Ionization Acids and Bases

IONIZATION OF ACIDS AND BASES

  • Arrhenius concept of acids and bases is useful in understanding the ionization of acids and bases in aqueous medium.
  • Strong acids like HCl, HNO3, H2SO4, etc. are almost completely dissociated into ions in an aqueous medium, giving H+ ions.
  • Strong bases like NaOH, KOH, Ba(OH)2, etc. are also almost completely dissociated into ions in an aqueous medium, giving OH- ions.
  • Strong acids and bases are those that are able to completely dissociate and produce H3O+ and OH- ions, respectively, in the medium.
  • The strength of an acid or base can also be gauged in terms of Brönsted-Lowry concept, wherein a strong acid means a good proton donor and a strong base implies a good proton acceptor.
  • The acid-base dissociation equilibrium is dynamic, involving a transfer of proton in forward and reverse directions.
  • The equilibrium moves in the direction of formation of weaker acid and weaker base because the stronger acid donates a proton to the stronger base.
  • Strong acids have very weak conjugate bases, while weak acids have very strong conjugate bases.
  • Certain water-soluble organic compounds like phenolphthalein and bromothymol blue behave as weak acids and are useful as indicators in acid-base titrations.

Ionization Constant of Water and its ionic product

In presence of an acid, HA it accepts a proton and acts as the base while in the presence of a base, B it acts as an acid by donating a proton. In pure water, one H2O molecule donates proton and acts as an acid and another water molecules accepts a proton and acts as a base at the same time. The following equilibrium exists:

The dissociation constant is represented by,

K = [H3O+] [OH] / [H2O]

The concentration of water is omitted from the denominator as water is a pure liquid and its concentration remains constant. [H2O] is incorporated within the equilibrium constant to give a new constant, Kw, which is called the ionic product of water.

Kw = [H+][OH] 

The concentration of H+ has been found out experimentally as 1.0 × 10–7 M at 298 K. And, as dissociation of water produces equal number of H+ and OH ions, the concentration of hydroxyl ions, [OH] = [H+] = 1.0 × 10–7 M. Thus, the value of Kw at 298K,

Kw = [H3O+][OH] = (1 × 10–7)2 = 1 × 10–14 M

The value of Kw is temperature dependent as it is an equilibrium constant.

The density of pure water is 1000 g / L and its molar mass is 18.0 g /mol. From this the molarity of pure water can be given as,

[H2O] = (1000 g /L)(1 mol/18.0 g) = 55.55 M.

Therefore, the ratio of dissociated water to that of undissociated water can be given as:

10–7 / (55.55) = 1.8 × 10–9 or ~ 2 in 10–9 (thus, equilibrium lies mainly towards undissociated water)

We can distinguish acidic, neutral and basic aqueous solutions by the relative values of the H3O+ and OH concentrations:

Acidic: [H3O+] > [OH– ]

Neutral: [H3O+] = [OH– ]

Basic : [H3O+] < [OH]

pH scale

 Hydronium ion concentration in molarity is more conveniently expressed on a logarithmic scale known as the pH scale. The pH of a solution is defined as the negative logarithm to base 10 of the activity of hydrogen ion. In dilute solutions (< 0.01 M), activity of hydrogen ion (H+) is equal in magnitude to molarity represented by [H+]. It should be noted that activity has no units and is defined as:

= [H+] / mol L–1

From the definition of pH, the following can be written,

pH = – log aH+ = – log {[H+] / mol L–1}

Thus, an acidic solution of HCl (10–2 M) will have a pH = 2. Similarly, a basic solution of NaOH having [OH] =10–4 M and [H3O+] =
10–10 M will have a pH = 10. At 25 °C, pure water has a concentration of hydrogen ions,
[H+] = 10–7 M. Hence, the pH of pure water is given as:

pH = –log(10–7) = 7

Acidic solutions possess a concentration of hydrogen ions, [H+] > 10–7 M, while basic solutions possess a concentration of hydrogen ions, [H+] < 10–7 M. thus, we can summarise that

Acidic solution has pH < 7

Basic solution has pH > 7

Neutral solution has pH = 7

K= [H3O+] [OH] = 10–14

Taking negative logarithm on both sides of equation, we obtain

–log K= – log {[H3O+] [OH]}

= – log [H3O+] – log [OH]

= – log 10–14

pKw = pH + pOH = 14

Note that although Kw may change with temperature the variations in pH with temperature are so small that we often ignore it.

pKw is a very important quantity for aqueous solutions and controls the relative concentrations of hydrogen and hydroxyl ions as their product is a constant. It should be noted that as the pH scale is logarithmic, a change in pH by just one unit also means change in [H+] by a factor of 10. Similarly, when the hydrogen ion concentration, [H+] changes by a factor of 100, the value of pH changes by 2 units.

