SCIENCE · INVESTIGATE AND EXPLAIN

Construct conjugate-salt constants and species ledgers

Derive a hydrolysis constant from its parent, distinguish ion charge from acid/base direction and keep missing numerical evidence explicit.

Learning outcome: Construct a reciprocal conjugate constant, validate hydrolysis direction through conserved charge and distinguish supported qualitative inference from unsupported pH.

Starting recap

For a conjugate pair at the same temperature, KaKb=Kw. A charged salt ion may react with water after the salt has dissociated; the spectator remains in the charge balance.

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Try

NaA contains A−, the conjugate base of HA with pKa 5. Reusing that5 as pKb and calling the salt acidic confuses both the constant and the reaction direction.

Open the experiment

Predict

Predict the correct child pK and the hydrolysis direction. Predict whether a wrong child constant can still produce a charge-balanced candidate.

Your prediction and reason

Experiment

Repair direction and pK separately. Compare parent pK 5 and9 at the same total concentration. Transfer from NaA to BHCl with its parent base constant. Inspect the missing-parent-constant packet: retain a supported qualitative direction without inventing numerical pH. Capture a failed and a supported inference.

Construct a conjugate-salt inference

Worked teaching model · synthetic values · Fictional dissolved NaA or BHCl,0.010mol/L at 25°C, inert Na+ or Cl− spectator and one hydrolyzing ion. Parent pKa/pKb values are stipulated; unknown remains unknown. Classroom ideal concentration Kw=1e−14. No two-reactive-ion salts, amphiprotic ions, activities, gas exchange, complexes or multiple ionizations. Complete salt dissociation is distinct from hydrolysis.

Original synthetic salt packet: NaA; parent HA pKa 5 packet

Reset keeps your prediction, captures and practice history.

Stipulated dissolved NaA, total 0.01mol/L. Parent HA pKa = 5. The salt identity supplies the hydrolyzing ion; the other ion is inert in this model.

Your hydrolysis directionYour conjugate pK

Do not infer the constant from a balanced result
Check	Your proposal	Evidence
Direction	Acidic	Does not match the hydrolysis reaction
Conjugate pK	5	14 − 5 = 9; unsupported
Parent K × proposed child K	1.00000e-10	Must equal classroom Kw=10⁻¹⁴
Target pH	Withheld	Repair the unsupported inference.

Candidate calculated from your proposed constant and direction
Species or check	Value
Remaining A⁻	9.6887327e-3mol/L
Neutral HA	3.1126728e-4mol/L
Family total	1.0000000e-2mol/L
Na⁺ spectator	0.01mol/L
Hydronium / hydroxide	3.1126731e-4 / 3.2126728e-11mol/L
h + [Na⁺] − o − [A⁻]	6.225346e-4mol charge/L
Hypothetical pH	3.5068665 — not accepted as the target pH

A correct direction with a wrong constant can balance charge, while still failing KaKb=Kw. A correct numerical constant with the wrong direction gives a spectator-charge contradiction. Stronger parent acid or base means a weaker conjugate at the same temperature; it does not mean the same pH at every concentration.

Source, reused solver and limits

OpenStax Chemistry 2e, 14.4 explains conjugate hydrolysis and inert-spectator distinctions. These packets and constants are original, not real-compound measurements. The full water-inclusive monotonic solver is reused, but its hydrolysis extent here represents a neutral product, while the unconverted family member remains charged. It retains water, family mass balance and the actual spectator charge.

Classroom25°C Kw=10⁻¹⁴ uses the ideal concentration approximation. Both-reactive-ion salts, amphiprotic ions, hydrated-metal acidity, activities, gas exchange and multiple ionizations are not modeled. Sodium and chloride are explicitly inert here; the task does not generalize that all metal ions or all anions are inert.

Target pH withheld: the direction and/or reciprocal-constant proposal is unsupported.

Hypothetical candidate pH 3.5068665; spectator-charge residual 6.22535e-4 mol charge/L. A balanced candidate alone does not verify its equilibrium constant.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

Dissociation does not answer the hydrolysis question

A fictional dissolved salt NaA supplies Na⁺ and A⁻. The parent acid HA has stipulated pKa 5. Sodium is inert in this model, but A⁻ can accept a proton from water: A⁻+H₂O⇌HA+OH⁻. Complete separation of the salt into ions does not mean this second reaction goes to completion.

The initial proposal reuses pK 5 and selects acidic behavior. Repair the direction first. Notice that charge can now balance even though the proposed equilibrium constant remains wrong. Then repair the constant. Explain why the two checks are independent.

Derive the conjugate constant

The acid reaction HA+H₂O⇌H₃O⁺+A⁻ and its conjugate-base hydrolysis add to the water-ionization reaction. Multiplying their equilibrium constants gives KaKb=Kw. With the classroom 25°C value, pKa+pKb=14. Thus parent pKa 5 gives conjugate pKb 9, not 5.

For the chloride salt of a conjugate acid, BHCl, the parent is a neutral base B. BH⁺ donates a proton to water, giving B and H₃O⁺. Parent pKb 5 gives conjugate pKa 9. The ion’s relationship to its parent matters; a positive ion is not automatically an inert counterion.

At equal analytical concentration, compare parent pK 5 and9. Increasing parent pK weakens the parent but strengthens the conjugate. Do not confuse this inverse relationship with a statement that pK equals the solution pH.

Keep the spectator in the ledger

For NaA, the family inventory is [A⁻]+[HA]=C and the spectator remains [Na⁺]=C. Charge balance is h+[Na⁺]=o+[A⁻]. The neutral product [HA] equals o−h, not all of o when water’s minority ion matters.

For BHCl, [BH⁺]+[B]=C and [Cl⁻]=C. Charge balance is h+[BH⁺]=o+[Cl⁻], so neutral product [B]=h−o. The activity reuses the water-inclusive scalar solver from the earlier lesson while mapping the species correctly: the product is neutral and the remaining salt-family ion is charged.

A hypothetical calculation made from the wrong direction is still displayed for inspection. Its family total may balance while the actual spectator-charge equation fails. A calculation using an invented constant may balance both ledgers, yet still lack evidence for the target pH.

Withhold what the evidence cannot determine

The final NaA packet identifies HA as a weak parent acid but does not supply its constant. The basic hydrolysis direction is supported under the stated assumptions. Its numerical pH is not identified from that information alone. Select “Not assigned” instead of silently inventing a constant or replacing it with zero.

Capture a rejected inference and a supported one. Explain which inputs support direction, which support the numerical constant, and why neither conservation alone nor a plausible pH substitutes for the missing parameter. The unfamiliar practice reverses the task to a parent base with pKb 4.

Sources and boundaries

OpenStax Chemistry 2e, 14.4 supports the salt-hydrolysis and conjugate-constant relationships. All constants, packets, questions and diagrams are original synthetic teaching material. No measured salt pH is claimed.

Only one ion hydrolyzes in each packet. The model does not cover two-reactive-ion salts, amphiprotic ions, hydrated-metal acidity, gas exchange, activities or multiple ionizations. The inert-spectator assumption is specific, not a rule that all metals or anions are inert. Return to the weak-equilibrium assumption audit to distinguish water and solute-depletion approximations.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

Explain why complete salt dissociation does not mean complete hydrolysis. Identify the spectator, remaining charged family member and neutral product. Show the reciprocal constant relation and explain why charge balance cannot determine an unknown equilibrium constant.

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Construct buffer reaction inventories before equilibrium Next: Separate water and solute-depletion approximations

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