Give reason why `BaSO_(4)` will precipitate out when equal volumes of `2xx10^(-3) M BaCl_(2)` solution and `2xx10^(-4)M Na_(2)SO_(4)` solution are mixed. Given that the solubility product of `BaSO_(4)` is `1xx10^(-10).`

Explanation

To determine why barium sulfate (BaSO₄) will precipitate when equal volumes of 2 x 10⁻³ M BaCl₂ and 2 x 10⁻⁴ M Na₂SO₄ solutions are mixed, we can follow these steps:

### Step 1: Determine the concentrations of ions after mixing
When equal volumes of the two solutions are mixed, the concentrations of the ions will change due to dilution.

- The concentration of Ba²⁺ ions from BaCl₂ is 2 x 10⁻³ M. After mixing equal volumes, the new concentration will be:
\[
\text{Concentration of Ba}^{2+} = \frac{2 \times 10^{-3}}{2} = 1 \times 10^{-3} \, \text{M}
...