Acids and bases

• acid (חומצה)
• base (בסיס)
• acid–base reaction
• Arrhenius definition
• Brønsted–Lowry definition

Arrhenius definition

• acid: produces $\mathrm{H}{}^{+}$ in water
  • $\mathrm{HA}(\mathrm{aq})\to \mathrm{H}{}^{+}(\mathrm{aq})+\mathrm{A}{}^{-}(\mathrm{aq})$
  • $\mathrm{HA}(\mathrm{aq})+\mathrm{H}{}_2\mathrm{O}(\mathrm{l})\rightleftharpoons \mathrm{H}{}_3\mathrm{O}{}^{+}(\mathrm{aq})+\mathrm{A}{}^{-}(\mathrm{aq})$
• base: produces $\mathrm{OH}{}^{-}$ in water
  • $\mathrm{BOH}(\mathrm{aq})\to \mathrm{B}{}^{+}(\mathrm{aq})+\mathrm{OH}{}^{-}(\mathrm{aq})$

Brønsted–Lowry definition

• Brønsted–Lowry theory (aka: proton theory of acids and bases)

• “An acid and a base react not to produce a salt and a solvent, but to form a new acid and a new base. The concept of neutralization is thus absent.” (Wikipedia)

• “An acid–base reaction is, thus, the removal of a proton from the acid and its addition to the base.” (Wikipedia)

• acid: proton ($\mathrm{H}{}^{+}$) donor

• base: proton ($\mathrm{H}{}^{+}$) acceptor

• conjugate acid (חומצה צמודה)

• conjugate base (בסיס צמוד)

• conjugate acid base pairs

  • For any conjugate acid-base pair (where $K_a$ and $K_b$ are their dissociation constants) in an aqueous solution at a constant temperature: $K_a\times K_b=K_w$

• heuristics for determining whether a species is a Brønsted acid/base:

  • has ionizable $\mathrm{H}$ atoms → acid
    • (e.g. $\mathrm{HA}$, where $\mathrm{A}$ is highly electronegative)
  • has lone pairs that can accept $\mathrm{H}{}^{+}$ → basicity indicator
  • net positive charge → acidity indicator
  • net negative charge → basicity indicator

• metal and nonmetal oxidestodo

  • most nonmetals oxide are acidic
  • water soluble metal oxides + water → metal hydroxide
  • water insoluble metal oxides + acid → salt + water
  • water soluble nonmetal oxide + water → acid
  • water insoluble nonmetal oxide + base → salt + water

• In a acid–base reaction $\mathrm{HA}+\mathrm{B}\rightleftharpoons \mathrm{A}{}^{-}+\mathrm{BH}{}^{+}$, equilibrium favors the side containing the weaker acid and the weaker base. The equilibrium constant for the reaction:

  • $K_{\text{eq}}=\frac{[\mathrm{A}{}^{-}][\mathrm{BH}{}^{+}]}{[\mathrm{HA}][\mathrm{B}]}=\frac{K_a(\mathrm{HA})}{K_a(\mathrm{BH}{}^{+})}=10^{\mathrm{p}{K}_a(\mathrm{BH}{}^{+})-\mathrm{p}{K}_a(\mathrm{HA})}$, therefore:
    • if the product acid is stronger than the reactant acid, then $K_a(\mathrm{HA})<K_a(\mathrm{BH}{}^{+})$, then $K_{\text{eq}}>1$, then products favored
    • if the product acid is weaker than the reactant acid, then $K_a(\mathrm{HA})>K_a(\mathrm{BH}{}^{+})$, then $K_{\text{eq}}<1$, then reactants favored
  • e.g., in $\mathrm{HCl}+\mathrm{H}{}_2\mathrm{O}\to \mathrm{H}{}_3\mathrm{O}{}^{+}+\mathrm{Cl}{}^{-}$ $\mathrm{HCl}$ is a stronger acid than $\mathrm{H}{}_3\mathrm{O}{}^{+}$ and $\mathrm{H}{}_2\mathrm{O}$ is a stronger base than $\mathrm{Cl}{}^{-}$

