To find the percentage of NaCl in a mixture of CaCO₃ and NaCl that reacts with HCl, we can follow these steps:
### Step 1: Calculate the moles of HCl used
Given that 120 ml of N/10 HCl is used, we first convert the volume from ml to liters:
\[
\text{Volume of HCl} = 120 \, \text{ml} = \frac{120}{1000} \, \text{L} = 0.120 \, \text{L}
\]
The normality (N) of HCl is given as 1/10, which is equivalent to 0.1 M (since normality = molarity for monoprotic acids like HCl).
Using the formula for moles:
\[
\text{Moles of HCl} = \text{Normality} \times \text{Volume in L} = 0.1 \, \text{mol/L} \times 0.120 \, \text{L} = 0.012 \, \text{moles}
\]
### Step 2: Determine the moles of CaCO₃ that reacted
The balanced reaction between CaCO₃ and HCl is:
\[
\text{CaCO}_3 + 2 \text{HCl} \rightarrow \text{CaCl}_2 + \text{CO}_2 + \text{H}_2\text{O}
\]
From the stoichiometry of the reaction, 2 moles of HCl react with 1 mole of CaCO₃. Therefore, the moles of CaCO₃ can be calculated as:
\[
\text{Moles of CaCO}_3 = \frac{\text{Moles of HCl}}{2} = \frac{0.012}{2} = 0.006 \, \text{moles}
\]
### Step 3: Calculate the mass of CaCO₃
The molar mass of CaCO₃ is calculated as follows:
- Calcium (Ca) = 40 g/mol
- Carbon (C) = 12 g/mol
- Oxygen (O) = 16 g/mol (3 O atoms = 48 g/mol)
Thus, the molar mass of CaCO₃ is:
\[
\text{Molar mass of CaCO}_3 = 40 + 12 + 48 = 100 \, \text{g/mol}
\]
Now, we can calculate the mass of CaCO₃:
\[
\text{Mass of CaCO}_3 = \text{Moles} \times \text{Molar mass} = 0.006 \, \text{moles} \times 100 \, \text{g/mol} = 0.6 \, \text{g}
\]
### Step 4: Calculate the mass of NaCl in the mixture
The total mass of the mixture is given as 1.0 g. Therefore, the mass of NaCl can be calculated as:
\[
\text{Mass of NaCl} = \text{Total mass} - \text{Mass of CaCO}_3 = 1.0 \, \text{g} - 0.6 \, \text{g} = 0.4 \, \text{g}
\]
### Step 5: Calculate the percentage of NaCl in the mixture
Finally, we can find the percentage of NaCl in the mixture:
\[
\text{Percentage of NaCl} = \left( \frac{\text{Mass of NaCl}}{\text{Total mass}} \right) \times 100 = \left( \frac{0.4 \, \text{g}}{1.0 \, \text{g}} \right) \times 100 = 40\%
\]
### Final Answer
The percentage of NaCl in the mixture is **40%**.
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