Topic 18: Acids and Bases

  Use this outline in conjunction with the IB syllabus.

 

18.1 Calculations involving acids and bases

18.1.1

H₂O(l) ⇌ H⁺ (aq) + OH^-(aq)

·         H⁺ is a simplified notation of H₃O⁺, in fact H⁺ always bonds to H₂O

K_w – ionic product constant of water

K_w = [H⁺][OH^-]

18.1.2

For pure water at any temperature, the concentration of hydrogen cations always equals the concentration of hydroxide anions. Though, with shifting temperature, the ionic product constant of water changes: ionic product constant is just an equilibrium constant of water, so when the temperature changes the ionic product of water also shifts. However, ionic product of water is:

K_w = [H⁺][OH^-]

Thus, when K_w changes, [H⁺] and [OH^-] change, too. Because both [H⁺] and [OH^-] are equal, for the purpose of the calculation, we can set both concentrations equal to x and solve the equation K_w = x². Hence, either concentration equals to the square root of K_w.

18.1.3

When solving problems involving [H⁺], [OH^-], pH and pOH, we must know the following relationships:

For aqueous solution at STDP:

pH + pOH = 14

[H⁺][OH^-] = 1x10^-14

For any solution:

pH = -log[H⁺]

pOH = -log[OH^-]

Note that for strong acids and bases [H⁺] and [OH^-] are directly related to the concentration of the acid/base, so doubling the concentration of the acid will double [H⁺] and halve [OH^-] (and the reverse is true for bases).

18.1.4

When a weak base or acid reacts with water, the equations go to equilibrium because weak acids/bases ionize only partially. The general equations for the dissociation of weak acid/base:

HA (aq) ⇌ H⁺(aq) + A^-(aq)

B (aq) + H₂O(l) ⇌ BH⁺(aq) + OH^-(aq)

The equilibrium constants for a dissociation of a weak acid and a weak base are denoted by K_a and K_b, respectively.

K_a = [H⁺][A^-] ∕ [HA]

K_b = [BH⁺][OH^-] ∕ [B]

When we do calculations involving weak acids and bases and know a dissociation cosntant and initial concentration of the acid/base, we asume that the change in the concentration of acid/base was negligible. By this we to avoid a quadratic equation. During the calculations, [H⁺/OH^-] and [A^-/BH⁺] are made equal x and instead of subtracting x from [HA/B], we assume that the latter concentration stayed constant.

We are to know how to deal with dissociation constants and concentrations of monoprotic acids and base (transfer of one proton occurs).

18.1.5

K_a x K_b = K_w

pK_a + pK_b = pK_w

pH + pOH = pK_w

As noted in 18.1.4, we assume the change in concentration of a weak base or acid is negligible during calculations. This helps us to avoid quadratics.

18.1.6

	pKa	Ka
Strong Acids	Very small	Very large
Weak Acids	2-7	Relatively large

	pKb	Kb
Strong Base	13-14	Very small
Weak Base	7-13	Relatively small

18.2 Buffer Solutions

18.2.1

Buffer is a solution, which contains relatively high amount of a weak acid or base and its conjugate pair. Buffers maintain pH at a relatively constant value despite small additions of acids or bases.

Considering an illustration for acids, even though the same works for bases:

We add an acid to water, which creates equilibrium. Subsequently, we add more conjugate base ions, usually in the form of sodium or potassium ions. Thus, there is a large amount of reactants on the both sides. Whenever we add acids or base, it reacts with hydrogen ions or creates more hydrogen ions. Whenever there is an increase or decrease in the H⁺ ions, the reaction equilibrium will shift to reduce the stress (Le Chatelier’s Principle). Thus, buffer solution maintains the pH relatively constant.

Buffer zone is the proportion of a pH curve in which a buffer action of a buffer occurs. Buffering action occurs in all reactions except for the reactions of acids and bases. 

Notice, that there is a relatively constant area on the pH curve (marked by red). This is an area before the jump from basic to acidic where a buffer action occurs.

18.2.2

We find pH of a buffer using Henderson-Hesselbach equation (again, same works for bases):

We must consider two examples:

Before we start, note that we assume that sodium ethanoate and ammonium chloride are completely soluble in water.

Solution of ethanoic acid and salt sodium ethanoate, which supplies the conjugate ions

 

Solution of ammonia and salt ammonium chloride, which supplies the conjugate ions

 

18.3 Salt hydrolysis

Salts dissociate completely in aqueous solutions. Thus, they provide solutions with ions. Some ions react with the H⁺ and OH^-, naturally present in water. If an ion reacts with H⁺ or OH^-, it draws them from the solution transforming them into the ion’s acid or base. The salt ions and water ions establish equilibrium with the salt ion’s acid or base. Thus, this works only for weak acids and bases.

General rules:

• When the negative ion is from a weak acid then the salt is basic by hydrolysis
• When the positive ion is from a weak base then the salt is acidic by hydrolysis
• If the salt is formed from a strong acid and strong base then it is neutral
• If the salt is formed from a weak acid and weak base then its hydrolysis is determined by the relative Ka and Kb values

Compounds with high charge density also indulge in hydrolysis. If a specie has a high charge, it forms coordinate bond water. This bond is so strong that it weakens the water’s bond, so one water’s hydrogen becomes cast out into a solution. The hydrogen ions cast away by coordinate bonds with water make the solution acidic. 

Water molecules bond to an ion with a high charge with the oxygen’s lone pair. Six water molecules usually surround the ion, forming octahedral. The examples of highly charged ions making acidic solutions are:

Aluminum hexaaqua ion

[Al(H₂O)₆]³⁺ ⇌ [Al(OH)(H₂O)₅]²⁺ + H⁺

Iron III ion

[Fe(H₂O)₆]³⁺ ⇌ [Fe(OH)(H₂O)₅]²⁺ + H⁺

18.4 Acid-Base Titrations

Equivalence point (p. of inflection) – point at which the amount of acid equals the amount of base and the solution is neutral

 

 

18.5 Indicators

18.5.1

Indicators are weak acids (or bases) which have a different color in the ionic and molecular forms.

HIn(aq) ⇌ In^-(aq)  + H⁺(aq)

Color A            Color B    .

Addition of hydrogen ions will force the equilibrium in the direction of the molecular form (left hand side), so more of the Color A is seen whereas when base is added to the equilibrium it moves in the direction of the ionic form (the conjugate base) and Color B is seen.

18.5.2

The point at which an indicator changes color is when [HIn] = [In^-]. We can plug this point into the indicator’s dissociation constant:

Taking negative log of the both sides:

Thus, the point at which the indicator changes color depends on the pH of solution in which it is. It will change the color when the pH of the solution equals indicator’s dissociation constant.

18.5.3

Indicators and their pK_a values can be found in the Data Booklet, Table 16. It is logical to choose indicator, whose pK_a is at the equivalence point. This is not so important for strong acid and base titrations as the change of pH is very swift, but makes a great deal for all other combinations of acids and bases

.

In titrations, involving weak bases and strong acids use methyl orange.
For weak acids and strong bases use phenolphthalein.