---

• amphoterism
  • amphoteric compound (תרכובת אַמְפוֹטֵרִית)
  • amphichromatic
  • amphiprotic

Neutralization

• neutralization (סתירה)
• “a chemical reaction in which acid and a base react with an equivalent quantity of each other” (Wikipedia)
• “In general, a neutralization reaction between an acid and a metal hydroxide produces water and a salt” (Brown, 2012)

Examples

• $\mathrm{HA}(\mathrm{aq})+\mathrm{BOH}(\mathrm{aq})\to \mathrm{BA}(\mathrm{aq})+\mathrm{H}{}_2\mathrm{O}(\mathrm{l})$
  • net ionic equation:
    • $\mathrm{H}{}_3\mathrm{O}{}^{+}(\mathrm{aq})+\mathrm{OH}{}^{-}(\mathrm{aq})\to 2\mathrm{H}{}_2\mathrm{O}(\mathrm{l})$
      • (or $\mathrm{H}{}^{+}(\mathrm{aq})+\mathrm{OH}{}^{-}(\mathrm{aq})\to \mathrm{H}{}_2\mathrm{O}(\mathrm{l})$)
  • $\mathrm{strong}\mathrm{acid}(\mathrm{aq})+\mathrm{strong}\mathrm{base}(\mathrm{aq})\to \underset{\mathrm{neutral}}{\mathrm{salt}(\mathrm{aq})}+\mathrm{H}{}_2\mathrm{O}(\mathrm{l})$
    • (e.g. $\mathrm{HCl}(\mathrm{aq})+\mathrm{NaOH}(\mathrm{aq})\to \mathrm{NaCl}(\mathrm{aq})+\mathrm{H}{}_2\mathrm{O}(\mathrm{l})$)
  • $\mathrm{strong}\mathrm{acid}(\mathrm{aq})+\mathrm{weak}\mathrm{base}(\mathrm{aq})\to \underset{\mathrm{acidic}}{\mathrm{salt}(\mathrm{aq})}+\mathrm{H}{}_2\mathrm{O}(\mathrm{l})$
  • $\mathrm{weak}\mathrm{acid}(\mathrm{aq})+\mathrm{strong}\mathrm{base}(\mathrm{aq})\to \underset{\mathrm{basic}}{\mathrm{salt}(\mathrm{aq})}+\mathrm{H}{}_2\mathrm{O}(\mathrm{l})$
  • $\mathrm{weak}\mathrm{acid}(\mathrm{aq})+\mathrm{weak}\mathrm{base}(\mathrm{aq})\to \mathrm{salt}(\mathrm{aq})+\mathrm{H}{}_2\mathrm{O}(\mathrm{l})$
  • $\mathrm{acid}(\mathrm{aq})+\text{metal oxide}(\mathrm{aq})\to \mathrm{salt}(\mathrm{aq})+\mathrm{H}{}_2\mathrm{O}(\mathrm{l})$
  • $\mathrm{acid}(\mathrm{aq})+\text{metal carbonate}(\mathrm{aq})\to \mathrm{salt}(\mathrm{aq})+\mathrm{H}{}_2\mathrm{O}(\mathrm{l})+\mathrm{CO}{}_2(\mathrm{g})$
  • $\mathrm{acid}(\mathrm{aq})+\text{metal hydroxide}(\mathrm{aq})\to \mathrm{salt}(\mathrm{aq})+\mathrm{H}{}_2\mathrm{O}(\mathrm{l})$
• $\mathrm{HA}(\mathrm{aq})+\mathrm{H}{}_2\mathrm{O}(\mathrm{l})\to \mathrm{H}{}_3\mathrm{O}{}^{+}(\mathrm{aq})+\mathrm{A}{}^{-}(\mathrm{aq})$
• $\underset{\mathrm{weak}\mathrm{base}}{\mathrm{B}(\mathrm{aq})}+\underset{\mathrm{weak}\mathrm{acid}}{\mathrm{H}{}_2\mathrm{O}(\mathrm{l})}\rightleftharpoons \underset{\text{conj. acid}}{\mathrm{BH}{}^{+}(\mathrm{aq})}+\underset{\text{conj. base}}{\mathrm{OH}{}^{-}(\mathrm{aq})}$
• $\underset{\mathrm{weak}\mathrm{acid}}{\mathrm{HA}(\mathrm{aq})}+\underset{\mathrm{weak}\mathrm{base}}{\mathrm{H}{}_2\mathrm{O}(\mathrm{l})}\rightleftharpoons \underset{\text{conj. base}}{\mathrm{A}{}^{-}(\mathrm{aq})}+\underset{\text{conj. acid}}{\mathrm{H}{}_3\mathrm{O}{}^{+}(\mathrm{aq})}$
• $\mathrm{acid}(\mathrm{g})+\mathrm{base}(\mathrm{g})\to \mathrm{salt}(\mathrm{s})$
• $\mathrm{NH}{}_4{}^{+}(\mathrm{aq})+\mathrm{OH}{}^{-}(\mathrm{aq})\to \mathrm{NH}{}_3(\mathrm{aq})+\mathrm{H}{}_2\mathrm{O}(\mathrm{l})$
• $\underset{\text{acid}}{\mathrm{HA}(\mathrm{aq})}+\underset{\text{base}}{\mathrm{B}(\mathrm{aq})}\rightleftharpoons \underset{\text{conj. base}}{\mathrm{A}{}^{-}(\mathrm{aq})}+\underset{\text{conj. acid}}{\mathrm{BH}{}^{+}(\mathrm{aq})}$

