Introductory General Chemistry · Unit 15

Acids & Bases

Start here: acid-base chemistry is really about proton transfer, equilibrium, and concentration all working together. In this unit, you will identify acids and bases, calculate pH, compare strong vs weak acids, and work through buffers and titrations without mixing up the rules. This picks up directly from chemical equilibrium and brings together ideas from solutions and concentration.

What you'll learn

Identify Brønsted-Lowry acids, bases, and conjugate pairs in any reaction. Calculate pH, pOH, and concentration for strong and weak acids and bases. Relate Ka and Kb values to acid and base strength. Solve buffer problems with Henderson-Hasselbalch and interpret titration curves.

15.1 Start Here: How to Identify the Acid, Base, and Conjugate Pair

A Brønsted-Lowry acid donates a proton (H⁺). A Brønsted-Lowry base accepts that proton.

Every acid-base reaction is a proton transfer. The acid loses H⁺ and becomes its conjugate base, while the base gains H⁺ and becomes its conjugate acid.

HA + B ⇌ A⁻ + BH⁺ acid + base ⇌ conjugate base + conjugate acid

A species is amphiprotic if it can either donate or accept a proton, depending on the conditions.

Water is the most important amphiprotic species, and it undergoes autoionization:

2 H₂O(l) ⇌ H₃O⁺(aq) + OH⁻(aq)

The equilibrium constant for autoionization is the ion-product of water, K_w:

K_w = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ (at 25 °C)

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Every conjugate acid-base pair is connected by exactly one proton.
HCl donates H⁺ to become Cl⁻, so HCl/Cl⁻ is a conjugate pair.
Do not miss this: if two species differ by more than one proton, they are not a conjugate pair.

15.2 pH and pOH: Reading the Log Scale Correctly

Because hydronium and hydroxide concentrations are often tiny numbers, chemists use a logarithmic scale. The pH and pOH compress those wide ranges into values you can actually compare.

If this feels shaky, start with the neutral benchmark first, then decide whether the solution is acidic or basic before you calculate anything else.

pH = −log[H₃O⁺] pOH = −log[OH⁻]

pH + pOH = 14 (at 25 °C)

pH Scale — Solution Classification at 25 °C
Condition	[H₃O⁺] vs [OH⁻]	pH	Example
Acidic	[H₃O⁺] > [OH⁻]	< 7	Stomach acid (pH ≈ 1.5)
Neutral	[H₃O⁺] = [OH⁻]	= 7	Pure water
Basic	[H₃O⁺] < [OH⁻]	> 7	Bleach (pH ≈ 12)

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Each unit change in pH represents a tenfold change in [H₃O⁺].
A solution of pH 3 has 100 times the hydronium concentration of a pH 5 solution, not 2 times.
Notice the common mistake: the pH scale is logarithmic, not linear.

15.3 Strong vs. Weak Acids and Bases: Do Not Mix Up Strength and Concentration

A strong acid ionizes essentially completely in water. A weak acid ionizes only partially, so an equilibrium is established.

Strong and weak describe how much a substance ionizes. Concentrated and dilute describe how much of the substance is present.

Do not use strength and concentration as if they mean the same thing. A concentrated weak acid can still have a lower pH than a dilute strong acid.

The acid ionization constant K_a describes that equilibrium. The larger the K_a, the stronger the acid.

HA(aq) + H₂O(l) ⇌ H₃O⁺(aq) + A⁻(aq) K_a = [H₃O⁺][A⁻][HA]

For bases, the analogous constant is K_b. A key relationship connects a conjugate pair:

K_a × K_b = K_w = 1.0 × 10⁻¹⁴

Common Strong Acids and Bases (memorize these)
Strong Acids	Strong Bases
HCl, HBr, HI	NaOH, KOH, LiOH
HNO₃, H₂SO₄, HClO₄	Ca(OH)₂, Ba(OH)₂, Sr(OH)₂

Three patterns connect acid strength to structure — use these when comparing acids that are not on the strong acid list.

For matched binary acids in the same group, acid strength increases as you go down the group because the H–X bond becomes easier to break.

For matched binary acids across the same period, acid strength generally increases as the bonded atom becomes more electronegative.

For oxyacids with the same central atom, more oxygen atoms usually mean a stronger acid because electron density is pulled away from the O–H bond more strongly.

15.4 pK_a and pK_b: The Strength Scale That Runs Backward

Just as pH is the negative log of a concentration, pK_a and pK_b are the negative logs of the ionization constants K_a and K_b.

Using a log scale makes these equilibrium constants easier to compare and easier to use in buffer calculations. It also creates a common mistake: the direction flips, and that is easy to lose track of.

pK_a = −log(K_a) pK_b = −log(K_b)

A stronger acid has a larger K_a, so it has a smaller pK_a.

