Question

Calculate the minimum concentration of ammonia needed in 1.0 L of solution to dissolve 3.0 × 10⁻³ mol of silver bromide.

a) 3.0 × 10⁻³ M

b) 6.0 × 10⁻³ M

c) 1.5 × 10⁻³ M

d) 0.75 × 10⁻³ M

Answer 1

The minimum concentration of ammonia needed to dissolve 3.0 × 10⁻³ mol of silver bromide in 1.0 L of solution is 6.0 × 10⁻³ M. The correct option is b.

Step-by-step explanation:

To calculate the minimum concentration of ammonia needed in 1.0 L of solution to dissolve 3.0 × 10⁻³ mol of silver bromide, we need to first write down the relevant chemical equation:

AgBr(s) + 2 NH₃(aq) → [Ag(NH₃)₂]+(aq) + Br⁻(aq)

This is a complex formation reaction where ammonia acts as a ligand to silver ion, forming a complex ion. The equilibrium expression based on the solubility product constant (Ksp) for silver bromide and the formation constant (Kf) for the silver-ammonia complex is:

Ksp = [Ag+][Br⁻]

Kf = [Ag(NH₃)₂]+/[Ag+][NH₃]2

However, the exact value of Kf for [Ag(NH₃)₂]+ is not given, but the concept remains that ammonia forms a complex ion with silver, increasing the solubility of AgBr.

Since 3.0 × 10⁻³ mol of AgBr need to be dissolved, that means 3.0 × 10⁻³ mol of [Ag(NH₃)₂]+ will be formed. Each mole of [Ag(NH₃)₂]+ requires 2 moles of NH₃, therefore we need at least 2 × 3.0 × 10⁻³ mol of NH₃. The minimum concentration of NH₃ will be:

(2 × 3.0 × 10⁻³ mol) / 1.0 L = 6.0 × 10⁻³ M

Therefore, the minimum concentration of ammonia needed is 6.0 × 10⁻³ M. The correct option is b.