When there is dynamic equilibrium between the dissolved solute and the solid solute in the solution the solution is said to be?

Solubility is sensitive to changes in temperature. For example, sugar is more soluble in hot water than cool water. It occurs because solubility products, like other types of equilibrium constants, are functions of temperature. In accordance with Le Chatelier's Principle, when the dissolution process is endothermic (heat is absorbed), solubility increases with rising temperature. This effect is the basis for the process of recrystallization, which can be used to purify a chemical compound. When dissolution is exothermic (heat is released) solubility decreases with rising temperature.[1]Sodium sulfate shows increasing solubility with temperature below about 32.4 °C, but a decreasing solubility at higher temperature.[2] This is because the solid phase is the decahydrate (Na
2SO
4·10H
2O) below the transition temperature, but a different hydrate above that temperature.

The dependence on temperature of solubility for an ideal solution (achieved for low solubility substances) is given by the following expression containing the enthalpy of melting, ΔmH, and the mole fraction x i {\displaystyle x_{i}}   of the solute at saturation:

( ∂ ln ⁡ x i ∂ T ) P = H ¯ i , a q − H i , c r R T 2 {\displaystyle \left({\frac {\partial \ln x_{i}}{\partial T}}\right)_{P}={\frac {{\bar {H}}_{i,\mathrm {aq} }-H_{i,\mathrm {cr} }}{RT^{2}}}}

H ¯ i , a q {\displaystyle {\bar {H}}_{i,\mathrm {aq} }}  

H i , c r {\displaystyle H_{i,\mathrm {cr} }}  

This differential expression for a non-electrolyte can be integrated on a temperature interval to give:[4]

ln ⁡ x i = Δ m H i R ( 1 T f − 1 T ) {\displaystyle \ln x_{i}={\frac {\Delta _{m}H_{i}}{R}}\left({\frac {1}{T_{f}}}-{\frac {1}{T}}\right)}

For nonideal solutions activity of the solute at saturation appears instead of mole fraction solubility in the derivative with respect to temperature:

( ∂ ln ⁡ a i ∂ T ) P = H i , a q − H i , c r R T 2 {\displaystyle \left({\frac {\partial \ln a_{i}}{\partial T}}\right)_{P}={\frac {H_{i,\mathrm {aq} }-H_{i,\mathrm {cr} }}{RT^{2}}}}

Common-ion effect

The common-ion effect is the effect of decreased solubility of one salt when another salt that has an ion in common with it is also present. For example, the solubility of silver chloride, AgCl, is lowered when sodium chloride, a source of the common ion chloride, is added to a suspension of AgCl in water.[5]

A g C l ( s ) ⇋ A g + ( a q ) + C l − ( a q ) {\displaystyle \mathrm {AgCl(s)\leftrightharpoons Ag^{+}(aq)+Cl^{-}(aq)} }

K s p = [ A g + ] [ C l − ] = x 2 {\displaystyle K_{\mathrm {sp} }=\mathrm {[Ag^{+}][Cl^{-}]} =x^{2}}

Solubility = [ A g + ] = [ C l − ] = x = K s p {\displaystyle {\text{Solubility}}=\mathrm {[Ag^{+}]=[Cl^{-}]} =x={\sqrt {K_{\mathrm {sp} }}}}

1.77×10−10 mol2 dm−6

1.33×10−5 mol dm−3

Now suppose that sodium chloride is also present, at a concentration of 0.01 mol dm−3 = 0.01 M. The solubility, ignoring any possible effect of the sodium ions, is now calculated by

K s p = [ A g + ] [ C l − ] = x ( 0.01 M + x ) {\displaystyle K_{\mathrm {sp} }=\mathrm {[Ag^{+}][Cl^{-}]} =x(0.01\,{\text{M}}+x)}

x 2 + 0.01 M x − K s p = 0 {\displaystyle x^{2}+0.01\,{\text{M}}\,x-K_{sp}=0}

Solubility = [ A g + ] = x = K s p 0.01 M = 1.77 × 10 − 8 m o l d m − 3 {\displaystyle {\text{Solubility}}=\mathrm {[Ag^{+}]} =x={\frac {K_{\mathrm {sp} }}{0.01\,{\text{M}}}}=\mathrm {1.77\times 10^{-8}\,mol\,dm^{-3}} }

