Ionic Equilibrium B.Sc. 2nd Year

Ionic Equilibrium B.Sc. 2nd Year

Ionic Equilibria

Ostwald Dilution Law

According to Arrhenius electrolytic dissociation theory, ions and unionized electrolytic molecules are in dynamic equilibrium. Ostwald applied the law of mass action to this equilibrium as follows:
Let a weak electrolyte AB in aqueous solution has the degree of dissociation 伪 , then-
ostwald law
This equation is called Ostwald dilution law. Lower the K value, lower the 伪 value i.e. weaker the electrolyte.

Experimental Verification of Ostwald's Law

The Ostwald's Dilution law can be verified if the values of the degree of dissociation (伪), at different dilutions are known and the values are placed in the equation K = C伪2/(1 − 伪) and thus values of K at different dilutions are calculated. If these values come out to be nearly constant, the law is correct.
The degree of dissociation (伪), is determined by conductance measurements since the degree of ionisation (伪), of a weak electrolyte at a particular dilution is related as-
伪 = 位V/位

Where 位V is the equivalent conductance at V- dilution. It can be calculated by conductance measurements and 位 can be caculated by Kohlrausch's law-
V = 位+ + 位
Where, 位 is the equivalent conductance at infinite dilution, 位+ is equivalent conductance of cation at infinite dilution and 位 is equivalent conductance of anion at infinite dilution.

Limitation of Ostwald's Law

Ostwald's Dilution law holds good only for weak electrolytes and fails completely when appliedto strong electrolytes (i.e. HCl, KOH, KCl, etc.).For strong electrolytes, which are highly ionised in solution, the value of the dissociation constant K, far from remaining constant, rapidly falls with dilution.

Factors that explain the failure of Ostwald's law in case of strong electrolytes

1. The law is based on Arrhenius theory which assumes that only a fraction of the electrolyteis dissociated at ordinary dilutions and complete dissociation occurs only at infinite dilution. However, this is true for weak electrolytes. Strong electrolytes are almost completely ionised at all dilutions and 位V/位 does not give the accurate value of degree of dissociation (伪).
2. The Ostwald's law is derived on the assumption that the Law of Mass Action holds for theionic equilibria as well. But when the concentration of ions is very high, the presence of charges affects the equilibrium. Thus the Law of Mass Action in its simple form can not be applied.
3. The ions obtained by dissociation may get hydrated and may affect the concentration terms. Better results are obtained by using activities instead of concentrations.

Ionic Product of Water

Pure water is a very weak electrolyte and is ionises as,
H2O ⇌ H+ + OH
Applying law of mass action at equilibrium, the value of dissociation constant-
K=[H+] [OH] / [H2O]
or, K [H2O]=[H+] [OH]
Concentration of undissociated water molecules [H2O], may be regarded as constant as dissociation takes place to a very small extent. Thus, the product K [H2O] gives another constant which is written as Kw called ionic product of water.

So, Kw=[H+] [OH]
The product of concentrations of H+ and OH ions in water at a particular temperature is known as ionic product of water. The value of Kw increases with the increase of temperature, i.e., the concentration of H+ and OH ions increases with increase in temperature.

Buffer Solution

A buffer solution is an aqueous solution consisting of a mixture of a weak acid and its conjugate base, or vice versa. Its pH does not change or changes very little when a small amount of strong acid or base is added to it.
It is of three types, i.e. Acidic Buffer, Basic Buffer and Neutral buffer.
Acidic Buffer
Mixture of the solution of weak acid and salt of its conjugate base in equal amount.( e.g. acetic acid and sodiumacetate). pH of acidic buffer is less than seven.
Basic Buffer
Mixture of the solution of weak base and salt of its conjugate acid in equal amount.(e.g. ammoniumhydroxide and ammoniumchloride).pH of basic buffer is more than seven.
Neutral Buffer
It is single substance showing properties of buffers. (e.g. ammonium acetate).

Buffer capacity

The property of buffer solution to resist the change its pH value is known as buffer capacity. It has been found that if the ratio [Salt] / [Acid] or [Salt] / [Base] is unity, the pH of a particular buffer does not change at all.
Quantitatively, buffer capacity is defined as number of moles of acid or base added in one litre of solution to change the pH by unity.
Buffer Capacity = No. of moles of acid or base added to one liter of buffer / Change in pH.
or, 尾 = n / 螖pH
where: 尾 is buffer capacity, n is the number of moles of an acid or a base added one liter of buffer solution and 螖pH is the change in pH.
螖pH=final pH - initial pH
A buffer capacity always has a positive value.
Buffer capacity is maximum when:
[Salt] = [Acid], i.e., pH = pKa for acid buffer
[Salt] = [Base], i.e., pOH = pKb for base buffer under above conditions, the buffer is called efficient.

