JEE Chemistry Ionic Equilibrium Notes Set 01

pH Scale and Logarithms

\( pH=-\log[\ce{H+}] \) and \( pOH=-\log[\ce{OH-}] \). At 25 C, \( pH+pOH=14 \) and \( K_w=[\ce{H+}][\ce{OH-}]=10^{-14} \). Each unit of pH is a tenfold change in \( [\ce{H+}] \).
Useful values: log 2 = 0.30, log 3 = 0.48, log 5 = 0.70. Write a concentration like \( 3\times10^{-4} \) as \( 10^{-(4-0.48)} \) to read off the pH quickly.
Kw rises with temperature, so pure water is neutral at pH 7 only at 25 C; at higher temperatures neutral pH is lower than 7 though the water stays neutral because \( [\ce{H+}]=[\ce{OH-}] \).

Strong Acids and Bases, Mixtures and Dilution

A strong acid or base is taken as fully ionised. Moles of \( \ce{H+} \) = molarity x basicity x volume, and for a base use acidity in place of basicity.
On mixing an acid and a base, neutralise first: the excess moles divided by the total volume give the concentration that fixes the pH.
On diluting a solution n times, the concentration falls n times. A strong acid of concentration below about \( 10^{-6} \) M must include the hydrogen ions from water: solve \( x=c+\frac{K_w}{x} \). An acid can never give a pH above 7 however dilute it is.

Weak Acids and Bases: Ostwald's Dilution Law

For a weak acid HA of concentration C and degree of ionisation \( \alpha \): \( K_a=\frac{C\alpha^2}{1-\alpha} \), which for small alpha becomes \( K_a=C\alpha^2 \) and \( \alpha=\sqrt{K_a/C} \).
Then \( [\ce{H+}]=C\alpha=\sqrt{K_aC} \). Dilution increases alpha but lowers the hydrogen ion concentration. Two weak acids with the same \( [\ce{H+}] \) satisfy \( K_{a1}V_2=K_{a2}V_1 \) if their volumes (dilutions) are \( V_1 \) and \( V_2 \).
For a weak base use the same relations with Kb and \( [\ce{OH-}]=\sqrt{K_bC} \). Valid only when alpha is small, say below 5 percent.

Polyprotic Acids

A dibasic or tribasic acid ionises in steps with \( K_{a1}>K_{a2}>K_{a3} \), because it is harder to remove a proton from an ion that already carries a negative charge.
For weak polyprotic acids the first step almost always decides the pH. Basicity counts only the hydrogens on oxygen: phosphorous acid is dibasic and hypophosphorous acid is monobasic, since hydrogen bonded to phosphorus does not ionise.
A zwitterion such as glycine has \( pH=\tfrac12(pK_{a1}+pK_{a2}) \).

Common Ion Effect

Adding a salt that supplies an ion already present in a weak electrolyte pushes the ionisation back. Acetic acid with sodium acetate, or ammonia with ammonium chloride, ionise far less.
The same idea lowers the solubility of a sparingly soluble salt when a common ion is present, and explains why NaCl is precipitated from a saturated solution by passing HCl gas.

Hydrolysis of Salts

A salt of a strong acid and strong base (NaCl) does not hydrolyse and is neutral. A salt of a weak acid and strong base (NaCN) gives a basic solution through anion hydrolysis; a salt of a strong acid and weak base (\( \ce{NH4Cl} \)) gives an acidic solution through cation hydrolysis.
Relations: weak acid with strong base: \( K_h=\frac{K_w}{K_a} \), \( h=\sqrt{\frac{K_h}{C}} \), \( pH=7+\tfrac12pK_a+\tfrac12\log C \).
Weak base with strong acid: \( K_h=\frac{K_w}{K_b} \), \( pH=7-\tfrac12pK_b-\tfrac12\log C \).
Weak acid with weak base: \( K_h=\frac{K_w}{K_aK_b} \), the degree of hydrolysis does not depend on concentration, and \( pH=7+\tfrac12(pK_a-pK_b) \). Salts such as \( \ce{NH4CH3COO} \) with equal Ka and Kb are neutral. The salt of a very weak ion like \( \ce{Al^3+} \) or \( \ce{Fe^3+} \) is strongly acidic.

Buffer Solutions

A buffer resists a change of pH when small amounts of acid or alkali are added. It contains a weak acid with its conjugate base (acidic buffer) or a weak base with its conjugate acid (basic buffer) in comparable amounts.
Acidic buffer: \( pH=pK_a+\log\frac{[\text{salt}]}{[\text{acid}]} \). Basic buffer: \( pOH=pK_b+\log\frac{[\text{salt}]}{[\text{base}]} \) (Henderson equation).
Buffer capacity is the moles of strong acid or base added per litre per unit change in pH. It is greatest when salt and acid are in the ratio 1 : 1, where \( pH=pK_a \), and a buffer is useful only within about one unit of pKa.
Half neutralisation of a weak acid by a strong base gives pH = pKa. Adding strong acid to a buffer converts salt into acid; adding strong base converts acid into salt. Diluting a buffer does not change its pH.

