Acids and Bases

The earliest criteria for the characterization of acids and bases were the experimentally observed properties of aqueous solutions. An acid  was defined as a substance whose water solution tastes sour, turns blue litmus red, neutralizes bases and so on. A substance was a base if its aqueous solution tasted bitter, turns red litmus blue, neutralizes acids and so on.

Faraday termed acids, bases and salts as electrolytes and Liebig proposed that acids are compounds containing hydrogen that can be replaced by metals. Different concepts have been put forth by different investigators to characterize acids and bases but the following are the three important modern concepts of acids and bases:
 

• Arrhenius Concept

 According to Arrhenius concept all substances which give H⁺ ions when dissolved in water are called acids while those which ionize in water to furnish OH^- ions are called bases.

 HA   H⁺ + A^- (Acid)

BOH B⁺ + OH^- (Base)

Thus, HCl is an acid because it gives H+ ions in water. similarly, NaOH is a base as it yields OH^- ions in water.

HCl H⁺ + Cl^-

NaOH   Na⁺ + OH^-

Some acids and bases ionize completely in solutions and are called string acids and bases. Others are dissociated to a limited extent in solutions and are termed weak acids and bases. HCl, HNO₃, H₂SO₄, HCIO₄, etc., are examples of strong acids and NaOH, KOH, (CH₃)₄NOH are strong bases.

Every hydrogen compound cannot be regarded as an acid, e.g., CH₄ is not an acid. Similarly, CH₃OH, C₂H₅OH, etc., have OH groups but they are not bases, they must generate H⁺ or OH^- ions in aqueous solution in order to be defined as acid or base

Actually free H⁺ ions are highly reaction so they do not exist in water. They combine with water molecules to form hydronium ion (H₃O⁺) molecules, i.e., have strong tendency to get hydrated.

 HX + H₂O H₃O⁺ + X^-
                    (Hydronium ion)

The proton in aqueous solution is generally represented as H⁺ (aq). It is now known that almost all the ion are hydrated to more or less extent and it is customary to put (aq) after each ion.

The oxides of many non-metals react with water to form acids and are called acidic oxides or acid anhydrides.

CO₂ + H₂O  H₂CO₃  2H⁺(aq) +  (aq)

 N₂O₅ + H₂O  2HNO₃  2H⁺(aq) +  (aq)

Many oxides of metals dissolve in water to form hydroxides. Such oxides are termed basic oxides.

Na₂O + H₂O →  2NaOH    2Na⁺(aq) + 2OH^- (aq)

The substance like NH₃ and N₂H₄ act as bases as they react with water to produce OH^- ions.

NH₃ + H₂O →  NH₄OH    NH⁺₄ (aq) + OH^- (aq)

The reaction between an acid and a base is termed neutralization. According to Arrhenius concept, the neutralization in aqueous solution involves the reaction between H⁺ and OH^- ions or hydronium and OH^-. This can be represented as

H₃O⁺ + OH^-   2H₂O
 

Limitations of Arrhenius Concept

1. For the acidic or basic properties, the presence of water is absolutely necessary. Dry HCl shall not act as an acid. HCl is regarded as an acid only when dissolved in water and not in any other solvent.

2. The concept does not explain acidic and basic character of substances in non-aqueous solvents.

3. The neutralization process is limited to those reactions which can occur in aqueous solutions only, although reactions involving salt formation do occur in the absence of solvent.

4. It cannot explain the acidic character of certain salts such as AlCl₃ in aqueous solution.

5. An artificial explanation is required to explain the basic nature of NH₃ and metallic oxides and acidic nature of non-metal oxides.
    

• Bronsted-Lowry Concept - The Proton-Donor-Acceptor Concept

Refer to the following video for Bronsted-Lowry concept 

In 1923, Bronsted and Lowry independently proposed a broader concept of acids and bases. According to Bronsted-Lowry concept an acid is a substance (molecule or ion) that can donate proton, i.e., a hydrogen ion, H⁺, to some other substance and a base is a substance that can accept a proton from an acid. More simply, an acid is a proton donor (protogenic) and a base is a proton acceptor (protophilic).