1.33×10−5 mol dm−3

The thermodynamic solubility constant is defined for large monocrystals. Solubility will increase with decreasing size of solute particle (or droplet) because of the additional surface energy. This effect is generally small unless particles become very small, typically smaller than 1 μm. The effect of the particle size on solubility constant can be quantified as follows:

log ⁡ ( ∗ K A ) = log ⁡ ( ∗ K A → 0 ) + γ A m 3.454 R T {\displaystyle \log(^{*}K_{A})=\log(^{*}K_{A\to 0})+{\frac {\gamma A_{\mathrm {m} }}{3.454RT}}}

Salt effects

The salt effects[7] (salting in and salting-out) refers to the fact that the presence of a salt which has no ion in common with the solute, has an effect on the ionic strength of the solution and hence on activity coefficients, so that the equilibrium constant, expressed as a concentration quotient, changes.

Phase effect

Equilibria are defined for specific crystal phases. Therefore, the solubility product is expected to be different depending on the phase of the solid. For example, aragonite and calcite will have different solubility products even though they have both the same chemical identity (calcium carbonate). Under any given conditions one phase will be thermodynamically more stable than the other; therefore, this phase will form when thermodynamic equilibrium is established. However, kinetic factors may favor the formation the unfavorable precipitate (e.g. aragonite), which is then said to be in a metastable state.

In pharmacology, the metastable state is sometimes referred to as amorphous state. Amorphous drugs have higher solubility than their crystalline counterparts due to the absence of long-distance interactions inherent in crystal lattice. Thus, it takes less energy to solvate the molecules in amorphous phase. The effect of amorphous phase on solubility is widely used to make drugs more soluble.[8][9]

Pressure effect

For condensed phases (solids and liquids), the pressure dependence of solubility is typically weak and usually neglected in practice. Assuming an ideal solution, the dependence can be quantified as:

( ∂ ln ⁡ x i ∂ P ) T = − V ¯ i , a q − V i , c r R T {\displaystyle \left({\frac {\partial \ln x_{i}}{\partial P}}\right)_{T}=-{\frac {{\bar {V}}_{i,\mathrm {aq} }-V_{i,\mathrm {cr} }}{RT}}}

x i {\displaystyle x_{i}}  

i {\displaystyle i}  

P {\displaystyle P}  

T {\displaystyle T}  

V ¯ i , aq {\displaystyle {\bar {V}}_{i,{\text{aq}}}}  

i {\displaystyle i}  

V i , cr {\displaystyle V_{i,{\text{cr}}}}  

i {\displaystyle i}  

R {\displaystyle R}  

The pressure dependence of solubility does occasionally have practical significance. For example, precipitation fouling of oil fields and wells by calcium sulfate (which decreases its solubility with decreasing pressure) can result in decreased productivity with time.

Dissolution of an organic solid can be described as an equilibrium between the substance in its solid and dissolved forms. For example, when sucrose (table sugar) forms a saturated solution

C 12 H 22 O 11 ( s ) ⇋ C 12 H 22 O 11 ( a q ) {\displaystyle \mathrm {C_{12}H_{22}O_{11}(s)\leftrightharpoons C_{12}H_{22}O_{11}(aq)} }

K ⊖ = { C 12 H 22 O 11 ( a q ) } { C 12 H 22 O 11 ( s ) } {\displaystyle K^{\ominus }={\frac {\left\{\mathrm {{C}_{12}{H}_{22}{O}_{11}(aq)} \right\}}{\left\{\mathrm {{C}_{12}{H}_{22}{O}_{11}(s)} \right\}}}}

K ⊖ = { C 12 H 22 O 11 ( a q ) } {\displaystyle K^{\ominus }=\left\{\mathrm {{C}_{12}{H}_{22}{O}_{11}(aq)} \right\}}