Ionization Constants of Weak Acids

The dissociation or ionisation of a weak acid, HA, can be represented as

As you know that in case of strong acids the ionisation is almost complete or close to 100% or we may say that the equilibrium lies far to the right. In such cases the sign of equilibrium may be replaced by a single arrow (→)

The reaction given above is referred to as ionisation equilibrium and is characterized by an equilibrium constant

Since the concentration of a pure liquid or a solid is taken as 1, we can rewrite the above expression can as

where Ka is a new constant called acid dissociation constant or ionisation constant of the acid.

 The magnitude of the equilibrium constant is a measure of the strength of the acid. Higher the value of the equilibrium constant the stronger is the acid. For all strong acids the values of the equilibrium constants is quite high and does not help much in suggesting their relative strengths. However, for a weak acid , this constant is quite useful.

Ionization of Weak Bases

The ionisation of weak bases (BOH) can be expressed as :

The solution contains the base, B the protonated base, BH+ , hydroxide ion OH , and water in equilibrium. The equilibrium constant expression for the reaction is

For example, the dissociation of NH4OH is represented as

and is characterized by

The constant Kb is called dissociation constant of the base. Similar to values of Ka , Kb values also give us the idea about the relative strengths of weak bases. Higher the value of Kb the stronger is the base.

 

Relation between Ka and Kb

 As seen earlier in this chapter, Ka and Kb represent the strength of an acid and a base, respectively. In case of a conjugate acid-base pair, they are related in a simple manner so that if one is known, the other can be deduced. Considering the example of NH4+ and NH3

we see,

NH4+(aq) + H2O(l)  H3O+(aq) + NH3(aq)

Ka = [H3O+][ NH3] / [NH4+] = 5.6 × 10–10

NH3(aq) + H2O(l)  NH4+(aq) + OH(aq)

Kb =[ NH4+][ OH] / NH3 = 1.8 × 10–5

Net: 2 H2O(l)  H3O+(aq) + OH(aq)

Kw = [H3O+][ OH– ] = 1.0 × 10–14 M

Where, Ka represents the strength of NH4+ as an acid and Kb represents the strength of NH3 as a base.

It can be seen from the net reaction that the equilibrium constant is equal to the product of equilibrium constants Ka and Kb for the reactions added. Thus,

Ka × Kb = {[H3O+][ NH3] / [NH4+ ]} × {[NH4+ ]

[ OH] / [NH3]}

= [H3O+][ OH] = Kw

= (5.6x10–10) × (1.8 × 10–5) = 1.0 × 10–14 M

This can be extended to make a generalisation. The equilibrium constant for a net reaction obtained after adding two (or more) reactions equals the product of the equilibrium constants for individual reactions:

KNET = K1 × K2 × ……

Similarly, in case of a conjugate acid-base pair,

Ka × Kb = K

Knowing one, the other can be obtained. It should be noted that a strong acid will have a weak conjugate base and vice-versa.

Alternatively, the above expression
K
w = Ka × Kb, can also be obtained by considering the base-dissociation equilibrium reaction:

B(aq) + H2O(l) BH+(aq) + OH(aq)

Kb = [BH+][OH] / [B]

As the concentration of water remains constant it has been omitted from the denominator and incorporated within the dissociation constant. Then multiplying and dividing the above expression by [H+], we get:

Kb = [BH+][OH][H+] / [B][H+]

={[ OH][H+]}{[BH+] / [B][H+]}

Kw / Ka

or Ka × Kb = Kw

It may be noted that if we take negative logarithm of both sides of the equation, then pK values of the conjugate acid and base are related to each other by the equation:

pKa + pKb = pKw = 14 (at 298K)

Henderson hasselbalch equation

The Henderson-Hasselbalch equation is a mathematical expression that relates the pH of a solution containing a weak acid and its conjugate base to the dissociation constant of the weak acid. It is given by the following equation:

pH = pKa + log([A-]/[HA])

where pH is the negative logarithm of the hydrogen ion concentration, pKa is the negative logarithm of the acid dissociation constant (Ka) of the weak acid, [A-] is the concentration of the conjugate base of the weak acid, and [HA] is the concentration of the weak acid itself.