Acid strength

• acid strength
  • ”strength of a weak acid is quantified by its acid dissociation constant” (Wikipedia)
  • “The usual measure of the strength of an acid is its acid dissociation constant ($K_a$), which can be determined experimentally by titration methods” (Wikipedia)
  • “Two key factors that contribute to the ease of deprotonation are the polarity of the H−A bond and the size of atom A, which determine the strength of the H−A bond. Acid strengths also depend on the stability of the conjugate base.” (Wikipedia)
• strong acid: completely deprotonated in solution
  • $K_a$ value: very large ($K_a\gg 1$)
• weak acid:
  • incompletely deprotonated in solution
    • $\mathrm{HA}\rightleftharpoons \mathrm{H}{}^{+}+\mathrm{A}{}^{-}$
  • $K_a$ value: small ($K_a<1$)
• strong base:
  • completely protonated in solution
  • $K_b\gg 1$
• weak base:
  • incompletely protonated in solution
    • $\mathrm{B}+\mathrm{H}{}_2\mathrm{O}\rightleftharpoons \mathrm{BH}{}^{+}+\mathrm{OH}{}^{-}$

Dissociation constant

• The $K_a$ (and $K_b$) value measures the tendency of an acid (or base) solute to donate (or accept) a proton to (or from) a solvent (typically water or DMSO) at a given temperature.

• The acid dissociation constant ($K_a$) of a solute acid $\mathrm{HA}$ in a solvent $\mathrm{S}$ at a specified temperature $T$ is the equilibrium constant defined by the expression: $K_a=\frac{a_{\mathrm{A}{}^{-}}\cdot a_{\mathrm{SH}{}^{+}}}{a_{\mathrm{HA}}}$

