Q.Determine the degree of ionization and pH of a 0.05M of ammonia solution. The ionization constant of ammonia can be taken from Table 6.7. Also, calculate the ionization constant of the conjugate acid of ammonia.
Imagine you're making lemonade. If you add a few drops of lemon juice to a glass of water, the pH drops sharply — it becomes very acidic. But if you add the same few drops to a glass of already acidic lemonade, the pH barely changes. Why? Because lemonade contains a buffer — a mixture that resists pH change when small amounts of acid or base are added.
A buffer solution is a mixture of a weak acid and its conjugate base (or a weak base and its conjugate acid). It "soaks up" added H⁺ or OH⁻ ions without letting the pH swing wildly.
Note
The key is that both components must be present in significant amounts. A weak acid alone won't buffer — you need its conjugate base partner too.
The Intuition: A Chemical Sponge
Think of a buffer as a two-way sponge:
If you add acid (H⁺): The conjugate base in the buffer grabs the extra H⁺, turning into the weak acid. The H⁺ is "absorbed" — pH barely drops.
If you add base (OH⁻): The weak acid donates an H⁺ to neutralise the OH⁻, turning into the conjugate base. The OH⁻ is "absorbed" — pH barely rises.
The buffer works best when the amounts of weak acid and conjugate base are roughly equal. That's when the sponge is most "spongy" — it can absorb shocks in either direction.
The Precise Statement: The Henderson–Hasselbalch Equation
For a buffer made from a weak acid HA and its conjugate base A−, the pH is given by:
pH=pKa+log10([HA][A−])
Where:
pKa=−log10Ka (a measure of the weak acid's strength — lower pKa = stronger acid)
[A−] = concentration of the conjugate base
[HA] = concentration of the weak acid
This equation tells you exactly how the pH depends on the ratio of base to acid, not their absolute amounts.
Tip
When [A−]=[HA], the ratio is 1, log(1)=0, so pH=pKa. This is the buffer's optimal pH — it resists change most strongly here.
Why This Works: A Quick Derivation
Start from the weak acid equilibrium:
HA⇌H++A−
The acid dissociation constant is:
Ka=[HA][H+][A−]
Take negative logs of both sides:
−logKa=−log[H+]−log[HA][A−]
Which gives:
pKa=pH−log[HA][A−]
Rearrange:
pH=pKa+log[HA][A−]
That's it. The derivation is just algebra on the definition of Ka.
Watch out
The Henderson–Hasselbalch equation assumes that the concentrations [HA] and [A−] are the initial concentrations you mixed. It works well when both are much larger than [H+] or [OH−] from dissociation — which is true for a properly made buffer.
Example: Making an Acetate Buffer
You mix 0.1 M acetic acid (pKa=4.76) with 0.1 M sodium acetate. What's the pH?
Concept: Buffer Solution pH — but here it's a weak base (ammonia) in water, so we use the base dissociation constant Kb and the relation [OH−]=Kb⋅C for a weak base.
Step 1 — Find Kb and Ka of conjugate acid
From Table 6.7, Kb for NH3 = 1.77×10−5.
For the conjugate acid NH4+,
Ka=KbKw=1.77×10−51.0×10−14=5.65×10−10.
Step 2 — Degree of ionization (α)
For a weak base, α=CKb=0.051.77×10−5=3.54×10−4=0.0188 (or 1.88%).
For a weak base like ammonia, the degree of ionization (α) is found from Kb=Cα2/(1−α), and pH follows from [OH−]=Cα. Using Kb=1.77×10−5 for 0.05 M NH₃, we get α≈0.0188, pH ≈10.95, and Ka for NH₄⁺ is 5.65×10−10.
Why This Approach Works
Ammonia in water is a classic weak base — it doesn't fully ionize. Instead, it establishes an equilibrium:
NH3(aq)+H2O(l)⇌NH4+(aq)+OH−(aq)
The ionization constant Kb tells us how far this reaction goes. From Table 6.7 (NCERT), Kb for ammonia is 1.77×10−5 at 25°C.
The degree of ionization α is the fraction of ammonia molecules that have accepted a proton. For a weak base, α is small, so we can often simplify calculations — but we'll check that assumption.
The conjugate acid of ammonia is the ammonium ion, NH₄⁺. For any conjugate acid-base pair, Ka×Kb=Kw, where Kw=1.0×10−14 at 25°C. This lets us find Ka for NH₄⁺ directly.