The direction flips on the log scale: low pK_a means strong acid, and high pK_a means weak acid. The same idea applies to bases.

pK_a Values for Common Weak Acids at 25 °C
Acid	K_a	pK_a	Relative strength
Hydrofluoric acid (HF)	6.8 × 10⁻⁴	3.17	Relatively strong weak acid
Acetic acid (CH₃COOH)	1.8 × 10⁻⁵	4.74	Moderate
Carbonic acid (H₂CO₃)	4.3 × 10⁻⁷	6.37	Moderate–weak
Ammonium ion (NH₄⁺)	5.6 × 10⁻¹⁰	9.25	Very weak acid
Hydrogen cyanide (HCN)	4.9 × 10⁻¹⁰	9.31	Very weak acid

For a conjugate acid-base pair, pK_a and pK_b always sum to 14 at 25 °C — the same relationship as pH and pOH:

pK_a + pK_b = 14 (at 25 °C)

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For a buffer made from a weak acid and its conjugate base, pH = pK_a when [HA] = [A⁻].
At that point the Henderson-Hasselbalch log term equals zero.
This is why buffers work best near the acid's pK_a.

15.5 Polyprotic Acids: One Proton at a Time

A polyprotic acid can lose more than one proton, but it loses them one step at a time.

Each step has its own ionization constant. Later ionizations are usually much weaker because the next proton is being removed from a species that is already more negatively charged.

H₂SO₃: K_a1 = 1.5 × 10⁻² (first proton — relatively easy) K_a2 = 6.3 × 10⁻⁸ (second proton — much harder)

Because K_a1 ≫ K_a2, the first ionization usually controls the pH. For most introductory problems, you can calculate the pH using only K_a1 unless you are told to analyze later steps.

15.6 Buffers: Why pH Stays Nearly Steady

A buffer is a solution that resists changes in pH when small amounts of strong acid or strong base are added. Buffers contain an appreciable amount of both members of a weak conjugate acid-base pair. The acid component neutralizes added base, and the base component neutralizes added acid.

The pH of a buffer is calculated using the Henderson-Hasselbalch equation:

pH = pK_a + log([A⁻][HA])

A buffer works best when [A⁻] ≈ [HA], meaning pH ≈ pK_a. Adding too much acid or base exhausts one component and destroys the buffer. This limit is called the buffer capacity.

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Blood is buffered primarily by the carbonic acid / bicarbonate pair (H₂CO₃ / HCO₃⁻, pK_a ≈ 6.1) and maintains a pH of 7.35–7.45.
Notice the key idea: a buffer only works if both parts of the conjugate pair are present in useful amounts.

15.7 Acid-Base Titrations: When Neutralization Does and Does Not Mean pH 7

A titration finds the concentration of an unknown acid or base by reacting it with a solution of known concentration.

The equivalence point is reached when the acid and base have reacted in the correct stoichiometric amounts. A titration curve plots pH vs. volume of titrant and helps you locate that point.

Here is the point that catches everyone off guard: the pH at the equivalence point is not always 7. It depends on what species are present after neutralization.

Equivalence Point pH for Common Titration Types
Titration Type	pH at Equivalence Point	Why
Strong acid + Strong base	= 7	Salt does not hydrolyze
Weak acid + Strong base	> 7	Conjugate base hydrolyzes to give OH⁻
Strong acid + Weak base	< 7	Conjugate acid hydrolyzes to give H₃O⁺

An indicator is a weak acid or base that changes color near its own pK_a. Choose an indicator whose color-change range overlaps with the steep part of the titration curve.

Use these tools the way you would work through acid-base chemistry in class: classify first, choose the right model second, then check the reasoning. If you want a mixed review set after this, move into the Unit 15 Practice page and use it to lock in the weak spots you notice here.

Acidic, Basic, or Neutral?

Read This First

Classify the solution before you calculate anything else.

Compare the given value to the neutral reference first, then choose one answer.

Card: pH = 3.2

Choose one answer, then click Check.

Where Is the Buffer pH?

Read This First

Place the buffer pH relative to pK_a.

Compare the weak acid and conjugate base amounts before you choose an answer.

Buffer card: pK_a = 4.74, [HA] = 0.20 M, [A⁻] = 0.05 M

Choose one answer, then click Check.

Neutralization at the Endpoint

Read This First

Decide the valid setup for the titration before you solve.

At the phenolphthalein endpoint, check whether the reaction is 1:1 before using M_aV_a = M_bV_b.

Titration card: A 25.0 mL HCl sample is titrated to a faint pink phenolphthalein endpoint with 0.100 M NaOH. It takes 30.0 mL of base. Find the molarity of the acid.

Choose one setup, then click Check.

Ex 1 Identifying Conjugate Acid-Base Pairs

Problem: Identify both conjugate acid-base pairs in the reaction.

Given: NH₃ + H₂O ⇌ NH₄⁺ + OH⁻

Find: Both conjugate pairs

Identify the proton donor (acid)

H₂O donates one H⁺ to NH₃. So H₂O is the Brønsted-Lowry acid in this reaction.

