SCIENCE · INVESTIGATE AND EXPLAIN

Dilute both packets before deciding how much can precipitate

Supersaturation is a quotient comparison; precipitated amount additionally needs finite inventories.

Learning outcome: Calculate combined volume first, then Q and the feasible precipitated extent. Retain final free ions, solid amount and an explanation of why the constraint curve is not a time trace.

Starting recap

Refresh normalized free-ion activities, charge-balanced stoichiometry, finite analytical inventories, coupled constants and independent versus shared assay errors.

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Try

Equal10 mL packets at .001 M give immediate M=X=.000500 M. With Ksp10⁻⁸, each falls to .000100 M and .000400 M precipitates, or8.00×10⁻⁶ mol in20 mL.

Open the experiment

Predict

Why is multiplying the two original stock concentrations the wrong immediate mixed quotient?

Your prediction and reason

Experiment

Calculate combined volume first, then Q and the feasible precipitated extent. Retain final free ions, solid amount and an explanation of why the constraint curve is not a time trace.

Apply dilution before testing precipitation and depletion

Worked teaching model · synthetic values · Combine virtual10 mL .001 M M+ with selected volume of .001*b M X−; additive volume, inert counterions, ideal Ksp10⁻⁸. Immediate Q precedes any precipitation. Equilibrium is calculated assuming solid can form; nucleation delay and colloid kinetics are omitted. No physical mixing.

Virtual anion packet volume: 10 mL Anion packet concentration multiplier: 1 times .001 M

Reset keeps your prediction, captures and practice history.

Remaining product versus candidate extent: solid
Saturation product: long dashes

Axes rescale. A solubility comparison, depletion constraint and conditional reservoir scan have different horizontal meanings. Read the axes; these are not measured time traces.

All calculated plot coordinates

Remaining product versus candidate extent
candidate precipitated concentration extent (mol/L)	normalized ion product
0	2.500000e-7
8.333333e-6	2.417361e-7
1.666667e-5	2.336111e-7
2.500000e-5	2.256250e-7
3.333333e-5	2.177778e-7
4.166667e-5	2.100694e-7
5.000000e-5	2.025000e-7
5.833333e-5	1.950694e-7
6.666667e-5	1.877778e-7
7.500000e-5	1.806250e-7
8.333333e-5	1.736111e-7
9.166667e-5	1.667361e-7
0.0001	1.600000e-7
0.0001083333	1.534028e-7
0.0001166667	1.469444e-7
0.000125	1.406250e-7
0.0001333333	1.344444e-7
0.0001416667	1.284028e-7
0.00015	1.225000e-7
0.0001583333	1.167361e-7
0.0001666667	1.111111e-7
0.000175	1.056250e-7
0.0001833333	1.002778e-7
0.0001916667	9.506944e-8
0.0002	9.000000e-8
0.0002083333	8.506944e-8
0.0002166667	8.027778e-8
0.000225	7.562500e-8
0.0002333333	7.111111e-8
0.0002416667	6.673611e-8
0.00025	6.250000e-8
0.0002583333	5.840278e-8
0.0002666667	5.444444e-8
0.000275	5.062500e-8
0.0002833333	4.694444e-8
0.0002916667	4.340278e-8
0.0003	4.000000e-8
0.0003083333	3.673611e-8
0.0003166667	3.361111e-8
0.000325	3.062500e-8
0.0003333333	2.777778e-8
0.0003416667	2.506944e-8
0.00035	2.250000e-8
0.0003583333	2.006944e-8
0.0003666667	1.777778e-8
0.000375	1.562500e-8
0.0003833333	1.361111e-8
0.0003916667	1.173611e-8
0.0004	1.000000e-8
0.0004083333	8.402778e-9
0.0004166667	6.944444e-9
0.000425	5.625000e-9
0.0004333333	4.444444e-9
0.0004416667	3.402778e-9
0.00045	2.500000e-9
0.0004583333	1.736111e-9
0.0004666667	1.111111e-9
0.000475	6.250000e-10
0.0004833333	2.777778e-10
0.0004916667	6.944444e-11
0.0005	0

