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acids & bases

Brønsted–Lowry & Lewis, pH & pOH, weak equilibria & Ka/Kb, salts, buffers, titration curves, indicators.

definitions · pH & pOH · weak equilibria · salt pH · buffers · titrations & indicators

Definitions

Brønsted–Lowry. Acid = proton donor; base = proton acceptor; conjugate pairs differ by \(\ce{H+}\). Amphiprotic species can donate or accept (e.g. \(\ce{H2O}\), \(\ce{HCO3^-}\), \(\ce{HSO4^-}\)).

Lewis. Lewis acid = electron-pair acceptor; Lewis base = electron-pair donor.

Strength. Strong acid/base = complete ionization/dissociation; weak = partial, an equilibrium. Strong acids: \(\ce{HCl}\), \(\ce{HBr}\), \(\ce{HI}\), \(\ce{HNO3}\), \(\ce{HClO4}\), \(\ce{H2SO4}\) (first proton). Strong bases: group 1 hydroxides, heavier group 2 hydroxides.

Strength vs concentration. Distinguish concentration from strength: a dilute strong acid may have a higher pH than a concentrated weak acid.

Neutralization. \(\ce{H+ + OH- -> H2O}\); acid + carbonate → salt + \(\ce{CO2}\) + \(\ce{H2O}\); acid + metal → salt + \(\ce{H2}\).

pH & pOH

Scales. \(\mathrm{pH}=-\log[\ce{H3O+}]\), \([\ce{H+}]=10^{-\mathrm{pH}}\); \(\mathrm{pOH}=-\log[\ce{OH-}]\); at 298 K, \(\mathrm{pH}+\mathrm{pOH}=14.00\).

Ionic product. \(K_w=[\ce{H+}][\ce{OH-}]\); increases with temperature, so neutral pH shifts below 7 at higher \(T\) — but neutrality still means \([\ce{H+}]=[\ce{OH-}]\).

Weak acid/base equilibria

Weak acid. \(\ce{HA + H2O <=> H3O+ + A-}\); \(K_a=\dfrac{[\ce{H+}][\ce{A-}]}{[\ce{HA}]}\); \(\mathrm{p}K_a=-\log K_a\).

Weak base. \(\ce{B + H2O <=> BH+ + OH-}\); \(K_b=\dfrac{[\ce{BH+}][\ce{OH-}]}{[\ce{B}]}\); \(\mathrm{p}K_b=-\log K_b\); e.g. \(\ce{NH3 + H2O <=> NH4+ + OH-}\).

Conjugate hydrolysis. \(\ce{A- + H2O <=> HA + OH-}\).

Conjugate pairs. \(K_aK_b=K_w\); \(\mathrm{p}K_a+\mathrm{p}K_b=\mathrm{p}K_w=14.00\) at 298 K. Stronger acid: larger \(K_a\), smaller \(\mathrm{p}K_a\); its conjugate base is weaker.

Approximations. Weak acid: \([\ce{H+}]\approx\sqrt{K_aC}\); weak base: \([\ce{OH-}]\approx\sqrt{K_bC}\). Percent ionization \(=\frac{x}{C}\times100\); increases with dilution.

Salt pH

Salt hydrolysis. Strong acid + strong base → neutral salt. Strong acid + weak base → acidic (\(\ce{BH+}\) hydrolyzes). Weak acid + strong base → basic (\(\ce{A-}\) hydrolyzes). Weak acid + weak base → depends on \(K_a\) vs \(K_b\).

Buffers

Buffer. Weak acid/base + its conjugate salt; resists pH change by consuming added \(\ce{H+}\) or \(\ce{OH-}\).

Henderson–Hasselbalch. \(\mathrm{pH}=\mathrm{p}K_a+\log\dfrac{[\ce{A-}]}{[\ce{HA}]}\); \(\mathrm{pOH}=\mathrm{p}K_b+\log\dfrac{[\ce{BH+}]}{[\ce{B}]}\). Maximum capacity at \(\mathrm{pH}\approx\mathrm{p}K_a\); effective range \(\mathrm{p}K_a\pm1\).

Titrations & indicators

Equivalence pH. SA/SB pH 7; WA/SB pH >7; SA/WB pH <7; WA/WB no sharp endpoint. Half-equivalence for WA/SB: \(\mathrm{pH}=\mathrm{p}K_a\).

Indicators. Weak acids/bases whose two forms differ in color; endpoint range ≈ \(\mathrm{p}K_a\pm1\); choose an indicator whose range lies within the steep vertical region of the curve.