Consider the reaction,

 HCl + H₂O   H₃O + Cl^-

In this reaction HCl acts as an acid because it donates a proton to the water molecule. Water, on the other hand, behaves as a base by accepting a proton from the acid.

The dissolution of ammonia in water may be represented as

NH₃ + H₂O  NH₄⁺ + OH^-

In this, reaction, H₂O acts as an acid it donated a proton to NH₃ molecule and NH₃molecule behaves as a base as it accepts a proton.

When an acid loses a proton, the residual part of it has a tendency to regain a proton. Therefore, it behaves as a base.

 Acid H⁺ + Base

The acid and base which differ by a proton are known to form a conjugate pair. Consider the following reaction.

 CH₃COOH + H₂O   H₃O⁺ + CH₃COO^-

It involves two conjugate pairs. The acid-base pairs are:

Such pairs of substances which can be formed form one another by loss or gain of a proton are known as conjugate acid-base pairs.

If in the above reaction, the acid CH₃COOH is labelled acid₁ and its conjugate base, CH₃COO^- as base₁. H₂O is labelled as base₂ and its conjugate acid H₃O⁺ as acid₂, the reaction can be written as:

Acid₁ + Base₂  Base₁ + Acid₂

Thus, any acid-base reaction involves two conjugate pairs, i.e., when an acid reacts with a base, another acid and base are formed. 

Thus, every acid has its conjugate base and every base has its conjugate acid. It is further observed that strong acids have weak conjugate bases while weak acids have strong conjugate bases.

HCl        +           Cl^-                CH₃COOH     +   CH₃COO^-

Strong acid       Weak base      Weak acid        Strong base

There are certain molecules which have dual character of an acid and a base. These are called amphiprotic or atmospheric.

Examples are NH₃, H₂O, CH₃COOH, etc.

The strength of an acid depends upon its tendency to lose its proton and the strength of the base depends upon its tendency to gain the proton.

Acid-Base chart containing some common conjugate acid-base pairs

In acid-base strength series, all acids above H₃O⁺ in aqueous solution fall to the strength of H₃O⁺. Similarly the basic strength of bases below OH^- fall to the strength of OH^- in aqueous solution. This is known as leveling effect.

The strength of an acid also depends upon the solvent. The acids HCIO₄, H₂S0₄, HCl and HN0₃ which have nearly the same strength in water will be in the order of HClO₄> H₂SO₄ > HCl > HNO₃ in acetic acid, since the proton accepting ten­dency of acetic acid is much weaker than water. So the real strength of acids can be judged by solvents. On the basis of proton interaction, solvents can be classified into four types: 

• Protophilic solvents:  Solvents which have greater tendency to accept protons, i.e., water, alcohol, liquid ammonia, etc.

• Protogenic solvents:  Solvents which have the tendency to produce protons, i.e., water, liquid hydrogen chloride, glacial acetic acid, etc.

• Amphiprotic solvents:  Solvents which act both as protophilic or protogenic, e.g., water, ammonia, ethyl alcohol, etc.

• Aprotic solvents:  Solvents which neither donate nor accept protons, e.g., benzene, carbon tetrachloride, carbon disulphide, etc.

HCI acts as acid in H₃O⁺, stronger acid in NH₃, weak acid in CH₃COOH, neutral in C₆H₆and a weak base in HF.

HCI   +   HF     →    H₂Cl⁺  +   F^-

Base      Acid          Acid             Base
 

• pH of Acids and Bases 

It is clear from the above discussion that nature of the solution (acidic, alkaline or neutral) can be represented in terms of either hydrogen ion concentration or hydroxyl ion concentration but it is convenient to express acidity or alkalinity of a solution by referring to the concentration of hydrogen ions only. pH measurement is done using pH paper and pH meter

Since H⁺ ion concentration can vary within a wide range from 1 mol per litre to about 1.0 × 10^-14mol per litre, a logarithmic notation has been devised by Sorensen, in 1909, to simplify the expression of these quantities. The notation used is termed as the pH scale.

