`1.0g` of `a` sample containing `NaCl, KCl` and some inert impurity is dissolved in excess of water and treated with excess of `AgNO_(3)` solution. `A 2.0 g` precipitate to `AgCl` separate out. Also sample is `23%` by mass in sodium. Determine mass percentage of `KCl` in the sample :

Explanation

To determine the mass percentage of KCl in the sample, we can follow these steps:

### Step 1: Calculate the mass of sodium in the sample
Given that the sample is 23% sodium by mass, we can calculate the mass of sodium in the 1.0 g sample.

\[ \text{Mass of Na} = \frac{23}{100} \times 1.0 \, \text{g} = 0.23 \, \text{g} \]

### Step 2: Calculate the mass of chlorine from NaCl
The molar mass of sodium (Na) is 23 g/mol, and the molar mass of chlorine (Cl) is 35.5 g/mol. The mass of chlorine that corresponds to the sodium in NaCl can be calculated using the ratio of their molar masses.

\[ \text{Mass of Cl from NaCl} = \frac{35.5}{23} \times 0.23 \, \text{g} = 0.355 \, \text{g} \]

### Step 3: Calculate the mass of chlorine in the AgCl precipitate
Given that 2.0 g of AgCl precipitate is formed, we can calculate the mass of chlorine in this precipitate.

\[ \text{Mass of Cl in AgCl} = \frac{35.5}{143.5} \times 2.0 \, \text{g} = 0.495 \, \text{g} \]

### Step 4: Calculate the mass of chlorine from KCl
Now, we can find the mass of chlorine that comes from KCl by subtracting the mass of chlorine from NaCl from the total mass of chlorine in AgCl.

\[ \text{Mass of Cl from KCl} = 0.495 \, \text{g} - 0.355 \, \text{g} = 0.140 \, \text{g} \]

### Step 5: Calculate the mass of KCl
Using the mass of chlorine from KCl, we can find the mass of KCl using the molar mass of KCl (74.6 g/mol).

\[ \text{Mass of KCl} = \frac{74.6}{35.5} \times 0.140 \, \text{g} = 0.2928 \, \text{g} \]

### Step 6: Calculate the mass percentage of KCl in the sample
Finally, we can calculate the mass percentage of KCl in the original sample.

\[ \text{Mass percentage of KCl} = \left( \frac{0.2928 \, \text{g}}{1.0 \, \text{g}} \right) \times 100 = 29.28\% \]

### Final Answer:
The mass percentage of KCl in the sample is **29.28%**.

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