Final answer:
The lower Ksp value for PbSO4 indicates that it will precipitate first from a solution containing equal concentrations of Br− and SO4²−. After establishing the solubility equilibrium expressions and calculating the concentrations, we can find the concentration of the first ion when the second precipitate begins to form.
Step-by-step explanation:
To determine which anion will precipitate first when a 0.204 M solution of lead(II) nitrate is slowly added to a 0.015 M solution containing both Br− and SO4²−, we need to use the solubility product constants (Ksp) provided. The anion that will precipitate first is the one that will reach its Ksp value first upon addition of Pb(NO3)2.
The Ksp values are:
- Ksp for PbBr2 = 6.60 × 10−6
- Ksp for PbSO4 = 2.53 × 10−8
The dissolution reactions are:
- PbBr2 (s) → Pb²+ (aq) + 2Br− (aq)
- PbSO4 (s) → Pb²+ (aq) + SO4²− (aq)
To find out which salt precipitates first, we compare the reaction quotient (Q) with the Ksp. The reaction quotient is calculated by multiplying the concentrations of the products. When Q equals Ksp, the solution is saturated and precipitation begins.
For PbBr2:
Q = [Pb²+][Br−]2
For PbSO4:
Q = [Pb²+][SO4²−]
Since the concentrations of Br− and SO4²− are initially equal, PbSO4 will precipitate first because it has a much lower Ksp value. Therefore, sulfate ions will precipitate as PbSO4 first, and the concentration of sulfate will be very low when lead bromide starts to precipitate.
The concentration of Br− when PbSO4 starts to precipitate can be found by setting up the equilibrium expression for PbSO4 and solving for [Pb²+], then substituting [Pb²+] into the Ksp expression for PbBr2 and solving for [Br−].