The hydrogen ion concentrations are expressed in terms of the numerical value of negative power to which 10 must be raised. This numerical value of negative power was termed as pH, i.e.,

pH  = – log a_H⁺ (Where a_H⁺ is the activity of H⁺ ions).

Activity of H⁺ ions is the concentration of free H⁺ ions in a solution. By free, we mean those that are at a large distance from the other ion so as not to experience  its pull. We can infer from this that in dilute solutions, the activity of an ion is same as its concentration since more number of solvent molecules would separate the two ions. For concentrated solutions the activity would be much less than the concentration itself.

Therefore, the earlier given expression of pH can be modified for dilute solutions as,
pH  = – log [H⁺].

This assumption can only be made when the solution is very much dilute, i.e, [H⁺]  1M. For higher concentration of H⁺ ions, one needs to calculate the activity experimentally and then calculate the pH.

pH of a solution is, thus, defined as the negative logarithm of the concentration (in mol per litre) of hydrogen ions which it contains or pH of the solution is the logarithm of the reciprocal of H⁺ ion concentration.

Just as pH indicates the hydrogen ion concentration, the pOH represents the hydroxyl ion concentration, i.e.,

pOH = -log [OH-] Considering the relationship,

[H⁺][OH^-] = K_w = 1 x 10^-14

 Taking log on both sides, we have

log [H⁺] + log [OH^-] = log K_w = log (1 x 10^-14)

or -log [H⁺] - log [OH^-] = -log K_w = -log (1 x 10^-14)

or    pH + pOH = PK_w^* = 14

i.e., sum of pH and pOH is equal to 14 in any aqueous solution at 25°C. The above discussion can be summarised in the following manner:

pH of Weak Acids and Bases 

Weak acids and bases are not completely ionised; an equilibrium is found to have been established between ions and unionised molecule. Let us consider a weak acid of basicity 'n'.

            AH_n    A^n-  +   nH⁺

           -C        0          0

t_eq      C(1-α)   Cα       nCα

[H⁺] = nCα;  .·. pH = -log₁₀ [nCα]                

For monobasic and,  n=1

 pH = -log₁₀ [Cα]                                       

Dissociation constant of acid K_a may be calculated as

 K_a = [A^n-][H⁺]ⁿ/[AH_n] = [Cα][nCα]ⁿ/[C(1-α)]

            =  α [nCα]ⁿ/(1-α)           For weak acids, α« 1

.·. (1-α) = 1

            = α[nCα ]ⁿ/(1-α)

nCK_a = nCα [nCα ]ⁿ = [nCα ]⁽ⁿ⁺¹⁾ 

= [nCα ] = [nCK_a]^1/(n+1)

= [H⁺] = [nCK_a]^1/(n+1)

.·. pH = -1/(n+1) log₁₀(nCK_a)            

For monobasic acid, n = 1

pH = -log√CK_α                               

Since K_a = α[nCα]ⁿ

ka/α = (nCα)ⁿ

 [nCα ] = [K_α/α]^1/n = [H⁺]

pH = -1/n log₁₀(K_α/α)                         

For n = 1       pH = -log₁₀(K_α/α)
 

Limitations of pH Scale

1. pH values of the solutions do not give us immediate idea of the relative strengths of the solutions. A solution of pH = 1 has a hydrogen ion concentra­tion 100 times that of a solution of pH = 3 (not three times). A 4 x 10^-5 N HCI is twice concentrated of a 2 x 10^-5 N HCI solution, but the pH values of these solutions are 4.40 and 4.70 (not double).

2. pH value of zero is obtained in 1 A' solution of strong acid. In case the concentration is 2 N, 3 N, 10 N, etc. The respective pH values will be negative.

3. A solution of an acid having very low concentration, say 10^-8 N, cannot have pH 8, as shown by pH formula, but the actual pH value will be less than 7.

