Solutions

• solution

  • ”A liquid or solid phase containing more than one substance, when for convenience one (or more) substance, which is called the solvent, is treated differently from the other substances, which are called solutes. When, as is often but not necessarily the case, the sum of the mole fractions of solutes is small compared with unity, the solution is called a dilute solution.” (IUPAC Gold Book)
  • true solution
    • ”a homogeneous mixture with uniform properties throughout. In a true solution, the solute cannot be isolated from the solution by filtration” (Denniston, 2022)

• solubility (מְסִיסוּת)

  • “like dissolves like” (Latin: “Similia similibus solventur”)
  • an increase in temperature usually increases solubility
  • insolubility

• solvation (הֲמָסָה)

• hydration (הִידְרַצְיָה)

• soluble (מָסִיס)

  • “A soluble substance is one that dissolves to a significant extent in a specified solvent. When solubility is mentioned without indicating a solvent, it normally means “soluble in water.”” (Jones, 2016)
  • “An insoluble substance is one that does not dissolve significantly in a specified solvent” (Jones, 2016)

• solute (מוּמָס) - dissolved substance

  • dissolved (adj.) - that has been disintegrated in a solvent (Wiktionary)

• solvent (מֵמֵס, מְמִסִּים)

  • “(1) The most abundant component of a solution. (2) The component of a solution in which the other components are considered to be dissolved.” (Jones, 2016)

• aqueous solution (תמיסה מימית)

• dissociation (דיסוציאציה, הִתְפָּרְדוּת, פירוק ליונים)

  • “The separation of an acid or a base into ions in water.” (Timberlake, 2017)
  • “The separation of ions that occurs when an ionic solid dissolves” (Jones, 2016)
  • “a general process in which molecules (or ionic compounds such as salts, or complexes) separate or split into other things such as atoms, ions, or radicals, usually in a reversible manner” (Wikipedia)
  • dissociation constant $K_{\mathrm{D}}$

• dispersion (תַּפְזִיר, תִּפְזוּר)

• colloidal dispersion

• suspension (תַּרְחִיף)

  • “a heterogeneous mixture that contains particles much larger than a colloidal dispersion” (Denniston, 2022)
  • “A mixture in which the solute particles are large enough and heavy enough to settle out and be retained by both filters and semipermeable membranes.” (Timberlake, 2017)
  • it is neither a solution nor a precipitate

• colloid (קולואיד)

  • “a dispersion of small particles (from 1 nm to 1 mm in diameter) in a solvent” (Jones, 2016)
  • “A mixture having particles that are moderately large. Colloids pass through filters but cannot pass through semipermeable membranes.” (Timberlake, 2017)

• supersaturation (רוויית יתר)

  • “The condition of a solution being more highly concentrated than is normally possible” (Wiktionary)
  • supersaturated solution (תמיסה רווית-יתר)

• saturated solution (תמיסה רוויה)

• supernate (or supernatant or supernatant liquid) (נוזל עליון)

• dilution

  • $M_1{V}_1=M_2{V}_2$
  • $V_1,V_2$ are the volumes of the solution before and after dilution, (resp.)
  • $M_1,M_2$ are the molarities of the solution before and after dilution (resp.)

• ideal solution (or ideal mixture)

  • “A solution that obeys Raoult’s law at any concentration; all solutions behave ideally as the concentration approaches zero” (Jones, 2016)
  • properties:
    • $\Delta H_{\text{mix}}=0$
    • $\Delta V_{\text{mix}}=0$
    • obeys Raoult’s law at any concentration
    • the activity coefficient is equal to one for each component

Raoult’s law

• Raoult’s law
  • given a mixture of substances, where each component $i$ present in the liquid (with amount $n_i$)
  • $P_i=x_i{P}_i^{\ast }$ is partial vapor pressure of component $i$
    • $x_i=\frac{n_i}{n_{\text{total}}}$ is the mole fraction of the component $i$
    • $P_i^{\ast }$ is the vapor pressure of the pure component $i$
      • (when $i$ is nonvolatile, $P_i^{\ast }\approx 0$)
  • $P_{\text{total}}={\sum }_i{P}_i$ is total vapor pressure of the ideal solution

Colligative properties

• $i$ is the van ‘t Hoff factor

• $b$ is the molality of the solute

• $M$ is the molarity

• $k_b$ and $k_f$ are the ebullioscopic constant (קבוע-רתיחה) and the cryoscopic constant (קבוע-קפיאה) (resp.). they are solvent-specific.

