What ratio of [NH₄⁺]/[NH₃] would provide a buffer of pH low enough to avoid precipitation of Co(OH)₂(s)from a 0.50 M Co²⁺(aq)solution? (K_b for NH₃ = 1.8 × 10^-5 and K_{sp for} Co(OH)₂= 2.0 × 10^-14 A)1/50 B)1/90 C)1/1 D)90/1 E)50/1

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To avoid the precipitation of Co(OH)₂ from a Co²⁺ solution, the pH must be kept low enough to prevent reaching the solubility product (K_sp) of Co(OH)₂. The buffer system NH₄⁺/NH₃ (ammonium/ammonia) can be used to control the pH. The K_a for NH₄⁺ is 1.8 × 10⁻⁵, which corresponds to a pK_a of -log(1.8 × 10⁻⁵) ≈ 4.74. To prevent Co(OH)₂ precipitation, the pH should be lower than the pOH at which Co(OH)₂ would precipitate. The K_sp for Co(OH)₂ is 2.0 × 10⁻¹⁴, and since Co(OH)₂ dissociates into Co²⁺ and 2 OH⁻, we can set up the equation K_sp = [Co²⁺][OH⁻]². Given a 0.50 M Co²⁺ solution, and assuming complete dissociation for simplicity, the concentration of OH⁻ needed to reach the K_sp can be calculated. However, without precise calculations, we know we need to shift the equilibrium of the NH₄⁺/NH₃ buffer towards NH₄⁺ to lower the pH. This requires a high ratio of NH₄⁺ (acidic component) to NH₃ (basic component), which corresponds to option D, 90/1. This high ratio ensures the solution remains acidic enough to prevent Co(OH)₂ precipitation by keeping the concentration of OH⁻ ions low.

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What Ratio of [NH₄⁺]/[NH₃] Would Provide a Buffer of PH