What is the concentration of nitrate ions if equal volumes of `0.1 M AgNO_(3)` and `0.1 M NaCl` are mixed together?

Options

A. 0.1 N
B. 0.25 M
C. 0.05 M
D. 0.2 M

Answer

To find the concentration of nitrate ions when equal volumes of 0.1 M AgNO₃ and 0.1 M NaCl are mixed together, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Dissociation of the Compounds:**
- AgNO₃ dissociates into Ag⁺ and NO₃⁻ ions.
- NaCl dissociates into Na⁺ and Cl⁻ ions.
- Therefore, when 0.1 M AgNO₃ is mixed, it provides 0.1 moles of NO₃⁻ ions per liter of solution.

2. **Determine the Moles of NO₃⁻ in the Solution:**
- Since we are mixing equal volumes of 0.1 M AgNO₃ and 0.1 M NaCl, let’s assume we take 1000 mL (1 L) of each solution.
- Moles of AgNO₃ in 1 L = 0.1 moles.
- Therefore, moles of NO₃⁻ ions from AgNO₃ = 0.1 moles.

3. **Calculate the Total Volume of the Mixture:**
- When we mix 1000 mL of AgNO₃ with 1000 mL of NaCl, the total volume becomes:
\[ \text{Total Volume} = 1000 \, \text{mL} + 1000 \, \text{mL} = 2000 \, \text{mL} \]

4. **Calculate the Concentration of NO₃⁻ Ions:**
- The concentration (Molarity) of NO₃⁻ ions can be calculated using the formula:
\[ \text{Molarity (M)} = \frac{\text{Number of moles of solute}}{\text{Volume of solution in liters}} \]
- Here, the number of moles of NO₃⁻ = 0.1 moles and the volume of the solution = 2000 mL = 2 L.
- Therefore, the concentration of NO₃⁻ ions is:
\[ \text{Molarity} = \frac{0.1 \, \text{moles}}{2 \, \text{L}} = 0.05 \, \text{M} \]

5. **Conclusion:**
- The concentration of nitrate ions (NO₃⁻) in the solution after mixing is **0.05 M**.