100 ml of 0.2 NHCl solution is added to 100 ml of 0.2 N `AgNO_(3)` solution. The molarity of nitrate ions in the resulting mixture will be

Options

A. 0.5M
B. 0.05M
C. 0.1 M
D. 0.2M

Explanation

To find the molarity of nitrate ions in the resulting mixture after mixing 100 ml of 0.2 N HCl with 100 ml of 0.2 N AgNO₃, we can follow these steps:

### Step 1: Understand the Reaction
When HCl reacts with AgNO₃, the following reaction occurs:
\[ \text{HCl} + \text{AgNO}_3 \rightarrow \text{AgCl} + \text{HNO}_3 \]

### Step 2: Calculate the Number of Moles of HCl and AgNO₃
Normality (N) is related to molarity (M) by the equation:
\[ N = M \times n \]
where \( n \) is the number of equivalents. For HCl, \( n = 1 \) (since it donates one H⁺ ion), so:
\[ \text{Normality of HCl} = \text{Molarity of HCl} \]
Thus, the molarity of HCl is also 0.2 M.

Now, calculate the number of moles of HCl and AgNO₃:
- Volume of HCl = 100 ml = 0.1 L
- Molarity of HCl = 0.2 M
\[ \text{Moles of HCl} = \text{Molarity} \times \text{Volume} = 0.2 \, \text{mol/L} \times 0.1 \, \text{L} = 0.02 \, \text{mol} \]

For AgNO₃:
- Volume of AgNO₃ = 100 ml = 0.1 L
- Molarity of AgNO₃ = 0.2 M
\[ \text{Moles of AgNO}_3 = 0.2 \, \text{mol/L} \times 0.1 \, \text{L} = 0.02 \, \text{mol} \]

### Step 3: Determine the Reaction Stoichiometry
From the balanced reaction, we see that 1 mole of HCl reacts with 1 mole of AgNO₃. Since we have equal moles of both (0.02 mol), they will completely react with each other.

### Step 4: Calculate the Moles of Nitrate Ions
After the reaction, the moles of nitrate ions (from AgNO₃) will be equal to the moles of AgNO₃ that reacted, which is 0.02 mol.

### Step 5: Calculate the Total Volume of the Mixture
The total volume after mixing the two solutions:
\[ \text{Total Volume} = 100 \, \text{ml} + 100 \, \text{ml} = 200 \, \text{ml} = 0.2 \, \text{L} \]

### Step 6: Calculate the Molarity of Nitrate Ions
Molarity (M) is calculated using the formula:
\[ M = \frac{\text{Number of moles}}{\text{Volume in L}} \]
Substituting the values:
\[ M = \frac{0.02 \, \text{mol}}{0.2 \, \text{L}} = 0.1 \, \text{M} \]

### Final Answer
The molarity of nitrate ions in the resulting mixture is **0.1 M**.

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