Note: 

1. Normality of strong acid = [H₃O⁺]
   Normality of strong base = [OH^-]
   .·. pH = -log [N]    for strong acids
      pOH = -log [N]    for strong acids

2. Sometimes pH of acid comes more than 7 and that of base comes less than 7. It shows that the solution is very dilute; in such cases, H⁺ or OH^- contribution from water is also considered, e.g., in 10   N HCI,

      [H⁺]_Total = [10^-8]_Acid + [10^-7]_Water

      = 11 × 10^-8 M= 1.1 × 10^-7 M

 
pH of Mixture

Let one litre of an acidic solution of pH 2 be mixed with two litre of other acidic solution of pH 3. The resultant pH of the mixture can be evaluated in the following way.

 M_lV_l+M₂V₂ = M_R(V_i + V₂) 10^-2 × 1 + 10^-3 × 2 = M_R (1 +2)

(12 + 10^-3)/3  = M_R

4 × 10^-3 = M_R(Here, M_R = Resultant molarity)

pH = -log (4 × 10^-3)

Total concentration of [H⁺] or  [H₃⁺O ] in a mixture of weak acid and a strong acid  = (C₂ + √(c²₂ + 4K_aC₁ ))/2

where C₁ is the concentration of weak acid (in mol litre having dissociation constantK_a

C₂ is the concentration of strong acid

Total [OH^-] concentration in a mixture of two weak bases =   √(K₁C₁+ K₂C₂)

where K₁ and K₂ are dissociation constants of two weak bases having C₁ and C₂ as their mol litre^-1 concentration respectively.
 

Periodic Variations of Acidic and Basic Properties
 

(a)  Hydracids of the Elements of the Same Periods

Consider the hydracids of the elements of II period, Viz., CH₄, NH₃, H₂0 and HF. These hydrides become increasingly acidic as we move from CH₄ to HF. CH₄ has negligible acidic properties while HF is a fairly stronger acid. The increase in acidic properties is due to the fact that the stability of their conjugate bases increases in the order

CH^-₃< NH^-₂  < OH^- < F^-

The increase in acidic properties is supported by the succes­sive increase in the dissociation constant.

CH₄(=10^-58)<NH₃ (=10^-35)<H₂0(=10^-14)<HF(=10^-4)
 

(b)  Hydracids of the Elements of Same Group

1. Hydrides of V group elements (NH₃, PH₃, AsH₃, SbH₃, BiH₃) show basic character which decreases due to increase in size and decrease in electronegativity from N to Bi. There is a decrease in electron density in, sp³ -hybrid orbital and thus electron donor capacity decreases.

2. Hydracids of VI group elements (H₂0, H₂S, H₂Se, H₂Te) act as weak acids. The strength increases in the order H₂0 < H₂S < H₂Se < H₂Te. The increasing acidic properties reflects decreasing trend in the electron donor capacity of OH^-, HS^-, HSe^- or HTe^- ions.

3. Hydracids of VII group elements (HF, HCI, HBr, HI) show acidic properties which increase from HF to HI. This is explained by the fact that bond energies decrease. (H-F = 135 kcal/mol, HCI = 103, HBr = 88 and HI = 71 kcal/mol).
    

(c) Oxyacids

The acidic properties of oxyacids of the same element which is in different oxidation states increases with increase in oxidation number.

       + 1            +3          +5            +7

     HCIO  <  HC1O₂   <   HC1O₃   <  HCIO₄

       +4            +6         +3            +5

     H₂SO₃  <   H₂SO₄;    HNO₂     <  HNO₃

But this rule fails in oxyacids of phosphorus.

H₃PO₂  >  H₃PO₃  >  H₃PO₄

The acidic properties of the oxyacids of different elements which are in the same oxidation state decreases as the atomic number increases. This is due to increase in size and decrease in electronegativity.

HC1O₄ > HBrO₄ > HIO₄

 H₂SO₃  > H₂SeO₃

But there are a number of acid-base reactions in which no proton transfer takes place, e.g.,

SO₂ + SO₂  ↔  SO²⁺ +  S  

Acid₁  Base₂    Acid₂   Base₁

Thus, the protonic definition cannot be used to explain the reactions occurring in non-protonic solvents such as COCl₂, S0₂, N₂O₄, etc.

