\text{Equivalents}}{\text{Volume in L}} \]

Given that the volume of the solution is 100 mL, we convert it to liters:
\[ \text{Volume} = 100 \, mL = 0.1 \, L \]

Calculating the concentration:
\[ \text{Concentration of OH⁻} = \frac{0.001 \, eq}{0.1 \, L} = 0.01 \, M \]

**Hint**: Molarity is calculated by dividing the number of equivalents by the volume of the solution in liters.

### Final Answer
The concentration of the final solution with respect to OH⁻ ions is **0.01 M**.