Step-by-Step Solution
1. Set up the equilibrium table
Let initial concentration of NH₃ be C=0.05 M. If α is the degree of ionization:
Species
Initial (M)
Change (M)
Equilibrium (M)
NH₃
C
−Cα
C(1−α)
NH₄⁺
0
+Cα
Cα
OH⁻
0
+Cα
Cα
2. Write the Kb expression
Kb=[NH3][NH4+][OH−]=C(1−α)(Cα)(Cα)=1−αCα2
Substitute known values:
1.77×10−5=1−α0.05⋅α2
3. Solve for α
This is a quadratic in α. Multiply through:
1.77×10−5(1−α)=0.05α2
1.77×10−5−1.77×10−5α=0.05α2
Rearrange:
0.05α2+1.77×10−5α−1.77×10−5=0
Using the quadratic formula α=2a−b±b2−4ac with a=0.05, b=1.77×10−5, c=−1.77×10−5:
The negative root gives a negative α (impossible), so take the positive root:
α=0.1−1.77×10−5+3.13×10−10+3.54×10−6
α=0.1−1.77×10−5+3.5403×10−6
α=0.1−1.77×10−5+1.8816×10−3
α=0.11.8639×10−3=0.01864
Tip
Since α≈0.019 is much less than 0.05, we could have used the approximation 1−α≈1, giving α=Kb/C=1.77×10−5/0.05=3.54×10−4=0.0188. The exact value (0.01864) is very close — the approximation works well here.
Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.
CBSE 2026Set ANNUAL1 mark
Q.The solutions which resist change in their pH on dilution are called ______ solution.
›Reveal solutionSolution
Solutions that resist a change in pH on dilution (or on adding small amounts of acid/base) are called buffer solutions.
A buffer solution typically consists of a weak acid together with its conjugate base (e.g. CH3COOH + CH3COO- from CH3COONa), or a weak base together with its conjugate acid (e.g. NH4OH + NH4+ from NH4Cl). Because both the acidic and basic components are present in appreciable, comparable amounts, any small addition of H+ or OH- (or dilution, which shifts conce …
Q.Equilibrium :
Assertion (A) : A solution containing a mixture of ammonium chloride and ammonium hydroxide maintains a constant value of pH on addition of small amounts of acid or alkali.
Reason (R) : A solution containing mixture of ammonium chloride and ammonium hydroxide act as a buffer solution around pH 9.25.
(Choose the correct option for the Assertion-Reason pair.)
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not correct explanation of Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.
›Reveal solutionSolution
Both the assertion and the reason are true, and the reason correctly explains the assertion: NH4Cl + NH4OH is a basic buffer solution with pH close to 9.25.
A buffer solution resists changes in pH upon addition of small amounts of acid or base. A basic buffer is typically made of a weak base and its salt with a strong acid — exactly the NH4OH (weak base) + NH4Cl (its salt with strong acid HCl) combination described here.
How the buffering works: NH4OH partially ionises to give NH4+ and OH-, while NH4Cl fully dissociates to give a large reservoir of NH4+ ions and Cl- ions.
On adding a small amount of acid (H+), the excess H+ is neutralised by the NH4OH present (NH4OH + H+ → NH4+ + H2O), so pH barely changes.
On adding a small amount of base (OH-), the NH4+ from the salt neutralises it (NH4+ + OH- → NH4OH), again keeping pH nearly constant.
…
A buffer resists pH change on adding small amounts of acid/base; made of a weak acid + its conjugate base (or weak base + its conjugate acid).
A buffer solution is a solution whose pH changes very little when a small amount of a strong acid or strong base is added to it, or on dilution. It is typically prepared by mixing:
a weak acid with a salt of its conjugate base (an acidic buffer, e.g. CH3COOH + CH3COONa), or
a weak base with a salt of its conjugate acid (a basic buffer, e.g. NH4OH + NH4Cl).
…
The Henderson-Hasselbalch equation: pH = pKa + log([salt]/[acid]), used to calculate the pH of a buffer solution.
For a buffer made of a weak acid (HA) and its conjugate base/salt (A-, e.g. from a sodium salt), the equilibrium HA <-> H+ + A- gives Ka = [H+][A-]/[HA].
A buffer solution maintains an almost constant pH despite small additions of acid, base, or dilution, because it contains a weak acid/conjugate-base or weak base/conjugate-acid pair that can absorb added H+ or OH-.
A buffer solution resists changes in pH upon the addition of small quantities of an acid or a base, or upon dilution. There are two main types:
Acidic buffer: a mixture of a weak acid and its salt with a strong base (e.g., CH3COOH + CH3COONa). It resists pH changes near acidic pH values.
Basic buffer: a mixture of a weak base and its salt with a strong acid (e.g., NH4OH + NH4Cl). It resists pH changes near basic pH values.
…