Assuming the complete dissociation of HCl and the lead salt, calculate how much HCl is to be added to a 0.001M lead salt solution to just prevent precipitation when saturated with `H_(2)S`. The concentration of `H_(2)S` in its saturated solution is 0.1M. `K_(a) (H_(2)S)=1.1 xx 10^(-23), K_(sp) (PbS)=3.4 xx 10^(-28)`

Explanation

To solve the problem, we need to calculate how much HCl is required to prevent the precipitation of lead sulfide (PbS) when the solution is saturated with hydrogen sulfide (H₂S). Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Dissociation and Equilibrium
- **HCl** dissociates completely in solution to give H⁺ and Cl⁻ ions.
- **H₂S** dissociates according to the following equilibrium:
\[ H_2S \rightleftharpoons H^+ + HS^- \]
...