K s = [ C 12 H 22 O 11 ( a q ) ] {\displaystyle K_{\mathrm {s} }=\left[\mathrm {{C}_{12}{H}_{22}{O}_{11}(aq)} \right]}

Dissolution with dissociation

Ionic compounds normally dissociate into their constituent ions when they dissolve in water. For example, for silver chloride:

A g C l ( s ) ⇋ A g ( a q ) + + C l ( a q ) − {\displaystyle \mathrm {AgCl_{(s)}} \leftrightharpoons \mathrm {Ag_{(aq)}^{+}} +\mathrm {Cl_{(aq)}^{-}} }

K ⊖ = { Ag + ( aq ) } { Cl − ( aq ) } { AgCl ( s ) } = { Ag + ( aq ) } { Cl − ( aq ) } {\displaystyle K^{\ominus }={\frac {\left\{{\ce {Ag+}}_{{\ce {(aq)}}}\right\}\left\{{\ce {Cl-}}_{{\ce {(aq)}}}\right\}}{\left\{{\ce {AgCl_{(s)}}}\right\}}}=\left\{{\ce {Ag+}}_{{\ce {(aq)}}}\right\}\left\{{\ce {Cl-}}_{{\ce {(aq)}}}\right\}}

K ⊖ {\displaystyle K^{\ominus }}  

When the solubility of the salt is very low the activity coefficients of the ions in solution are nearly equal to one. By setting them to be actually equal to one this expression reduces to the solubility product expression:

K sp = [ Ag + ] [ Cl − ] = [ Ag + ] 2 = [ Cl − ] 2 . {\displaystyle K_{{\ce {sp}}}=[{\ce {Ag+}}][{\ce {Cl-}}]=[{\ce {Ag+}}]^{2}=[{\ce {Cl-}}]^{2}.}

For 2:2 and 3:3 salts, such as CaSO4 and FePO4, the general expression for the solubility product is the same as for a 1:1 electrolyte

A B ⇋ A p + + B p − {\displaystyle \mathrm {AB} \leftrightharpoons \mathrm {A} ^{p+}+\mathrm {B} ^{p-}}

K s p = [ A ] [ B ] = [ A ] 2 = [ B ] 2 {\displaystyle K_{sp}=\mathrm {[A][B]} =\mathrm {[A]^{2}} =\mathrm {[B]^{2}} }  

With an unsymmetrical salt like Ca(OH)2 the solubility expression is given by

C a ( O H ) 2 ⇋ C a 2 + + 2 O H − {\displaystyle \mathrm {Ca(OH)_{2}\leftrightharpoons {Ca}^{2+}+2OH^{-}} }

K s p = [ C a ] [ O H ] 2 {\displaystyle \mathrm {K_{sp}=[Ca][OH]^{2}} }

K s p = 4 [ C a ] 3 {\displaystyle \mathrm {K_{sp}=4[Ca]^{3}} }  

In general, with the chemical equilibrium

A p B q ⇋ p A n + + q B m − {\displaystyle \mathrm {A_{p}B_{q}\leftrightharpoons p{A}^{n+}+q{B}^{m-}} }

[ B ] = q p [ A ] {\displaystyle \mathrm {[B]={\frac {q}{p}}[A]} }

Solubility products are often expressed in logarithmic form. Thus, for calcium sulfate, with Ksp = 4.93×10−5 mol2 dm−6, log Ksp = −4.32. The smaller the value of Ksp, or the more negative the log value, the lower the solubility.

Some salts are not fully dissociated in solution. Examples include MgSO4, famously discovered by Manfred Eigen to be present in seawater as both an inner sphere complex and an outer sphere complex.[12] The solubility of such salts is calculated by the method outlined in dissolution with reaction.

