Salt and constant

Salt from the catalogue

Dissolution equilibrium

\mathrm{AgCl}\,(s) \rightleftharpoons \mathrm{Ag^{+}}\,(aq) + \mathrm{Cl^{-}}\,(aq)

Ksp expression

K_{sp} = \left(\frac{[\mathrm{Ag^{+}}]}{c^\circ}\right)\,\left(\frac{[\mathrm{Cl^{-}}]}{c^\circ}\right)

Ksp (dimensionless)

dimensionless

Solid phase:: AgCl(s) cristalino (clorargirita)
Molar mass:: 143.32 g/mol

What do you want to calculate?

Decides whether the solution stays undersaturated, dissolves or precipitates.

Initial state

Initial concentration of Ag⁺

mol/L

Initial concentration of Cl⁻

mol/L

Solid present

With no solid nothing dissolves; a finite amount can run out.

Solution volume

Saturation as a function of the extent δ

Start (δ = 0) Final stateSI = 0 (saturation)

Dashed segments indicate that the curve exceeds ±12; clipping is visual only and the tooltip and summary report the real SI.

System state

Initial state

Undersaturated

Process

Solid dissolves

Final state

Saturated

Solid phase: Present in excess

Ksp

1.770e-10

dimensionless

pKsp = 9.752

Final Qsp

1.770e-10

dimensionless

Initial Qsp: 0

Final SI

log₁₀(Qsp/Ksp)

Initial SI: −∞

Molar solubility in pure water

1.330e-5

mol/L

0.001907 g/L

Change δ: 1.330e-5 mol/L
Amount dissolved / precipitated: 1.330e-5 mol
Mass dissolved / precipitated: 0.001907 g

Concentration balance

Ions: mol/L · Solid: mol/L of formula unit.

Concentration balance. Ions: mol/L · Solid: mol/L of formula unit.
Species	Initial	Change	Final
Ag⁺ (aq)	0	1.330e-5	1.330e-5
Cl⁻ (aq)	0	1.330e-5	1.330e-5
AgCl (s)	Present in excess	-1.330e-5	Present in excess

Fundamentals & Explanation

Solubility equilibrium

For a sparingly soluble salt that dissociates into two ions, the solubility product is the dissolution equilibrium constant for a specified solid phase at a given temperature:

\mathrm{S}(s) \rightleftharpoons \nu_M\,\mathrm{M}(aq)+\nu_X\,\mathrm{X}(aq)

K_{sp}=a(\mathrm{M})^{\nu_M}a(\mathrm{X})^{\nu_X}

A pure solid has unit activity and does not appear in the expression. $\;K_{sp}$ depends on phase and temperature. If the solid is absent, the constant does not change; only $Q_{sp}=K_{sp}$ ceases to be mandatory.

The ideal-solution approximation uses $a(i)\approx[i]/c^\circ$ , with $c^\circ=1\ \mathrm{mol\,L^{-1}}$ . Thus $K_{sp}$ and $Q_{sp}$ are dimensionless, while concentrations are expressed in mol/L.

Saturation and phase state

The ion product describes the current composition. The saturation index expresses its relation to $K_{sp}$ :

Q_{sp}=\left(\frac{[\mathrm{M}]}{c^\circ}\right)^{\nu_M}\left(\frac{[\mathrm{X}]}{c^\circ}\right)^{\nu_X}

SI=\log_{10}\!\left(\frac{Q_{sp}}{K_{sp}}\right)

SI < 0: undersaturated solution; it can dissolve solid if any is available.
SI = 0: saturated solution; $Q_{sp}=K_{sp}$ .
SI > 0: supersaturated solution; precipitation is favoured.

Equilibrium must also satisfy $n_S\ge 0,\ Q_{sp}\le K_{sp},\ n_S(K_{sp}-Q_{sp})=0$ , where $n_S$ is the amount of solid. Thus, when the solid is exhausted the solution may remain undersaturated. A zero concentration gives $Q_{sp}=0$ and $SI=-\infty$ , a physically valid state.

Material balance and extent

A single extent $\delta$ , in mol/L of formula unit, preserves dissolution stoichiometry:

[\mathrm{M}]_f=[\mathrm{M}]_0+\nu_M\delta\qquad [\mathrm{X}]_f=[\mathrm{X}]_0+\nu_X\delta

These relations express the exact material balance. When an ion is nearly depleted, its final concentration is evaluated with an equivalent numerically stable form to avoid loss of precision from subtracting nearly equal quantities.

$\delta>0$ denotes dissolution and $\delta<0$ precipitation. The final state reaches $Q_{sp}=K_{sp}$ if allowed by two bounds: concentrations cannot be negative, and no more solid can dissolve than is available.

