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.