Hydroxides

The solubility product for the hydroxide of a metal ion, Mn+, is usually defined, as follows:

M ( O H ) n ⇋ M n + + n O H − {\displaystyle \mathrm {M(OH)_{n}\leftrightharpoons \mathrm {M^{n+}+nOH^{-}} } }

K s p = [ M n + ] [ O H − ] n {\displaystyle K_{sp}=\mathrm {[M^{n+}][OH^{-}]^{n}} }

M ( O H ) n + n H + ⇋ M n + + n H 2 O {\displaystyle \mathrm {M(OH)_{n}+nH^{+}\leftrightharpoons M^{n+}+nH_{2}O} }

K sp ∗ = [ M n + ] [ H + ] − n {\displaystyle K_{\text{sp}}^{*}=\mathrm {[M^{n+}][H^{+}]^{-n}} }

For hydroxides, solubility products are often given in a modified form, K*sp, using hydrogen ion concentration in place of hydroxide ion concentration. The two values are related by the self-ionization constant for water, Kw.[13]

K w = [ H + ] [ O H − ] {\displaystyle K_{\mathrm {w} }=[\mathrm {H^{+}} ][\mathrm {OH^{-}} ]}

K sp ∗ = K sp ( K w ) n {\displaystyle K_{\text{sp}}^{*}={\frac {K_{\text{sp}}}{(K_{\text{w}})^{n}}}}

L g K sp ∗ = l g K sp − n L g K w {\displaystyle LgK_{\text{sp}}^{*}=lgK_{\text{sp}}-nLgK_{\text{w}}}

Dissolution with reaction

A typical reaction with dissolution involves a weak base, B, dissolving in an acidic aqueous solution.

B ( s ) + H + ( a q ) ⇋ B H + ( a q ) {\displaystyle \mathrm {B} \mathrm {(s)} +\mathrm {H} ^{+}\mathrm {(aq)} \leftrightharpoons \mathrm {BH} ^{+}(\mathrm {aq)} }

H A ( s ) + O H − ( a q ) ⇋ A − ( a q ) + H 2 O {\displaystyle \mathrm {HA(s)+OH^{-}(aq)\leftrightharpoons A^{-}(aq)+H_{2}O} }

Leaching of aluminium salts from rocks and soil by acid rain is another example of dissolution with reaction: alumino-silicates are bases which react with the acid to form soluble species, such as Al3+(aq).

Formation of a chemical complex may also change solubility. A well-known example is the addition of a concentrated solution of ammonia to a suspension of silver chloride, in which dissolution is favoured by the formation of an ammine complex.

A g C l ( s ) + 2 N H 3 ( a q ) ⇋ [ A g ( N H 3 ) 2 ] + ( a q ) + C l − ( a q ) {\displaystyle \mathrm {AgCl(s)+2NH_{3}(aq)\leftrightharpoons [Ag(NH_{3})_{2}]^{+}(aq)+Cl^{-}(aq)} }

The determination of solubility is fraught with difficulties.[6] First and foremost is the difficulty in establishing that the system is in equilibrium at the chosen temperature. This is because both precipitation and dissolution reactions may be extremely slow. If the process is very slow solvent evaporation may be an issue. Supersaturation may occur. With very insoluble substances, the concentrations in solution are very low and difficult to determine. The methods used fall broadly into two categories, static and dynamic.

Static methods

In static methods a mixture is brought to equilibrium and the concentration of a species in the solution phase is determined by chemical analysis. This usually requires separation of the solid and solution phases. In order to do this the equilibration and separation should be performed in a thermostatted room.[15] Very low concentrations can be measured if a radioactive tracer is incorporated in the solid phase.

A variation of the static method is to add a solution of the substance in a non-aqueous solvent, such as dimethyl sulfoxide, to an aqueous buffer mixture.[16] Immediate precipitation may occur giving a cloudy mixture. The solubility measured for such a mixture is known as "kinetic solubility". The cloudiness is due to the fact that the precipitate particles are very small resulting in Tyndall scattering. In fact the particles are so small that the particle size effect comes into play and kinetic solubility is often greater than equilibrium solubility. Over time the cloudiness will disappear as the size of the crystallites increases, and eventually equilibrium will be reached in a process known as precipitate ageing.[17]

Dynamic methods

Solubility values of organic acids, bases, and ampholytes of pharmaceutical interest may be obtained by a process called "Chasing equilibrium solubility".[18] In this procedure, a quantity of substance is first dissolved at a pH where it exists predominantly in its ionized form and then a precipitate of the neutral (un-ionized) species is formed by changing the pH. Subsequently, the rate of change of pH due to precipitation or dissolution is monitored and strong acid and base titrant are added to adjust the pH to discover the equilibrium conditions when the two rates are equal. The advantage of this method is that it is relatively fast as the quantity of precipitate formed is quite small. However, the performance of the method may be affected by the formation supersaturated solutions.