Identify the proton acceptor (base)

NH₃ accepts that H⁺ and becomes NH₄⁺. So NH₃ is the Brønsted-Lowry base.

Name both conjugate pairs

Pair 1: H₂O (acid) / OH⁻ (conjugate base) — they differ by one H⁺.
Pair 2: NH₄⁺ (conjugate acid) / NH₃ (base) — they differ by one H⁺.

Ex 2 Calculating pH of a Strong Acid

Problem: Find the pH and pOH of a strong acid solution.

Given: 0.025 M HCl

Find: pH and pOH

Recognize complete ionization

HCl is a strong acid — it ionizes 100% in water. Therefore [H₃O⁺] = 0.025 M exactly.

Calculate pH

Factor-Label Chain

pH = −log[H₃O⁺] = −log(0.025) = 1.60

Find pOH

pOH = 14 − pH = 14 − 1.60 = 12.40

Ex 3 pH of a Weak Acid Using K_a

Problem: Find the pH of a weak acid using K_a.

Given: 0.100 M CH₃COOH, K_a = 1.8 × 10⁻⁵

Find: pH

Decide which model applies

CH₃COOH is a weak acid, so it does not ionize completely like HCl. That means we cannot set [H₃O⁺] equal to 0.100 M directly. We must use an equilibrium setup.

Write the ionization equation and ICE table

CH₃COOH + H₂O ⇌ H₃O⁺ + CH₃COO⁻

	[CH₃COOH]	[H₃O⁺]	[CH₃COO⁻]
I	0.100	≈ 0	0
C	−x	+x	+x
E	0.100 − x	x	x

Set up the K_a expression and solve for x

1.8 × 10⁻⁵ = x² / (0.100 − x) ≈ x² / 0.100
x² = 1.8 × 10⁻⁶
x = [H₃O⁺] = 1.34 × 10⁻³ M

The approximation is valid because x / 0.100 = 1.34% < 5%.

Calculate pH

pH = −log(1.34 × 10⁻³) = 2.87

Ex 4 Buffer pH Using Henderson-Hasselbalch

Problem: Use Henderson-Hasselbalch to find the pH of a buffer.

Given: [HA] = 0.100 M acetic acid, [A⁻] = 0.150 M acetate, K_a = 1.8 × 10⁻⁵

Find: pH

Predict pH relative to pK_a

There is more conjugate base than weak acid: [A⁻] = 0.150 M and [HA] = 0.100 M. So the pH should be slightly above pK_a before we calculate anything.

Calculate pK_a

pK_a = −log(1.8 × 10⁻⁵) = 4.74

Apply Henderson-Hasselbalch

pH = pK_a + log([A⁻] / [HA])
pH = 4.74 + log(0.150 / 0.100)
pH = 4.74 + log(1.50)
pH = 4.74 + 0.176 = 4.92

Interpret the result

The pH is slightly above pK_a because there is more conjugate base than acid.

That matches what Henderson-Hasselbalch predicts for a buffer on the basic side of its range.

Ex 5 Converting Between K_a, pK_a, K_b, and pK_b

Problem: Convert among K_a, pK_a, K_b, and pK_b.

Given: Acetic acid has K_a = 1.8 × 10⁻⁵

Find: pK_a, K_b of acetate, and pK_b of acetate

Calculate pK_a from K_a

pK_a = −log(K_a) = −log(1.8 × 10⁻⁵) = 4.74

A pK_a of 4.74 means acetic acid is a moderately weak acid.

Find K_b of the conjugate base (acetate, CH₃COO⁻)

K_a × K_b = K_w = 1.0 × 10⁻¹⁴
K_b = K_w / K_a = (1.0 × 10⁻¹⁴) / (1.8 × 10⁻⁵) = 5.6 × 10⁻¹⁰

Calculate pK_b — and verify the sum rule

pK_b = −log(5.6 × 10⁻¹⁰) = 9.26
pK_a + pK_b = 4.74 + 9.26 = 14.00 ✓

The large pK_b confirms that acetate is a very weak base.

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After Unit 15

This unit pulls together equilibrium, solutions, and concentration into one last major chemistry system. If this feels shaky, go back through Unit 14: Chemical Equilibrium and the Unit 15 Practice page before moving on.

Introductory General Chemistry · Unit 15 · Acids & Bases

15.1 Start Here: How to Identify the Acid, Base, and Conjugate Pair

15.2 pH and pOH: Reading the Log Scale Correctly

15.3 Strong vs. Weak Acids and Bases: Do Not Mix Up Strength and Concentration

15.4 pKa and pKb: The Strength Scale That Runs Backward

15.5 Polyprotic Acids: One Proton at a Time

15.6 Buffers: Why pH Stays Nearly Steady

15.7 Acid-Base Titrations: When Neutralization Does and Does Not Mean pH 7

15.4 pK_a and pK_b: The Strength Scale That Runs Backward