Example 1:  The hydrogen ion concentration of a solution is 0.001 M. What will be the hydroxyl ion concentration of solution?

Solution: We know that [H⁺][OH^-] 1.0 × 10^-14

Given that,    

[H⁺] = 0.001 M = 10^-3 M

So, [OH^-] = 1.0 * 10^-14/[H⁺] = (1* 10^-14)/10^-3 = 10^-11M

Example 2:  What is the pH of the following solutions?

(a) 10^-3 M HCl

(b) 0.0001 M NaOH

(c)  0.0001 MH₂S0₄

Solution:   HCI is a strong electrolyte and is completely ionised.

HCl  H⁺ + CI^-

So   [H⁺] = 10^-3 M

pH = -log [H⁺] = -log (10^-3) = 3

(b)   NaOH is a strong electrolyte and is completely ionised.

        NaOH ↔ Na⁺ + OH^-
So    [OH⁺] = 0.0001 M = 10^-4 M

        pOH = -log(10^-4) = 4

        As   pH + pOH = 14

        So   pH + 4 = 14   or     pH=10

Alternative method:   [OH^-] = 10^-4 M

We know that    [H⁺][OH^-] = 1.0 x 10^-14

          So  [H⁺] = (1.0  10^-14)/10^-14

        pH = -log [H⁺] = -log(10^-10) = 10

(c) H₂SO₄ is a strong electrolyte and is ionized completely.

        H₂SO₄ ↔ 2H⁺ + SO^2-₄

        One molecule of H₂SO₄ furnishes ions.

        So [H⁺] = 2 × 10^-4 M

        pH = -log [H⁺]

        = -log (2×10^-4)

        = 3.70

Example 3: Find the pH of a 0.002 N acetic acid solution, if it is 2.3% ionised at a given dilution.

Solution: Degree of dissociation, α = 2.3/100 = 0.023

Concentration of acetic acid, C = 0.002 M

The equilibrium is

CH₃COOH  CH₃COO^- + H⁺

C(1-α)         Cα           Cα

So  [H⁺] = Cα  = 0.002 × 0.023 = 4.6 × 10^-5 M

pH = -log [H⁺]= -log (4.6 × 10^-5) = 4.3372

Example 4:   Calculate the pH value of a solution obtained by mixing 50 mh of 0.2 N HCl with 50 mL of 0.1 N NaOH.

Solution:    Number of milli-equivalents of the acid

= 50 × 0.2 = 10

Number of milli-equivalents of the base

= 50 × 0.1 =5

Number of milli-equivalents of the acid left after the addition of base

= (10-5) = 5 Total volume of the solution

= 50 + 50 = 100 mL

Thus, 5 milli-equivalents of the acid are present in 100 mL of solution.

or 50 milli-equivalents of the acid are present in one litre of solution.

or 0.05 equivalents of the acid are present in one litre of solution.

The acid is monobasic and completely ionised in solution.

0.05 N HCl = 0.05 M HCl

So     [H⁺] = 0.05 M

pH = -log [H⁺] = -log 5 × 10^-2 = -[log 5.0 + log 10^-2]

= -[0.70-2] = 1.3

Example 5:  What will be the pH of a solution obtained by mixing 800 mL of 0.05 A' sodium hydroxide and 200 mL of OA N HCl, assuming complete ionisation of the acid and the base ?

Solution:   Number of milli-equivalents of NaOH

= 800 × 0.05 = 40

Number of milli-equivalents of HCl

= 200 × 0.1 =20

Number of milli-equivalents of NaOH left after the addition of HCl

= (40 -20) = 20

Total volume = (200 + 800) mL = 1000 mL = 1 litre

20 milli-equivalents or 0.02 equivalents of NaOH are present in one litre, i.e.,

0.02 N NaOH = 0.02 M NaOH (Mono-acidic) and the base is completely ionised.

So     [OH^-] = 0.02 M

or     [OH^-]= 2 × 10^-2 M

pOH = -log(2 × 10^-2) = 1.7

We know that,   pH + pOH = 14

So   pH = (14-1.7)= 12.3

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