Buffer Range

The buffer range is the pH range where a buffer effectively neutralizes added acids and bases, while maintaining a relatively constant pH.

Salt Hydrolysis

Salt hydrolysis is the phenomenon of interaction of cations and anions of a salt with H2O in order to produce an acidic nature or an alkaline nature.
Salt + Water ⇌ Acid + Base      螖H =+ve
The net effect of dissolving a salt (which undergoes hydrolysis) is to break up the water molecules (hydrolysis) to produce a weak acid or weak base or both and thus, phenomenon is always endothermic.
The process of salt hydrolysis is actually reverse the process of neutralization.

1. Hydrolysis of Strong Acid and Strong Base (SA - SB) types of salt-

Hydrolysis of salt of Strong Acid and Strong Base is not possible as both cation and anion are not reactive. Aqueous solution of these type of salt is neutral in nature,so, pH of the solution is 7.

2. Hydrolysis of Strong Acid and Weak Base (SA - WB) types of salt-

NH4Cl + H2O ⇌ NH4OH + HCl
NH4+ H2O ⇌ NH4OH + H+
In this type of salt hydrolysis, cation reacts with H2O so it is called cationic hydrolysis. The cation of the salt which come from weak base is reactive. Solution is acidic in nature as [H+] is increased. So the pH of the solution is less than 7.

Relation between Kh, KW and Kb
NH4+ H2O ⇌ NH4OH + H+
so, Hydrolysis Constant (Kh)

Kh = [NH4OH] [H+]/[NH4+] -----(equation-1)
NH4OH ⇌ NH4+ + OH
so, Ionization Constant of base (Kb)
Kb = [NH4+] [OH]/[NH4OH] -----(equation-2)
and
H2O ⇌ H+ + OH
so, Ionic Product of water (KW)
KW = [H+] [OH]/[H2O] -----(equation-3)
Now if we multiplying equation-1 and equation-2, we get equation-3
Kh X Kb = KW

so, Kh = KW/Kb

Degree of Hydrolysis
                    NH4+ + H2O ⇌ NH4OH + H+
Initial Conc.: C                         0           0
Con. after
some times: C − Ch                Ch        Ch
so, Kh = Ch2/(1-h)
h is very less in comparision to 1
so, Kh = Ch2
or, h = √Kh/C

or, h = √KW/Kb.C     (as Kh = KW/Kb)

pH of the Solution
[H+] = Ch = C.√KW/Kb.C     (as h = √KW/Kb.C )
or, [H+] = √KWC/Kb
Taking negative log on both sides we get-
−log[H+] = −log√KWC/Kb
or, pH = −log(KWC/Kb)1/2
or, pH = −1/2[logKWC + logC − logKb]
or, pH = −1/2logKWC −1/2logC −(−1/2logKb)
or, pH = 1/2pKW −1/2logC −1/2pKb
or, pH = 7 −1/2logC −1/2pKb

3. Hydrolysis of Weak Acid and Strong Base (WA - SB) types of salt

Similar as Hydrolysis of Strong Acid and Weak Base (SA - WB) types of salt.
Kh = Kw/Ka
pH = 1/2pKW + 1/2logC + pKa
or, pH = 7 + 1/2logC + pKa

4. Hydrolysis of Weak Acid and Weak Base (WA - WB) type of Salts

Similar as Hydrolysis of Strong Acid and Weak Base (SA - WB) or Weak Acid and Strong Base (WA - SB) types of salt.
Kh = Kw/Ka.Kb
pH = 1/2pKW + 1/4pKa − 1/2pKb
or, pH = 7 + 1/4pKa − 1/2pKb

Choise of an indicator for an acid base titration

The acid-base indicator (is a dye that changes colour when pH changes) is usually an organic compound that is itself a weak acid or weak base. So, they have their own pH values. They change their colors within a definite pH range. For example Methylorange change its color at the pH range 3 - 4.5 and phenolphthalein change its color at the pH range 8 - 10. On the other hand pH at the equivalent point of acid-base react may not be 7 always. In some case it is greater than 7, less than 7 or in same case it is equal to 7 and it is decided by the nature of acid and base present in the reaction.