  • (also called the acidity constant or acid-ionization constant)
  • under ideal conditions, this is approximated by: $K_a=\frac{[\mathrm{A}{}^{-}][\mathrm{SH}{}^{+}]}{[\mathrm{HA}]}$
    • if the solvent is water, then: $K_a=\frac{[\mathrm{H}{}_3\mathrm{O}{}^{+}][\mathrm{A}{}^{-}]}{[\mathrm{HA}]}$
      • where the reaction is $\underset{\text{weak acid}}{\mathrm{HA}(\mathrm{aq})}+\underset{\text{weak base}}{\mathrm{H}{}_2\mathrm{O}(\mathrm{l})}\rightleftharpoons \underset{\text{conj. acid}}{\mathrm{H}{}_3\mathrm{O}{}^{+}(\mathrm{aq})}+\underset{\text{conj. base}}{\mathrm{A}{}^{-}(\mathrm{aq})}$
      • (this is often simplified to: $K_a=\frac{[\mathrm{H}{}^{+}][\mathrm{A}{}^{-}]}{[\mathrm{HA}]}$ for $\underset{\text{weak acid}}{\mathrm{HA}(\mathrm{aq})}\rightleftharpoons \mathrm{H}{}^{+}(\mathrm{aq})+\underset{\text{conj. base}}{\mathrm{A}{}^{-}(\mathrm{aq})}$)

• The base dissociation constant ($K_b$) of a solute base $\mathrm{B}$ in a solvent $\mathrm{S}$ at a specified temperature $T$ is the equilibrium constant defined by the expression: $K_b=\frac{a_{\mathrm{BH}{}^{+}}\cdot a_{\mathrm{S}{}^{-}}}{a_{\mathrm{B}}}$

  • (also called the basicity constant or base-ionization constant)
  • under ideal conditions, this is approximated by: $K_b=\frac{[\mathrm{BH}{}^{+}][\mathrm{S}{}^{-}]}{[\mathrm{B}]}$
    • if the solvent is water, then: $K_b=\frac{[\mathrm{BH}{}^{+}][\mathrm{OH}{}^{-}]}{[\mathrm{B}]}$
      • where the reaction is $\underset{\text{weak base}}{\mathrm{B}(\mathrm{aq})}+\underset{\text{weak acid}}{\mathrm{H}{}_2\mathrm{O}(\mathrm{l})}\rightleftharpoons \underset{\text{conj. acid}}{\mathrm{BH}{}^{+}(\mathrm{aq})}+\underset{\text{conj. base}}{\mathrm{OH}{}^{-}(\mathrm{aq})}$

• $\mathrm{p}{K}_a=-{\log }_{10}{K}_a$

• $\mathrm{p}{K}_b=-{\log }_{10}{K}_b$

• leveling effect

• protic solvent

• monoacidic base

• polyacidic base

  • diacidic base
  • triacidic base

• monoprotic (or monobasic) acid

• polyprotic (or polybasic) acid

  • diprotic acid
  • triprotic acid

Self-ionization of water

• molecular autoionization (or self-ionization)
• self-ionization of water (יינון עצמי של מים)
  • $2\mathrm{H}{}_2\mathrm{O}\rightleftharpoons \mathrm{H}{}_3\mathrm{O}{}^{+}+\mathrm{OH}{}^{-}$
  • equilibrium constant: $K_{\mathrm{eq}}=\frac{[\mathrm{H}{}_3\mathrm{O}{}^{+}][\mathrm{OH}{}^{-}]}{[\mathrm{H}{}_2\mathrm{O}{]}^2}$
  • (ionic product of water) $K_{\mathrm{w}}=[\mathrm{H}{}_3\mathrm{O}{}^{+}][\mathrm{OH}{}^{-}]$ ($=1.0\times 10^{-14}$ at $25^{\circ }\mathrm{C}$)
    • $\mathrm{p}{K}_{\mathrm{w}}=-{\log }_{10}{K}_{\mathrm{w}}=\mathrm{pH}+\mathrm{pOH}$ ($=14$ at $25^{\circ }\mathrm{C}$)