Absent: no dissolution occurs; a supersaturated solution can still precipitate.
Finite: solid may remain, run out at saturation, or run out first and leave the solution undersaturated.
Excess: an undersaturated solution reaches saturation and retains solid.

Molar solubility and the common-ion effect

In pure water with solid available, $[\mathrm{M}]=\nu_Ms_0$ and $[\mathrm{X}]=\nu_Xs_0$ . Therefore:

s_0=c^\circ\left[\frac{K_{sp}}{\nu_M^{\nu_M}\nu_X^{\nu_X}}\right]^{1/(\nu_M+\nu_X)}

If either ion is already present, the common-ion effect reduces dissolution. The change is $\delta$ , not $s_0$ ; $\;\delta/s_0$ measures that reduction only if enough solid is available to reach equilibrium.

Mixing and the onset of precipitation

When two solutions are combined, diluted concentrations are calculated first:

V_t=V_M+V_X\qquad [\mathrm{M}]_0=C_M\frac{V_M}{V_t}\qquad [\mathrm{X}]_0=C_X\frac{V_X}{V_t}

Volumes are assumed additive and constant, and counter-ions are spectators. With one ion fixed, $Q_{sp}=K_{sp}$ defines the critical concentration for precipitation. Without the partner ion, no finite threshold exists.

Interpreting the results

$Q_{sp}$ or $SI$ classifies the initial state. The sign of $\delta$ distinguishes dissolution from precipitation, and the balance shows each species change.

The $SI(\delta)$ curve joins the initial and final states; its crossing with $SI=0$ marks saturation. The phase view is conceptual and is not to scale.

In the inverse problem, solubility or concentrations determine $K_{sp}$ only when they describe saturation with the stated solid phase.

Reference examples

AgCl in water: with $K_{sp}=1.77\times10^{-10}$ , $s_0=\sqrt{K_{sp}}=1.33\times10^{-5}$ mol/L, equivalent to 1.91 mg/L.

CaF₂ in water: $K_{sp}=4(s_0/c^\circ)^3$ . For $K_{sp}=3.45\times10^{-11}$ , the result is $s_0=2.05\times10^{-4}$ mol/L, approximately 16.0 mg/L.

Ag⁺ and Cl⁻ mixture: 50 mL of 0.010 M and 50 mL of 0.020 M give 0.0050 M and 0.010 M after mixing. Since $Q_{sp}=5.0\times10^{-5}$ , AgCl precipitates and approximately $3.54\times10^{-8}$ mol/L Ag⁺ remains.

Assumptions and limits

One salt, one solid phase, and two aqueous ions, with no simultaneous reactions.
The $K_{sp}$ value corresponds to a given temperature and crystalline phase; its temperature dependence is not calculated.
Ideal solution, without activity coefficients. The 0.1 mol/L warning is only a guide and does not replace an ionic-strength calculation.
No protonation, hydrolysis, or complexation, which matter for species such as F⁻, CrO₄²⁻, PO₄³⁻, and the Pb²⁺/Cl⁻ system.
No kinetics or nucleation: $SI>0$ indicates the thermodynamic tendency, not how long crystals will take to appear.
Tabulated values are references. Analytical work requires evaluated data for the experimental phase, temperature, and medium.

References

IUPAC. Compendium of Chemical Terminology, 5th ed. — solubility product. DOI 10.1351/goldbook.S05742.
Gamsjäger, H. et al. “The IUPAC-NIST Solubility Data Series: A guide to preparation and use of compilations and evaluations”. Pure Appl. Chem. 82 (2010). DOI 10.1351/PAC-REP-09-10-33.
Petrucci, R. H. et al. General Chemistry: Principles and Modern Applications, 11th ed., Pearson, 2017.
Rumble, J. R. (ed.). CRC Handbook of Chemistry and Physics, 100th ed., CRC Press, 2019, “Solubility Product Constants of Inorganic Salts” table, catalogue values at 25 °C.

Solubility Product (Ksp)

Salt and constant

Initial state

Saturation as a function of the extent δ

System state

Concentration balance

Fundamentals & Explanation

Solubility equilibrium

Saturation and phase state

Material balance and extent

Molar solubility and the common-ion effect

Mixing and the onset of precipitation

Interpreting the results

Reference examples

Assumptions and limits

References

Solubility equilibrium

Saturation and phase state

Material balance and extent

Molar solubility and the common-ion effect

Mixing and the onset of precipitation

Interpreting the results

Reference examples

Assumptions and limits

References