10 g of bleaching powder on reaction with KI required 50 mL of 2N hypo solution. Thus, `%` of bleaching powder is

Options

A. `100`
B. `80`
C. `63.5`
D. `35.5`

Explanation

To solve the problem, we need to determine the percentage of bleaching powder in the given sample based on its reaction with hypo (sodium hypochlorite, NaOCl) and potassium iodide (KI). Here’s a step-by-step solution:

### Step 1: Understand the Reaction
The reaction between bleaching powder (Ca(OCl)₂) and potassium iodide (KI) can be represented as follows:

\[ \text{Ca(OCl)}_2 + 2 \text{KI} + \text{H}_2\text{SO}_4 \rightarrow \text{I}_2 + \text{CaCl}_2 + \text{H}_2\text{O} + \text{K}_2\text{SO}_4 \]

From the balanced equation, we see that 1 mole of bleaching powder reacts with 2 moles of KI.

### Step 2: Calculate Moles of Hypo Solution
We are given that 50 mL of 2N hypo solution is used. First, we calculate the number of moles of hypo solution:

\[ \text{Number of moles of hypo} = \text{Normality} \times \text{Volume (in L)} \]

Convert 50 mL to liters:

\[ 50 \text{ mL} = 0.050 \text{ L} \]

Now calculate the moles:

\[ \text{Number of moles of hypo} = 2 \, \text{N} \times 0.050 \, \text{L} = 0.1 \, \text{moles} \]

### Step 3: Relate Moles of Hypo to Moles of Bleaching Powder
From the balanced equation, we know that 2 moles of KI react with 1 mole of bleaching powder. Therefore, the moles of bleaching powder can be calculated as follows:

\[ \text{Moles of bleaching powder} = \frac{\text{Moles of hypo}}{2} = \frac{0.1}{2} = 0.05 \, \text{moles} \]

### Step 4: Calculate the Mass of Bleaching Powder
Next, we need to find the mass of bleaching powder that corresponds to the moles calculated. The molar mass of iodine (I) is approximately 127 g/mol.

Thus, the mass of bleaching powder is:

\[ \text{Mass of bleaching powder} = \text{Moles} \times \text{Molar mass} = 0.05 \, \text{moles} \times 127 \, \text{g/mol} = 6.35 \, \text{g} \]

### Step 5: Calculate the Percentage of Bleaching Powder
Finally, we can calculate the percentage of bleaching powder in the sample:

\[ \text{Percentage of bleaching powder} = \left( \frac{\text{Mass of bleaching powder}}{\text{Total mass of sample}} \right) \times 100 \]

Substituting the values:

\[ \text{Percentage of bleaching powder} = \left( \frac{6.35 \, \text{g}}{10 \, \text{g}} \right) \times 100 = 63.5\% \]

### Conclusion
The percentage of bleaching powder in the sample is **63.5%**.