Question

Predict whether a precipitate will form from each of the following combinations: (a) 25 mL of 1 × 10−5 M Co(NO3)2 and 75 mL of 5 × 10−4 M Na2S; (b) 500 mL of 7.5 × 10−4 M AlCl3 and 100 mL of 1.7 × 10−5 M Hg2(NO3)2; (c) 1.5 L of 0.025 M BaCl2 and 1.25 L of 0.014 M Pb(NO3)2

Answer 1

(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.