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

(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.