The Henderson-Hasselbalch equation is useful in understanding the behavior of weak acids and their conjugate bases in solution. It can be used to calculate the pH of a buffer solution, which is a solution containing a weak acid and its conjugate base that resists changes in pH when small amounts of an acid or base are added to it. It is also useful in determining the extent of ionization of weak acids and their degree of dissociation in solution.

Di- and Polybasic Acids and Di- and polyacidic bases

Many acids have more than one ionizable protons. These are called polyprotic acids. The acids are called diprotic if there are two ionizable protons per molecule. (e.g. H2SO3 , H2 CO3 ), and triprotic if there are three ionizable protons (e.g. H3 PO4 , etc). Such acids dissociate in more than one steps or stages, each with its own ionization constant. In the case of sulphurous acid, H2 SO3 , these steps are

The values of the two ionisation constants ( K1 and K2 ) are quite different ; K1 being twenty million times K2 . It suggests that the first ionisation of sulphurous acid is much more than the second one. In other words the sulphurous acid behaves as a much stronger acid than the bisulphite ion.

Factors Affecting Acid Strength

The acidity of a compound depends on several factors. Here are some of the factors that affect the acidity of an acid:

1.     Bond strength: The strength of the bond between the hydrogen atom and the rest of the molecule determines the acid strength. The weaker the bond, the stronger the acid. For example, HCl is a stronger acid than HF because the H-Cl bond is stronger than the H-F bond.

2.     Electronegativity: The electronegativity of the atom that is bonded to the hydrogen atom also affects the acidity. The higher the electronegativity of the atom, the more it attracts electrons away from the hydrogen atom, making it easier to remove the proton. For example, HCl is a stronger acid than HI because the electronegativity of Cl is higher than that of I.

3.     Size of the atom: The size of the atom that is bonded to the hydrogen atom also affects the acidity. The larger the atom, the weaker the bond between the hydrogen and the rest of the molecule, making it easier to remove the proton. For example, HI is a stronger acid than HF because iodine is larger than fluorine.

4.     Resonance: Resonance stabilization of the conjugate base of an acid makes it more stable, which makes the acid more acidic. For example, the carboxylic acid group (-COOH) is more acidic than the alcohol group (-OH) because the negative charge on the conjugate base can be stabilized by resonance.

5.     Inductive effect: The inductive effect is the effect of electronegative atoms or groups on the acidity of an acid. Electronegative groups adjacent to the acidic group pull electron density away from it, making it easier to remove the proton. For example, in chloroacetic acid, the Cl atom pulls electron density away from the carboxylic acid group, making it more acidic than acetic acid.

These factors affect the ability of an acid to donate a proton and therefore determine its acidity.

Common Ion Effect

The common ion effect is a phenomenon that occurs when a solution containing an ion in common with a sparingly soluble salt is reduced in solubility. It is based on the principle of Le Chatelier's principle, which states that if a system at equilibrium is subjected to a change in concentration, temperature, or pressure, the system will adjust to partially offset the effect of the change.

In the case of the common ion effect, the effect is caused by the addition of an ion that is already present in the solution, either as a dissolved ion or as a component of a sparingly soluble salt. When this happens, the equilibrium between the dissolved salt and its ions is shifted in such a way that the solubility of the salt is reduced.

For example, let's consider the equilibrium that exists between a sparingly soluble salt such as silver chloride (AgCl) and its ions in an aqueous solution:

AgCl (s) Ag+ (aq) + Cl- (aq)

If we add a source of chloride ions to the solution, such as hydrochloric acid (HCl), the concentration of Cl- ions in the solution will increase. According to Le Chatelier's principle, the equilibrium will shift to the left, favoring the formation of solid AgCl. This will cause the solubility of AgCl to decrease, resulting in the precipitation of more solid AgCl.

The common ion effect can also be used to control the solubility of sparingly soluble salts in a solution. For example, by adding a soluble salt that contains a common ion to a solution containing a sparingly soluble salt, we can decrease the solubility of the sparingly soluble salt and precipitate it out of solution.

