Question

Will a precipitate be formed when 0.150 L of 0.1 M Pb(NO₃)₂ and 0.100 L of 0.2 M NaCl are mixed? K_sp (PbCl₂) = 1.2 × 10⁻⁵.

Answer 1

When two are more solutions are mixed, the resulting concentrations are different from the original.

Total volume = 0.250 L

\[\ce{\underset{0.1 M}{Pb(NO3)2} ⇌ \underset{0.1 M}{Pb^{2+}} + \underset{0.2 M}{2NO^-_3}}\]

Number of moles Pb²⁺ = molarity × Volume of the solution in lit

= 0.1 × 0.15

[Pb²⁺]_mix = `(0.1 xx 0.15)/0.25` = 0.06 M

\[\ce{\underset{0.2 M}{NaCl} ⇌ \underset{0.2 M}{Na^+} + \underset{0.2 M}{Cl^-}}\]

No. of moles Cl⁻ = 0.2 × 0.1

[Cl⁻]_mix = `(0.2 xx 0.1)/0.25` = 0.08 M

Precipitation of PbCI_2(s) occurs if [Pb²⁺] [Cl^–]² > K_sp

[Pb²⁺] [Cl^–]² = (0.06) (0.08)²

= 3.84 × 10⁻⁴

Since ionic product [Pb²⁺] [Cl^–]² > K_sp, PbCl₂ is precipitated.