1.0 gm of a mixture of `CaCO_3 and NaCl` reacts completely with 120 ml of N/10 HCI. The percentage of NaCI in the mixture is:

Options

A. 40
B. 0.5
C. 0.6
D. 0.66

Answer

To solve the problem, we will follow these steps:

### Step 1: Calculate the moles of HCl used
We know that the concentration of HCl is N/10, which means it is 0.1 N. The volume of HCl used is 120 ml.

\[ \text{Moles of HCl} = \text{Normality} \times \text{Volume (in L)} \]
\[ \text{Moles of HCl} = \frac{1}{10} \times \frac{120}{1000} = 0.012 \text{ moles} \]

### Step 2: Determine the moles of CaCO3 that reacted
From the balanced reaction of CaCO3 with HCl, we know that 1 mole of CaCO3 reacts with 2 moles of HCl.

\[ \text{Moles of CaCO3} = \frac{\text{Moles of HCl}}{2} = \frac{0.012}{2} = 0.006 \text{ moles} \]

### Step 3: Calculate the mass of CaCO3
The molar mass of CaCO3 is 100 g/mol. Therefore, the mass of CaCO3 can be calculated as follows:

\[ \text{Mass of CaCO3} = \text{Moles of CaCO3} \times \text{Molar mass of CaCO3} \]
\[ \text{Mass of CaCO3} = 0.006 \times 100 = 0.6 \text{ grams} \]

### Step 4: Calculate the mass of NaCl in the mixture
The total mass of the mixture is given as 1 gram. Therefore, the mass of NaCl can be calculated as:

\[ \text{Mass of NaCl} = \text{Total mass of mixture} - \text{Mass of CaCO3} \]
\[ \text{Mass of NaCl} = 1 - 0.6 = 0.4 \text{ grams} \]

### Step 5: Calculate the percentage of NaCl in the mixture
To find the percentage of NaCl in the mixture, we use the formula:

\[ \text{Percentage of NaCl} = \left(\frac{\text{Mass of NaCl}}{\text{Total mass of mixture}}\right) \times 100 \]
\[ \text{Percentage of NaCl} = \left(\frac{0.4}{1}\right) \times 100 = 40\% \]

### Final Answer
The percentage of NaCl in the mixture is **40%**.

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