  • unit: $\mathrm{K}{\mathrm{m}}^{-1}=\mathrm{K}\mathrm{kg}\mathrm{mo}{\mathrm{l}}^{-1}$ (or ${}^{\circ }\mathrm{C}{\mathrm{m}}^{-1}$, and then $\Delta T$ are in ${}^{\circ }\mathrm{C}$)
  • (e.g. for water: $k_b=0.512\mathrm{K}\mathrm{kg}\mathrm{mo}{\mathrm{l}}^{-1}$ and $k_f=1.86\mathrm{K}\mathrm{kg}\mathrm{mo}{\mathrm{l}}^{-1}$)

• colligative properties

  • relative lowering of vapor pressure (derived from Raoult’s law)
    • $P_{\text{solution}}=x_{\text{solvent}}{P}_{\text{solvent}}^{\circ }$ is the vapor pressure of the solution
    • $\Delta P=P_{\text{solvent}}^{\circ }-P_{\text{solution}}=x_{\text{solute}}{P}_{\text{solvent}}^{\circ }$ is the decrease in vapor pressure of the solvent due to the presence of the nonvolatile solute
      • $P_{\text{solvent}}^{\circ }$: vapor pressure of the pure solvent
      • $x_{\text{solute}}$: the mole fraction of the solute in the solution
  • boiling-point elevation
    • $\Delta T_b=i{k}_{b}b$
  • freezing-point depression
    • $\Delta T_f=i{k}_{f}b$
  • Osmotic pressure

Osmotic pressure

• osmotic pressure $\pi$ (or $\Pi$)
  • $\pi =iMRT$
  • pressure units
• semipermeable membrane
• selectively permeable membrane
• osmosis (אוֹסְמוֹזָה)
• osmotic concentration (or osmolarity)
  • $\text{osmolarity}=M\cdot i$
    • SI unit: $Osm/{\mathrm{m}}^3$
    • other units: $\mathrm{osmolar}=Osm/L$
• (osmole, $\mathrm{Osm}$, $\mathrm{osmol}$) 1 osmole = 1 mole of particles that contribute to osmotic pressure
• osmolality
  • $Osm/kg$
• Given two solutions $A$ and $B$ with osmolarities $c_A$ and $c_B$:
  • if $c_A>c_B$, $A$ is hyperosmotic
  • if $c_A<c_B$, $A$ is hypoosmotic (or $A$ is to $B$)
  • if $c_A=c_B$, $A$ and $B$ are isoosmotic (or $A$ to $B$)
  • (cf. tonicity: hypertonic, hypotonic and isotonic)
• turgor pressure (לחץ טוּרְגּוֹר, מִלְחָץ)
• see also: diffusion

Water soluble compounds

water soluble compounds contain	exceptions
Alkali metal ions ($\mathrm{Li}{}^{+}$, $\mathrm{Na}{}^{+}$, $\mathrm{K}{}^{+}$, $\mathrm{Rb}{}^{+}$, $\mathrm{Cs}{}^{+}$) or the ammonium ion ($\mathrm{NH}{}_4{}^{+}$)
Nitrate ($\mathrm{NO}{}_3{}^{-}$), bicarbonate ($\mathrm{HCO}{}_3{}^{-}$), or chlorate ($\mathrm{ClO}{}_3{}^{-}$)	Chlorate compounds containing $\mathrm{Cs}{}^{+}$ and $\mathrm{Rb}{}^{+}$ are insoluble.
Halides ($\mathrm{Cl}{}^{-}$, $\mathrm{Br}{}^{-}$, $\mathrm{I}{}^{-}$)	Compounds containing halides of $\mathrm{Ag}{}^{+}$ or $\mathrm{Hg}{}_2{}^{2+}$ are insoluble. $\mathrm{CuI}$ and $\mathrm{PbI}{}_2$ are also insoluble.
Sulfate ($\mathrm{SO}{}_4{}^{2-}$)	Compounds containing sulfate of $\mathrm{Ag}{}^{+}$, $\mathrm{Ca}{}^{2+}$, $\mathrm{Sr}{}^{2+}$, $\mathrm{Ba}{}^{2+}$, $\mathrm{Hg}{}_2{}^{2+}$, or $\mathrm{Pb}{}^{2+}$
water insoluble compounds contain	exceptions
Carbonate ($\mathrm{CO}{}_3{}^{2-}$), phosphate ($\mathrm{PO}{}_4{}^{3-}$), chromate ($\mathrm{CrO}{}_4{}^{2-}$), or sulfide ($\mathrm{S}{}^{2-}$)	Compounds containing alkali metal ions or the ammonium ion are soluble. $\mathrm{SrS}$, $\mathrm{MgCrO}{}_4$, and $\mathrm{CaCrO}{}_4$ are also soluble.
Hydroxide ($\mathrm{OH}{}^{-}$)	Compounds containing alkali metal ions or the $\mathrm{Ba}{}^{2+}$, $\mathrm{Sr}{}^{2+}$, or $\mathrm{Ca}{}^{2+}$ ions are soluble.
(source: Denniston, K. J. General, organic, and biochemistry. McGraw-Hill Education.)

References

• Denniston (2022). General, Organic, and Biochemistry. McGraw-Hill Education.
• Jones, Loretta (2016). Chemical Principles. W. H. Freeman.
• Timberlake, Karen C. (2017). Chemistry: An Introduction to General, Organic, and Biological Chemistry. Pearson.