pH

• pH (ערך הֲגָבָה, רמת חומציות) of an aqueous solution (at a given temperature)
  • $\mathrm{pH}=-{\log }_{10}[\mathrm{H}{}_3\mathrm{O}{}^{+}]$
• $\mathrm{pOH}=-{\log }_{10}[\mathrm{OH}{}^{-}]$
• pH and pOH depend on the solute and its concentration
• an aqueous solution is said to be:
  • neutral, if $[\mathrm{H}{}_3\mathrm{O}{}^{+}]=[\mathrm{OH}{}^{-}]$
    • (equivalently $\mathrm{pH}=\frac{1}{2}\mathrm{p}{K}_w$)
  • basic, if $[\mathrm{H}{}_3\mathrm{O}{}^{+}]<[\mathrm{OH}{}^{-}]$
    • (equivalently $\mathrm{pH}>\frac{1}{2}\mathrm{p}{K}_w$)
  • acidic, if $[\mathrm{H}{}_3\mathrm{O}{}^{+}]>[\mathrm{OH}{}^{-}]$
    • (equivalently $\mathrm{pH}<\frac{1}{2}\mathrm{p}{K}_w$)
  • (or to have a higher acidity (or basicity))
• Henderson-Hasselbalch equation
  • $\mathrm{pH}\approx \mathrm{p}{K}_a+{\log }_{10}\frac{[\mathrm{A}{}^{-}]}{[\mathrm{HA}]}$
  • $\mathrm{pH}\approx \mathrm{p}{K}_a+{\log }_{10}\frac{[\text{base}{]}_{\text{initial}}}{[\text{acid}{]}_{\text{initial}}}$
• $C_0$ is the initial concentration (of the acid or base)
• The degree of dissociation ($\alpha$) (of the acid or base)
• For a monoprotic acid:
  • $K_a=\frac{10^{-2\mathrm{pH}}}{C_0-10^{-\mathrm{pH}}}=\frac{[\mathrm{H}{}_3\mathrm{O}{}^{+}{]}^2}{C_0-[\mathrm{H}{}_3\mathrm{O}{}^{+}]}$
  • $\alpha =\frac{[\mathrm{H}{}_3\mathrm{O}{}^{+}]}{C_0}=\frac{10^{-\mathrm{pH}}}{C_0}$
    • if $\alpha \ll 1$, the acid is weak
    • if $\alpha \approx 1$, the acid is strong
• For a monoprotic base:
  • $K_b=\frac{[\mathrm{BH}{}^{+}][\mathrm{OH}{}^{-}]}{[\mathrm{B}]}=\frac{[\mathrm{OH}{}^{-}{]}^2}{C_0-[\mathrm{OH}{}^{-}]}=\frac{10^{-2\mathrm{pOH}}}{C_0-10^{-\mathrm{pOH}}}$
  • $\alpha =\frac{[\mathrm{BH}{}^{+}]}{C_0}=\frac{[\mathrm{OH}{}^{-}]}{C_0}=\frac{10^{\mathrm{pH}-14}}{C_0}$
    • if $\alpha \ll 1$, the base is weak
    • if $\alpha \approx 1$, the base is strong

---

• titration (or titrimetry or volumetric analysis) (טיטוּר, טיטרציה, תהליך סתירה)
  • standard solution (or titrant or titrator) (תמיסה תיקנית)
• buffer solution (בוּפר, מתריס, תמיסת מגן)
  • buffer capacity (קיבול הבופר)
  • acid buffer
    • examples:
      • $\mathrm{CH}{}_3\mathrm{COOH}/\mathrm{CH}{}_3\mathrm{CO}{}_2{}^{-}$
      • $\mathrm{HNO}{}_2/\mathrm{NO}{}_2{}^{-}$
      • $\mathrm{H}{}_2\mathrm{CO}{}_3/\mathrm{HCO}{}_3{}^{-}$
  • base buffer

References

• Brown, Theodore L. (2012). Chemistry. Prentice Hall.