Overall, the common ion effect plays an important role in many chemical equilibria and can be used to control the solubility of sparingly soluble salts in a solution.

 

Hydrolysis of Salts and the pH of their solution

 Salts formed by the reactions between acids and bases in definite proportions, undergo ionization in water. The cations/anions formed on ionization of salts either exist as hydrated ions in aqueous solutions or interact with water to reform corresponding acids/bases depending upon the nature of salts. The later process of interaction between water and cations/anions or both of salts is called hydrolysis. The pH of the solution gets affected by this interaction. The cations (e.g., Na+, K+, Ca2+, Ba2+, etc.) of strong bases and anions (e.g., Cl, Br, NO3, ClO4 etc.) of strong acids simply get hydrated but do not hydrolyse, and therefore the solutions of salts formed from strong acids and bases are neutral i.e., their pH is 7. However, the other category of salts do undergo hydrolysis.

We now consider the hydrolysis of the salts of the following types :

(i) salts of weak acid and strong base e.g., CH3COONa.

(ii) salts of strong acid and weak base e.g., NH4Cl, and

(iii) salts of weak acid and weak base, e.g., CH3COONH4.

 In the first case, CH3COONa being a salt of weak acid, CH3COOH and strong base, NaOH gets completely ionised in aqueous solution.

CH3COONa(aq)  CH3COO– (aq)+ Na+(aq)

Acetate ion thus formed undergoes hydrolysis in water to give acetic acid and OH ions

CH3COO(aq)+H2O(l)CH3COOH(aq)+OH(aq)

Acetic acid being a weak acid
(Ka = 1.8 × 10–5) remains mainly unionised in solution. This results in increase of OH ion concentration in solution making it alkaline. The pH of such a solution is more than 7.

Similarly, NH4Cl formed from weak base, NH4OH and strong acid, HCl, in water dissociates completely.

NH4Cl(aq)  NH+4(aq) +Cl (aq)

Ammonium ions undergo hydrolysis with water to form NH4OH and H+ ions

NH+4 (aq) + H2O (1)  NH4OH(aq) + H+(aq)

Ammonium hydroxide is a weak base
(Kb = 1.77 × 10–5) and therefore remains almost unionised in solution. This results in increased of H+ ion concentration in solution making the solution acidic. Thus, the pH of NH4Cl solution in water is less than 7.

Consider the hydrolysis of CH3COONH4 salt formed from weak acid and weak base. The ions formed undergo hydrolysis as follow:

CH3COO– + NH4+ + H2O  CH3COOH + NH4OH

CH3COOH and NH4OH, also remain into partially dissociated form:

CH3COOH  CH3COO– + H+

NH4OH  NH4+ OH

H2O  H+ OH

Without going into detailed calculation, it can be said that degree of hydrolysis is independent of concentration of solution, and pH of such solutions is determined by their pK values:

pH = 7 + ½ (pKa – pKb)

The pH of solution can be greater than 7, if the difference is positive and it will be less than 7, if the difference is negative.

Acid base titration

An acid-base titration is a laboratory technique used to determine the concentration of an unknown acid or base by reacting it with a known amount of a standard solution of an acid or base. The point at which the reaction is complete is called the endpoint, and it is typically detected using an indicator that changes color at a specific pH.

The general procedure for an acid-base titration involves slowly adding the standard solution to the unknown solution while monitoring the pH of the mixture. When the pH of the solution reaches a particular value, called the equivalence point, the reaction is complete. At this point, the number of moles of acid or base in the unknown solution can be calculated from the volume and concentration of the standard solution that was added.

The equivalence point of an acid-base titration can be determined using different types of indicators, such as litmus paper, phenolphthalein, or methyl orange, depending on the type of reaction being carried out. For example, litmus paper is commonly used for strong acid-strong base titrations, while phenolphthalein is often used for weak acid-strong base titrations.

In addition to indicators, pH meters and other instruments can be used to monitor the pH of the solution during the titration process. This allows for more accurate measurements and greater precision in determining the endpoint and equivalence point of the reaction.

Overall, acid-base titrations are an essential tool in chemistry, and they are used in many different fields, including analytical chemistry, environmental science, and biochemistry.