15.4Coupled Equilibria
Section · module m68814
What this needs
Learn these first — this section will not make sense without them.
Combining coupled equilibria here means dividing constants (K = Ksp/Ka2 for the coral-reef reaction, reversing the acid-hydrolysis step) or multiplying them (K = Ksp·Kf = 22 for Al(OH)3 dissolving via complex formation) — the same product/reciprocal exponent-rule work as chapter 13, now the entire basis for predicting whether a reaction is dramatically more soluble.
The Al(OH)3-in-water molar solubility is computed as [Al³⁺] = (2×10⁻³²/27)^(1/4), a fourth-root (rational-exponent) solve arising from the 1:3 dissolution stoichiometry — one exponent higher than the cube-root case in 15.2, so the same radical-exponent skill has to generalize.
The photographic-fixer example rearranges the combined-equilibrium K expression and solves for [S2O3²⁻] with a square root, [S2O3²⁻] = √([Ag(S2O3)2³⁻][Br⁻]/K) — another radical-equation solve, this time on a two-step coupled-equilibrium expression rather than a simple Ksp.
- Alongside6.6Logarithmic Properties
The Al(OH)3-in-buffer example finds [OH⁻] via the Henderson-Hasselbalch equation before plugging it into Ksp — coupled equilibria routinely reuse the log-of-a-quotient buffer machinery from chapter 14 as an intermediate step, not a standalone topic.
What this touches
Algebra that turns up here. Not a blocker, but this is where you will see it used.
No algebra turns up here. Most of the descriptive sections need none.