The short answer
Decide from a Ksp whether a precipitate forms and which way solubility shifts, without ever ranking salts by Ksp alone.
Written and checked by GAMSAT tutors — not AI-generated.
Try the reasoning style
We treat forgetting as a failure — a lapse to be patched with reminders and records. Yet a mind that kept everything could not think; it would drown in the undifferentiated noise of every moment it had ever lived. To forget is not so much to lose information as to decide, mostly without our noticing, what was never worth keeping.
The author's argument relies most directly on which unstated assumption?
Pick an option to see how the tutor reasons to the answer — not just whether you were right.
Not quite — the answer is B.
Work backwards from the conclusion: a mind that ‘kept everything’ supposedly ‘could not think.’ That only follows if thinking means leaving most of experience out — so B is the premise the argument quietly rests on. A raises reliability, which the passage never weighs; C contradicts ‘mostly without our noticing’; D smuggles in a claim about intellect the passage never makes. The question rewards finding the hidden premise, not recalling a fact.
A Ksp arrives for a salt you have never met, with one of three questions: which dissolves more, will a solid appear, which way a change shifts solubility. Ksp is the constant for the solid dissolving, and each coefficient does two jobs — multiplying its ion's concentration and becoming its exponent.
One constant, two scales
MX (1:1)
- MX(s) ⇌ M⁺ + X⁻
- Ksp = [M⁺][X⁻] = s²
- s = √Ksp
MX₂ (1:2)
- MX₂(s) ⇌ M²⁺ + 2X⁻
- Ksp = [M²⁺][X⁻]² = (s)(2s)² = 4s³
- s = ∛(Ksp / 4)
| Salt | Dissolution | Ksp (25 °C) | Molar solubility (mol/L) |
|---|---|---|---|
| BaSO₄ | BaSO₄(s) ⇌ Ba²⁺ + SO₄²⁻ | 1.1 × 10⁻¹⁰ | 1.0 × 10⁻⁵ |
| AgCl | AgCl(s) ⇌ Ag⁺ + Cl⁻ | 1.8 × 10⁻¹⁰ | 1.3 × 10⁻⁵ |
| Ag₂CrO₄ | Ag₂CrO₄(s) ⇌ 2Ag⁺ + CrO₄²⁻ | 1.1 × 10⁻¹² | 6.5 × 10⁻⁵ |
| Mg(OH)₂ | Mg(OH)₂(s) ⇌ Mg²⁺ + 2OH⁻ | 5.6 × 10⁻¹² | 1.1 × 10⁻⁴ |
The trap: ranking off the Ksp column
Ksp for MX multiplies two concentrations; for MX₂, three — comparing them compares an area with a volume. Ksp orders solubility only within the same ion ratio; convert to molar solubility first.
Worked example
Equal volumes of AgNO₃ and NaCl, each 2.0 × 10⁻⁵ mol/L, are mixed. Ksp(AgCl) = 1.8 × 10⁻¹⁰. Precipitate?
Shifting solubility is Le Chatelier
Add a product ion and less dissolves: AgCl in 0.010 mol/L NaCl gives s = Ksp/[Cl⁻] = 1.8 × 10⁻⁸, seven hundred times below its pure-water value. Strip a product ion — acid on OH⁻ — and more dissolves.
Check yourself
Two sparingly soluble salts are given at 25 °C. QX dissolves as QX(s) ⇌ Q⁺ + X⁻, with Ksp = 4.0 × 10⁻¹⁰. RY₂ dissolves as RY₂(s) ⇌ R²⁺ + 2Y⁻, with Ksp = 4.0 × 10⁻¹². Which statement about their molar solubilities in pure water is correct?
Key takeaways
- A coefficient multiplies its ion and becomes its exponent: MX₂ gives 4s³.
- Ksp ranks solubility only within one ion ratio; otherwise convert to molar solubility.
- Precipitation is Q against Ksp — dilute mixed solutions before building Q.
- A common ion suppresses solubility; acid on a hydroxide raises it.
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