Will a precipitate of silver sulphate form if equal volumes of `1 N H_2SO_4" and "0.02 M AgNO_3` solutions are mixed? `K_(sp) (Ag_(2)SO_(4))=2 xx 10^(-5)`.

Answer

To determine whether a precipitate of silver sulfate (Ag₂SO₄) will form when equal volumes of 1 N H₂SO₄ and 0.02 M AgNO₃ solutions are mixed, we can follow these steps:

### Step-by-Step Solution:

1. **Calculate the concentration of sulfate ions (SO₄²⁻)**:
- When equal volumes of 1 N H₂SO₄ and 0.02 M AgNO₃ are mixed, the total volume doubles.
- The normality (N) of H₂SO₄ is 1 N, which means it provides 1 equivalent of sulfate ions per liter. Since we are mixing equal volumes, the concentration of sulfate ions after mixing will be:
\[ \text{Concentration of SO₄²⁻} = \frac{1 \, \text{N}}{2} = 0.5 \, \text{N} = 0.5 \, \text{M} \]

2. **Calculate the concentration of silver ions (Ag⁺)**:
- The concentration of Ag⁺ ions from the AgNO₃ solution is 0.02 M. When mixed with an equal volume of H₂SO₄, the concentration of Ag⁺ ions becomes:
\[ \text{Concentration of Ag⁺} = \frac{0.02 \, \text{M}}{2} = 0.01 \, \text{M} \]

3. **Calculate the ionic product (IP) for Ag₂SO₄**:
- The ionic product (IP) for the precipitation of Ag₂SO₄ can be calculated using the formula:
\[ \text{IP} = [\text{Ag}^+]^2 [\text{SO₄}^{2-}] \]
- Substituting the concentrations:
\[ \text{IP} = (0.01)^2 \times (0.5) = 0.0001 \times 0.5 = 0.00005 = 5 \times 10^{-5} \]

4. **Compare the ionic product with Ksp**:
- The solubility product constant (Ksp) for Ag₂SO₄ is given as \(2 \times 10^{-5}\).
- Now, compare the ionic product with Ksp:
\[ \text{IP} = 5 \times 10^{-5} > Ksp = 2 \times 10^{-5} \]
- Since the ionic product is greater than the Ksp, a precipitate of silver sulfate will form.

### Conclusion:
Yes, a precipitate of silver sulfate (Ag₂SO₄) will form when equal volumes of 1 N H₂SO₄ and 0.02 M AgNO₃ solutions are mixed.