Saturation product
candidate precipitated concentration extent (mol/L)	normalized ion product
0	1.000000e-8
8.333333e-6	1.000000e-8
1.666667e-5	1.000000e-8
2.500000e-5	1.000000e-8
3.333333e-5	1.000000e-8
4.166667e-5	1.000000e-8
5.000000e-5	1.000000e-8
5.833333e-5	1.000000e-8
6.666667e-5	1.000000e-8
7.500000e-5	1.000000e-8
8.333333e-5	1.000000e-8
9.166667e-5	1.000000e-8
0.0001	1.000000e-8
0.0001083333	1.000000e-8
0.0001166667	1.000000e-8
0.000125	1.000000e-8
0.0001333333	1.000000e-8
0.0001416667	1.000000e-8
0.00015	1.000000e-8
0.0001583333	1.000000e-8
0.0001666667	1.000000e-8
0.000175	1.000000e-8
0.0001833333	1.000000e-8
0.0001916667	1.000000e-8
0.0002	1.000000e-8
0.0002083333	1.000000e-8
0.0002166667	1.000000e-8
0.000225	1.000000e-8
0.0002333333	1.000000e-8
0.0002416667	1.000000e-8
0.00025	1.000000e-8
0.0002583333	1.000000e-8
0.0002666667	1.000000e-8
0.000275	1.000000e-8
0.0002833333	1.000000e-8
0.0002916667	1.000000e-8
0.0003	1.000000e-8
0.0003083333	1.000000e-8
0.0003166667	1.000000e-8
0.000325	1.000000e-8
0.0003333333	1.000000e-8
0.0003416667	1.000000e-8
0.00035	1.000000e-8
0.0003583333	1.000000e-8
0.0003666667	1.000000e-8
0.000375	1.000000e-8
0.0003833333	1.000000e-8
0.0003916667	1.000000e-8
0.0004	1.000000e-8
0.0004083333	1.000000e-8
0.0004166667	1.000000e-8
0.000425	1.000000e-8
0.0004333333	1.000000e-8
0.0004416667	1.000000e-8
0.00045	1.000000e-8
0.0004583333	1.000000e-8
0.0004666667	1.000000e-8
0.000475	1.000000e-8
0.0004833333	1.000000e-8
0.0004916667	1.000000e-8
0.0005	1.000000e-8

Calculated under the declared model
Quantity	Value	Unit
Combined volume	0.02	L
Immediate metal concentration	0.0005	mol/L
Immediate anion concentration	0.0005	mol/L
Immediate normalized quotient	2.500000e-7	dimensionless
Precipitated concentration extent	0.0004	mol/L
Precipitated amount	8.000000e-6	mol
Remaining free metal	0.0001	mol/L
Remaining free anion	0.0001	mol/L
Final normalized quotient	1.000000e-8	dimensionless

The diluted immediate state is supersaturated; a feasible depletion extent reaches the product constraint.

Use the combined volume for each dissolved amount before computing Q. Then remove equal1:1 amounts only within the smaller inventory. The curve is a constraint plot, not a measured time trace. Supersaturation favors precipitation thermodynamically but does not predict nucleation time, particle size or observed clarity.

These calculated packets are not performed chemical measurements or separation procedures. Keep feasible inventories, activity conventions, fitting observations and independent checks distinct.

The diluted immediate state is supersaturated; a feasible depletion extent reaches the product constraint.

Observation to attach to a capture

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

Understand

Separate three states

The stock packets, the immediately mixed liquid before reaction, and the later equilibrium state have different compositions. The fictional metal packet contains10 mL at .001 M; an anion packet is varied independently. Add their volumes and divide each conserved dissolved amount by that combined volume before computing Q.

For two equal10 mL stocks, each immediate concentration is .000500 M, not .001 M. Their normalized product is2.50×10⁻⁷, exceeding the supplied Ksp10⁻⁸. Precipitation is thermodynamically favored under the declared ideal assumptions.

Solve depletion within the available supply

For concentration extent z, final concentrations are M0−z and X0−z. Solve their product equal to Ksp while requiring0≤z≤min(M0,X0). In the symmetric example final free concentrations are each .000100 M, so z=.000400 M and the precipitated amount is z×.0200 L=8.00×10⁻⁶ mol.

The remaining free-ion product, not the original stock product, must match equilibrium. A negative reactant concentration would reveal an inadmissible algebraic root. If immediate Q does not exceed Ksp, the model must not create a negative amount of precipitate to force equality.

Transfer and check

Combine the original10 mL .001 M metal packet with30 mL .001 M anion packet. Immediate M=.000250 and X=.000750 M. Explain why the excess anion prevents the symmetric square-root shortcut. Write (M−z)(X−z)=10⁻⁸ with the feasible bracket before solving. This predicts an equilibrium amount, not nucleation time, particle size, visibility or a safe physical operation.

Source and evidence boundary

Conceptual reference checked 30 October 2026: OpenStax Chemistry 2e. All cases, prose and diagrams are original. Fictional species and explicitly ideal or supplied-activity constraints are not measured solubilities, real assay performance or safe physical separation protocols. No material handling, mixing, filtration or reagent procedure is requested. Retain free versus total species, inventory constraints, boundary conditions and independent evidence limits.

Apply

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

Which kinetic observations would be missing even if the thermodynamic calculation predicts a solid?

Your explanation and limitations

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Previous: Separate common-ion suppression from a prescribed activity correction Next: Test a quantitative selectivity target against the second onset

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