Solutions

• solution (abbreviated soln)

  • “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)

• 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)

• dilution (מיהול)

  • $M_1{V}_1=M_2{V}_2$
  • $V_1,V_2$ 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.)

• dissolution (הֲמָסָה)

  • enthalpy of solution: $\Delta H_{\text{solution}}=\Delta H_{\text{solute}}+\Delta H_{\text{solvent}}+\Delta H_{\text{solvation}}$
  • process:
    • breaking solute–solute attractions
      • $\Delta H_{\text{solute}}$: energy required to separate solute particles (endothermic, positive)
    • breaking solvent–solvent attractions
      • $\Delta H_{\text{solvent}}$: energy required to create spaces between solvent molecules (endothermic, positive)
    • solvation (מְסִיסָה) – forming solute–solvent attractions
      • $\Delta H_{\text{solvation}}$: energy released when solute particles interact with solvent molecules (exothermic, negative)
      • hydration (הִידְרַצְיָה, מִיּוּם)

• $\mathrm{solute}+\mathrm{solvent}\underset{\text{crystallize}}{\overset{\text{dissolve}}{\rightleftharpoons }}\mathrm{solution}$

• $\mathrm{A}\stackrel{+\mathrm{H}{}_2\mathrm{O}}{\rightleftharpoons }\mathrm{B}$

• aqueous solution (תמיסה מימית)

  • spectator ions (יונים משקיפים)

Solubility

• 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)
• solubility (מְסִיסוּת) (of a solute in a solvent)
  • “the ability of a substance, the solute, to form a solution with another substance, the solvent” (Wikipedia)
• insolubility
• quantification:
  • solute per quantity of solvent:
    • mass concentration: $g/100\mathrm{mL}$
    • $g/100\mathrm{g}$
    • $g/kg$
    • molality: ($m$ or $b$) $\frac{n_{\mathrm{solute}}}{m_{\mathrm{solvent}}}$
      • unit: $mol/kg=\mathrm{m}$ (molal)
  • solute per quantity of solution: $\frac{\text{solute}}{\text{saturated solution}}$
    • molarity: $mol/L$
    • mole fraction: $mol/mol$
    • mass fraction: $g/g$
• factors:
  • composition and structure of the solute and the solvent
    • ”like dissolves like” (Latin: “Similia similibus solventur”)
    • “the stronger the attractions between solute and solvent molecules, the greater the solubility of the solute in that solvent” (Brown, 2012)
    • “Nonpolar liquids tend to be insoluble in polar liquids” (Brown, 2012)
  • pressure. see Henry’s law
  • temperature: generally increases the solubility of solids in liquids, but decreases the solubility of gases in liquids
• solubility equilibrium
  • solubility product ($K_{sp}$) (מכפלת מסיסות)
  • reaction quotient ($Q_{sp}$)
• miscibility (מְזִיגוּת)
  • miscible (מָזִיג)
  • immiscible (לֹא-מָזִיג)

Henry’s law

• Henry’s law $C=kP$
  • $C$: molarity (concentration) of the dissolved gas in the liquid
  • $k$: Henry’s law constant (depends on the gas, solvent, and temperature)
  • $P$: partial pressure of the gas above the liquid

Saturated solution

• unsaturated solution
  • ”A solution containing less solute than a saturated solution” (Brown, 2012)
• saturated solution (תמיסה רוויה)
  • “A solution in which undissolved solute and dissolved solute are in equilibrium.” (Brown, 2012)
  • “a solution that is in equilibrium with undissolved solute” (Brown, 2012)
• supersaturation (רְוָיַת-יֶתֶר, רִוּוּי-יֶתֶר)
  • “The condition of a solution being more highly concentrated than is normally possible” (Wiktionary)
  • supersaturated solution (תמיסה רווית-יתר)
    • “A solution containing more solute than an equivalent saturated solution.”

Electrolyte

• electrolyte (אלקטרוליט)

  • “A substance that produces ions when dissolved in water; its solution conducts electricity.” (Timberlake, 2017)
  • “a substance that conducts electricity through the movement of ions, but not through the movement of electrons” (Wikipedia)
  • strong electrolyte
    • ”solutes that exist in solution completely or nearly completely as ions” (Brown, 2012)
  • weak electrolyte
    • ”solutes that exist in solution mostly in the form of neutral molecules with only a small fraction in the form of ions” (Brown, 2012)

• nonelectrolyte

  • ”A substance that dissolves in water as molecules; its solution does not conduct an electrical current.” (Timberlake, 2017)

• electrolyte identificationtodo

  • soluble ionic compound → strong electrolyte
  • covalent compound
    • ionize completely in water → strong electrolyte
    • strong acid → strong electrolyte
    • ionize partially in water → weak electrolyte
    • weak acid/base → weak electrolyte
    • not ionize in water → non-electrolytes

Ideal solution

• 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.
• Brown, Theodore L. (2012). Chemistry. Prentice Hall.
• Timberlake, Karen C. (2017). Chemistry: An Introduction to General, Organic, and Biological Chemistry. Pearson.