A laboratory mixture contains equal volumes of three separate aqueous solutions that provide the following initial ion concentrations:
[Pb2+]0=2.0×10−3M[Ag+]0=2.0×10−3M[Cu2+]0=2.0×10−3M
Relevant solubility products at 25 °C:
PbCl₂ Ksp=1.7×10−5
AgCl Ksp=1.8×10−10
Cu(OH)₂ Ksp=2.2×10−20
You have access to the following concentrated reagents: NaCl(aq), NaOH(aq), and HCl(aq). Assume temperature is held constant and no complex‐ion formation other than those implicit in the Ksp values occurs.
(a) If chloride ion is added slowly to the mixture, determine which of the two chloride salts (PbCl₂ or AgCl) begins to precipitate first. Support your answer quantitatively by calculating the chloride ion concentration required for the onset of precipitation for each salt.
(b) Calculate the chloride ion concentration at which 99 % of the first‐precipitating cation is removed from solution. At this same chloride concentration, what percentage of the second chloride‐forming cation has precipitated? Neglect volume change.
(c) After the chloride‐precipitation step is complete, propose a reagent (from the list provided) and a concentration strategy that would remove at least 95 % of the remaining metal ion(s) without redissolving the previously formed precipitates. Justify your choice with relevant equilibrium calculations.
(d) Discuss one practical limitation that might arise when implementing your proposed separation scheme on a preparative scale.