1. ^ Pauling, Linus (1970). General Chemistry. Dover Publishing. p. 450.
2. ^ Linke, W.F.; Seidell, A. (1965). Solubilities of Inorganic and Metal Organic Compounds (4th ed.). Van Nostrand. ISBN 0-8412-0097-1.
3. ^ Kenneth Denbigh, The Principles of Chemical Equilibrium, 1957, p. 257
4. ^ Peter Atkins, Physical Chemistry, p. 153 (8th edition)
5. ^ Housecroft, C. E.; Sharpe, A. G. (2008). Inorganic Chemistry (3rd ed.). Prentice Hall. ISBN 978-0-13-175553-6. Section 6.10.
6. ^ a b Hefter, G. T.; Tomkins, R. P. T., eds. (2003). The Experimental Determination of Solubilities. Wiley-Blackwell. ISBN 0-471-49708-8.
7. ^ Mendham, J.; Denney, R. C.; Barnes, J. D.; Thomas, M. J. K. (2000), Vogel's Quantitative Chemical Analysis (6th ed.), New York: Prentice Hall, ISBN 0-582-22628-7 Section 2.14
8. ^ Hsieh, Yi-Ling; Ilevbare, Grace A.; Van Eerdenbrugh, Bernard; Box, Karl J.; Sanchez-Felix, Manuel Vincente; Taylor, Lynne S. (2012-05-12). "pH-Induced Precipitation Behavior of Weakly Basic Compounds: Determination of Extent and Duration of Supersaturation Using Potentiometric Titration and Correlation to Solid State Properties". Pharmaceutical Research. 29 (10): 2738–2753. doi:10.1007/s11095-012-0759-8. ISSN 0724-8741. PMID 22580905. S2CID 15502736.
9. ^ Dengale, Swapnil Jayant; Grohganz, Holger; Rades, Thomas; Löbmann, Korbinian (May 2016). "Recent advances in co-amorphous drug formulations". Advanced Drug Delivery Reviews. 100: 116–125. doi:10.1016/j.addr.2015.12.009. ISSN 0169-409X. PMID 26805787.
10. ^ Gutman, E. M. (1994). Mechanochemistry of Solid Surfaces. World Scientific Publishing.
11. ^ Skoog, Douglas A; West, Donald M; Holler, F James (2004). "9B-5". Fundamentals of Analytical Chemistry (8th ed.). Brooks/Cole. pp. 238–242. ISBN 0030355230.
12. ^ Eigen, Manfred (1967). "Nobel lecture" (PDF). Nobel Prize.
13. ^ Baes, C. F.; Mesmer, R. E. (1976). The Hydrolysis of Cations. New York: Wiley.
14. ^ Payghan, Santosh (2008). "Potential Of Solubility In Drug Discovery And development". Pharminfo.net. Archived from the original on March 30, 2010. Retrieved 5 July 2010.
15. ^ Rossotti, F. J. C.; Rossotti, H. (1961). "Chapter 9: Solubility". The Determination of Stability Constants. McGraw-Hill.
16. ^ Aqueous solubility measurement – kinetic vs. thermodynamic methods Archived July 11, 2009, at the Wayback Machine
17. ^ Mendham, J.; Denney, R. C.; Barnes, J. D.; Thomas, M. J. K. (2000), Vogel's Quantitative Chemical Analysis (6th ed.), New York: Prentice Hall, ISBN 0-582-22628-7 Chapter 11: Gravimetric analysis
18. ^ Stuart, M.; Box, K. (2005). "Chasing Equilibrium: Measuring the Intrinsic Solubility of Weak Acids and Bases". Analytical Chemistry. 77 (4): 983–990. doi:10.1021/ac048767n. PMID 15858976.