In order to determine the accurate end point (when the indicator changes colour during a titration) of acid-base titration, the pH indicator should be selected in such a way that the pH range for the color change of the indicator must coincide with the pH at the equivalent point (the amount of acid and of base is just sufficient to cause complete consumption of both the acid and the base. i.e. neither the acid nor the base is in excess or neither the acid nor the base is the limiting reagent) of reaction. Litmus is not used in titrations because the pH range over which it changes colour is too great (pH range is 5.0 - 8.0

Indicator NamepH RangeColor Change
Methyl Orange3.1 - 4.4Red → Yellow
Bromothymol Blue6.0 - 7.6Yellow → Blue
Phenolphthalein8.3 -10.0Colourless → Pink
Acid-Base indicators are selected by classifying different acid-base reaction of the titration in different groups as follows-

1. Strong Acid Titration

HCl + NaOH → NaCl + H2O
The pH at this type of reaction is 7 (neutral) because the salt does not undergo hydrolysis with water. The pH change at the end of this type of titration is 3 - 10 approx. So, either methyl orange (3 - 4.5) or phenolphthalein (8 - 10) can be used to find the actual end point of this type of titration.

2. Strong Acid-Weak Base titration

HCl + NH4OH ⇋ NH4Cl + H2O
The pH at the equivalent point of this type of reaction is less than 7 (acidic) because the salt undergoes hydrolysis to give strong acid and weak base. The pH change at the end point of this type of titration is 3 - 7 approx. So, methyl orange (3 - 4.5) is good indicator for this type of titration.

3. Weak Acid-Strong Base titration

CH3COOH + NaOH ⇋ CH3COONa + H2O
The pH at the equivalent point of this type of reaction is more than 7 (basic) because the salt undergoes hydrolysis to give Strong base and weak acid. The pH change at the end point of this type of titration is 7 - 10 approx. The indicator used to find the end point of this type of titration should give the color change in basic range. Phenolphthalein is good indicator for this type of titration.

4. Weak Acid-Weak Base titration

CH3COOH + NH4OH ⇋ CH3COONH4 + H2O The pH at the equivalent point of this type of reaction may be either slightly greater than 7, less than 7 or equal to 7 and it is decided by the relative extent of ionization of Weak Acid and weak base produced after the hydrolysis of the salt. The pH change at the end point of this type of titration is not sharp and wide because the salt acts as a buffer. Because of no sharp and wide pH change at the end point of this indicator method of titration is not so accurate for weak acid and weak base titration.

Solubility Product (Ksp)

Solubility product is defined as- in the saturated solution, the product of concentrations of the ions raised to a power equal to the number of times, the ions occur in the equation representing the dissociation of the electrolyte at a given temperature.
Consider in general, the electrolyte of the type AxBywhich is dissociated as-
AxBy ⇌ xA+y + yB−x
Applying law of mass action-
K = [A+y]x [B−x]y/[AxBy]
or, K [AxBy] = [A+y]x [B−x]y
for saturated solution-
[AxBy] = constant
so, Ksp = [A+y]x [B−x]y

Q. The solubility of barium sulphate at 298 K is 1.05 x 10-5 mol dm-3. Calculate the solubility product.

BaSO4 ⇌ Ba+2 + SO4-2
Given-
[Ba+2] = 1.05 x 10-5 mol dm-3
[SO4-2] = 1.05 x 10-5 mol dm-3
So, Ksp = [Ba+2] [SO4-2]
or, Ksp = 1.05 x 10-5 X .05 x 10-5
or, Ksp = 1.10 x 10-10 mol2 dm-6

Q. If the solubility product of magnesium hydroxide is 2.00 X 10-11 mol3 dm-9 at 298 K, calculate its solubility in mol dm-3 at that temperature.

Answer: 1.71 X 10-4 mol dm-3

Common Ion Effect

The phenomenon in which the degree of dissociation of a weak electrolyte is suppressed by the addition of a strong electrolyte having an ion common to weak electrolyte is known as common ion effect.
Let us consider dissociation of a weak electrolyte (acetic acid)-
CH3COOH ⇌ CH3COO + H+
The equilibrium constant-
Ka = [CH3COO] [H+]/[CH3COOH]
Now, if sodium acetate is added to this solution-
The concentration of CH3COO ion in the solution increases and thus, in order to have Ka constant [H+] must decrease or the concentration of undissociated acetic acid must increase. In other words, the dissociation of acetic acid is suppressed on addition of CH3COONa to its solution.

pH and Common-Ion Effect

When the conjugate ion of a buffer solution is added to it, the pH of the buffer solution changes due to the common ion effect.


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