Commerical sodium hydroxide weighing 30 g has some sodium chloride in it. The mixture on dissolving in water and subsequent treatment with excess silver nitrate solution formed a precipitate weighing 14.3 g. What is the percentage of sodium chloride in the commercial sample of sodium hydroxide? The equation for the reaction is
`NaCl+AgNO_(3) to AgCl+NaNO_(3)`
(Relative molecular mass of `NaCl=58,AgCl=143)`

Explanation

To find the percentage of sodium chloride (NaCl) in the commercial sodium hydroxide (NaOH) sample, we can follow these steps:

### Step 1: Understand the Reaction
The reaction between sodium chloride and silver nitrate is given by:
\[ \text{NaCl} + \text{AgNO}_3 \rightarrow \text{AgCl} + \text{NaNO}_3 \]

From this reaction, we see that 1 mole of NaCl produces 1 mole of AgCl.

### Step 2: Calculate the Molar Masses
- Molar mass of NaCl = 58 g/mol
- Molar mass of AgCl = 143 g/mol

### Step 3: Use the Mass of Precipitate to Find NaCl
We are given that the mass of the precipitate (AgCl) formed is 14.3 g. We can use the stoichiometry of the reaction to find out how much NaCl was present.

Using the ratio of the molar masses:
\[ \text{Mass of NaCl} = \left( \frac{\text{Molar mass of NaCl}}{\text{Molar mass of AgCl}} \right) \times \text{Mass of AgCl} \]
Substituting the values:
\[ \text{Mass of NaCl} = \left( \frac{58 \, \text{g/mol}}{143 \, \text{g/mol}} \right) \times 14.3 \, \text{g} \]

### Step 4: Calculate the Mass of NaCl
Calculating the above expression:
\[ \text{Mass of NaCl} = \left( \frac{58}{143} \right) \times 14.3 \approx 5.8 \, \text{g} \]

### Step 5: Calculate the Percentage of NaCl in NaOH
Now that we have the mass of NaCl, we can calculate the percentage of NaCl in the commercial sodium hydroxide sample.
\[ \text{Percentage of NaCl} = \left( \frac{\text{Mass of NaCl}}{\text{Total mass of NaOH}} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage of NaCl} = \left( \frac{5.8 \, \text{g}}{30 \, \text{g}} \right) \times 100 \]
Calculating this gives:
\[ \text{Percentage of NaCl} = \left( \frac{5.8}{30} \right) \times 100 \approx 19.33\% \]

### Final Answer
The percentage of sodium chloride in the commercial sample of sodium hydroxide is approximately **19.33%**.

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