Acid-Base Titrations and Indicators

At the equivalence point the pH depends on the salt formed: 7 for strong acid with strong base, above 7 for weak acid with strong base, below 7 for strong acid with weak base.
An indicator is a weak acid or base whose two forms differ in colour: \( pH=pK_{In}+\log\frac{[\ce{In-}]}{[\ce{HIn}]} \). It changes colour over about \( pK_{In}\pm1 \).
Phenolphthalein (range about 8 to 10) suits weak acid against strong base and strong against strong, but not a weak base. Methyl orange (about 3 to 4.5) suits strong acid against weak base. Neither suits a weak acid against a weak base. Phenolphthalein is also unsuitable in redox titrations like oxalic acid with permanganate.

Solubility Product

For a sparingly soluble salt \( A_xB_y \) the saturated solution has \( K_{sp}=[A^{y+}]^x[B^{x-}]^y \). With solubility s mol/L: type AB gives \( K_{sp}=s^2 \); type \( AB_2 \) or \( A_2B \) gives \( 4s^3 \); type \( AB_3 \) gives \( 27s^4 \); type \( A_2B_3 \) gives \( 108s^5 \).
Ksp depends only on temperature. Compare solubilities from Ksp only for salts of the same type; otherwise calculate s.
Conversions: solubility in g/L divided by molar mass gives mol/L. Ionic product Q compared with Ksp: Q less than Ksp means unsaturated, equal means saturated, greater means precipitation.

Applications of Ksp

Common ion: the solubility falls to \( s=\frac{K_{sp}}{[\text{common ion}]^n} \) in a solution containing the common ion. Complex formation (silver chloride in ammonia) or protonation of a weak-acid anion raises solubility.
Selective precipitation: the salt with the smaller requirement of precipitant forms first. To find when a second ion begins to precipitate, find the common ion concentration at which the first just begins and then use the other Ksp.
In qualitative analysis, group II cations (Cu, Cd, Hg, Bi) are precipitated by \( \ce{H2S} \) in dilute HCl because the acid keeps the sulphide ion concentration low and only the very insoluble sulphides form. Group IV sulphides (Zn, Mn, Co, Ni) need an ammoniacal medium which removes \( \ce{H+} \) and raises \( [\ce{S^2-}] \). \( \ce{NH4Cl} \) is added in group III to suppress \( \ce{OH-} \) so only hydroxides of Fe, Al and Cr precipitate.

Acid-Base Theories

Arrhenius: an acid gives \( \ce{H+} \) and a base gives \( \ce{OH-} \) in water; it fails for non-aqueous media and for substances like \( \ce{NH3} \) and \( \ce{AlCl3} \).
Bronsted-Lowry: an acid is a proton donor and a base a proton acceptor. The acid and base on opposite sides of an equation form conjugate pairs that differ by one proton. The stronger the acid, the weaker its conjugate base.
Lewis: an acid accepts an electron pair and a base donates one. Lewis acids include \( \ce{BF3} \), \( \ce{AlCl3} \), \( \ce{SnCl4} \), \( \ce{Cu^2+} \) and \( \ce{H+} \); bases include \( \ce{NH3} \), \( \ce{OH-} \), \( \ce{F-} \) and water. Every Bronsted acid-base reaction is also Lewis, but \( \ce{Cu^2+ + 4NH3 -> [Cu(NH3)4]^2+} \) is Lewis only.

Amphoteric Species and Acid Strength

Species that can both give and take a proton are amphiprotic: water, \( \ce{HCO3-} \), \( \ce{HSO4-} \), \( \ce{H2PO4-} \) and \( \ce{NH3} \). Water is the classic example, acting as a base with HCl and as an acid with ammonia.
For oxyacids of the same element, acid strength rises with the number of oxygen atoms not bonded to hydrogen: \( \ce{HClO < HClO2 < HClO3 < HClO4} \). Boric acid is not protic; it is a Lewis acid that takes \( \ce{OH-} \) from water. Stronger Lewis acidity goes with higher charge and smaller size, so \( \ce{Al^3+} \) is a stronger Lewis acid than \( \ce{Mg^2+} \).

Normality and Quick Concentration Checks

Normality = molarity x n-factor, where n-factor is the basicity for acids and the acidity for bases. Milliequivalents = normality x volume in mL.
Dibasic sulphuric acid of 0.1 M is 0.2 N. A solution of NaOH with pH 13 has 0.1 M hydroxide, so 4 g per litre. In any titration the equivalents of acid and base are equal at the end point.