The stoichiometry and solubility product of a salt with the solubility curve given below is, respectively :

Solution

Chemistry ma’am · 4 steps

Read two points off the curve and test which product [X]ᵃ[Y]ᵇ stays the same at both.

1. Why one curve. Every point on a solubility curve is a saturated solution, so Kₛₚ has the same value everywhere on it. The right formula is the one whose Kₛₚ expression gives the same number at every point.
2. Read two points. The curve passes through [X] = 1 mM, [Y] = 2 mM. At [X] = 2 mM it sits at about [Y] = 1.4 mM, which is close to √2.

   Formula	Kₛₚ expression	At (1, 2)	At (2, 1.4)
   XY	[X][Y]	2	2.8, changes
   X₂Y	[X]²[Y]	2	5.6, changes
   XY₂	[X][Y]²	4	2 × 1.96 ≈ 3.9, constant

3. Convert units. So Kₛₚ = 4 mM³. Since 1 mM = 10⁻³ M, this is 4 × (10⁻³)³ = 4 × 10⁻⁹ M³.
4. So. The salt is XY₂ with Kₛₚ = 4 × 10⁻⁹ M³, option (c).

The idea to keep. A solubility curve is a curve of constant Kₛₚ. Test each formula's ion product at two points on the graph; only the true stoichiometry gives the same value at both.

Answer from the NTA final answer key. Solution by PrepWiser.