Answer:
(a) Yes; (b) yes; (c) no
Step-by-step explanation:
(a) CoS
The solutions dilute each other on mixing.
Total volume is 100 mL.
[Co²⁺] = 1 × 10⁻⁵ × 25/100 = 2.5 × 10⁻⁶ mol·L⁻¹
[S²⁻] = 5 × 10⁻⁴ × 75/100 = 3.8 × 10⁻⁴ mol·L⁻¹
CoS ⇌ Co²⁺ + S²⁻; K_sp = 4 × 10⁻²¹
I/mol·L⁻¹: 2.5 × 10⁻⁶ 3.8 × 10⁻⁴
Q_sp = [Co²⁺][S²⁻] = 2.5 × 10⁻⁶ × 3.8 × 10⁻⁴ = 9.4 × 10⁻¹⁰
Q_sp > K_sp. ∴ A precipitate will form.
(b) Hg₂Cl₂
Total volume is 600 mL.
[Cl⁻] = (3 × 7.5× 10⁻⁴) × 500/600 = 1.88 × 10⁻³ mol·L⁻¹
[Hg₂²⁺] = 1.7 × 10⁻⁵ × 100/600 = 2.83 × 10⁻⁶ mol·L⁻¹
Hg₂Cl₂ ⇌ Hg₂²⁺ + 2Cl⁻; K_sp = 1.3 × 10⁻¹⁸
I/mol·L⁻¹: 2.83 × 10⁻⁶ 1.88 × 10⁻³
Q_sp = [Hg₂²⁺][Cl⁻]² = 2.83 × 10⁻⁶ × (1.88 × 10⁻³)² = 1.0 × 10⁻¹¹
Q_sp > K_sp. ∴ A precipitate will form.
(c) PbCl₂
Total volume is 2.75 L.
[Cl⁻] = (2 × 0.025) × 1.5/2.75 = 2.73 × 10⁻² mol·L⁻¹
[Pb²⁺] = 0.014 × 1.25/2.75 = 6.36 × 10⁻³ mol·L⁻¹
PbCl₂ ⇌ Pb²⁺ + 2Cl⁻; K_sp = 1.6 × 10⁻⁵
I/mol·L⁻¹: 6.36 × 10⁻³ 2.73 × 10⁻²
Q_sp = [Pb²⁺][Cl⁻]² = 6.36 × 10⁻³ × (2.73 × 10⁻²)² = 4.7 × 10⁻⁶
Q_sp < K_sp. ∴ A precipitate will not form.
