1. Arrhenius definition
The simplest acid-base model. Svante Arrhenius defined acids and bases by what they release in water.
- Arrhenius acid: a substance that releases H⁺ ions (hydrogen ions, also written as H₃O⁺ in solution) when dissolved in water.
- Arrhenius base: a substance that releases OH⁻ ions (hydroxide ions) when dissolved in water.
Examples
Arrhenius acids: HCl, HNO₃, H₂SO₄, CH₃COOH (vinegar)
Arrhenius bases: NaOH, KOH, Ca(OH)₂, Mg(OH)₂
The H⁺ ion is basically a bare proton. In water it bonds to a water molecule to form a hydronium ion (H₃O⁺). On the Regents, H⁺ and H₃O⁺ both refer to acidic species and can be used interchangeably.
2. Brønsted-Lowry definition
A broader model. Acids and bases are defined by what they do with protons, not what they release.
- Brønsted-Lowry acid: a proton donor (H⁺ donor).
- Brønsted-Lowry base: a proton acceptor (H⁺ acceptor).
Why this matters
Brønsted-Lowry includes everything Arrhenius does (HCl is still an acid because it donates H⁺ to water) and adds bases that don't contain OH⁻. Ammonia, NH₃, is a Brønsted-Lowry base because it accepts H⁺ from water: NH₃ + H₂O → NH₄⁺ + OH⁻.
Conjugate acid-base pairs
In a Brønsted-Lowry reaction, when an acid donates a proton, it becomes its conjugate base. When a base accepts a proton, it becomes its conjugate acid. The two species in each pair differ by exactly one H⁺.
Example: HCl + H₂O → H₃O⁺ + Cl⁻
- HCl (acid) donates H⁺, becoming Cl⁻ (its conjugate base).
- H₂O (base) accepts H⁺, becoming H₃O⁺ (its conjugate acid).
- Conjugate pairs: HCl/Cl⁻ and H₂O/H₃O⁺.
3. Properties of acids and bases
| Property | Acids | Bases |
|---|---|---|
| Taste | Sour (citrus, vinegar) | Bitter (soap) |
| Feel | — | Slippery |
| Litmus paper | Turns blue litmus red | Turns red litmus blue |
| Phenolphthalein | Colorless | Pink |
| pH range | Less than 7 | Greater than 7 |
| Reacts with active metals | Yes (H₂ gas released) | No (most cases) |
| Reacts with carbonates | Yes (CO₂ released) | No |
| Electrical conductivity | Yes (electrolytes) | Yes (electrolytes) |
Never taste or touch
Real-world warning: never test for acids or bases with taste or touch. Strong acids and bases cause severe burns. Use indicators or pH paper. The Regents may list these as properties, but lab safety overrides them in practice.
4. Reference Tables K, L, and M
Three tables you must know cold for this topic.
| Table | What it lists | Examples |
|---|---|---|
| K: Common Acids | Formulas and names of 7 common acids | HCl, HNO₃, H₂SO₄, H₃PO₄, H₂CO₃, CH₃COOH, others |
| L: Common Bases | Formulas and names of 4 common bases | NaOH, KOH, Ca(OH)₂, NH₃ (aq) |
| M: Common Acid-Base Indicators | 5 indicators with their color change pH ranges | Methyl orange, bromothymol blue, phenolphthalein, others |
How to recognize an acid in a formula
An acid typically has H written first (HCl, H₂SO₄, HNO₃). Organic acids are the exception: the H of the —COOH is at the end (CH₃COOH). You can usually tell by looking for a hydrogen attached to something electronegative.
5. Strong vs weak
Strength refers to how completely an acid or base ionizes in water. It is unrelated to concentration.
Strong acids
Ionize completely. HCl, HBr, HI, H₂SO₄, HNO₃, HClO₄. 100% dissociates into ions.
Weak acids
Ionize partially. CH₃COOH (vinegar), H₂CO₃, H₃PO₄. Most acid molecules remain intact in solution. An equilibrium exists between ionized and un-ionized forms.
Strong bases
Group 1 hydroxides (NaOH, KOH, LiOH) and Group 2 hydroxides (Ca(OH)₂, Ba(OH)₂). Ionize completely.
Weak bases
NH₃ (ammonia) and most amines. Only a small fraction reacts with water to produce OH⁻.
Strong vs concentrated
A "strong" acid is one that ionizes completely. A "concentrated" acid has a lot of acid dissolved per liter. They are independent. A dilute strong acid (0.001 M HCl) is still a strong acid. A concentrated weak acid (12 M CH₃COOH) is still a weak acid.
6. Electrolytes
An electrolyte is a substance that dissolves in water to produce ions, which allow the solution to conduct electricity.
- Strong electrolytes: ionize fully. Strong acids, strong bases, soluble salts. Solution conducts well.
- Weak electrolytes: ionize partially. Weak acids, weak bases. Solution conducts weakly.
- Non-electrolytes: don't ionize in water. Sugar, alcohol, most molecular organic compounds. Solution does not conduct.
7. pH scale
The pH scale runs from 0 to 14 and measures how acidic or basic a solution is. It is logarithmic: each whole-number change is a factor of 10 in H⁺ concentration.
| pH range | Nature | [H⁺] vs [OH⁻] |
|---|---|---|
| 0 – 6.99 | Acidic | [H⁺] > [OH⁻] |
| 7.00 | Neutral (pure water) | [H⁺] = [OH⁻] |
| 7.01 – 14 | Basic (alkaline) | [H⁺] < [OH⁻] |
Logarithmic = factor-of-10 changes
- pH 5 has 10× more H⁺ than pH 6.
- pH 3 has 100× more H⁺ than pH 5.
- pH 1 has 1,000,000× more H⁺ than pH 7.
The Regents loves to ask this kind of comparison.
Quick examples
- Stomach acid: ~1.5
- Lemon juice: ~2
- Coffee: ~5
- Pure water: 7
- Blood: ~7.4
- Baking soda solution: ~9
- Drain cleaner: ~14
8. Indicators (Reference Table M)
An indicator is a substance that changes color over a specific pH range. Table M lists five and their color-change intervals.
| Indicator | Approx. pH range of change | Color change (acidic → basic) |
|---|---|---|
| Methyl orange | 3.1 – 4.4 | Red → Yellow |
| Bromothymol blue | 6.0 – 7.6 | Yellow → Blue |
| Phenolphthalein | 8.2 – 10 | Colorless → Pink |
| Litmus | ~5 – ~8 | Red → Blue |
| Bromocresol green | 3.8 – 5.4 | Yellow → Blue |
How to read Table M
The pH range is where the color is changing. Below the range, the indicator is its acid color. Above the range, it is its base color. Pick the indicator whose range straddles the expected pH at the endpoint of your titration.
9. Neutralization
When an acid and a base react, they neutralize each other to form water and a salt.
General form: acid + base → salt + water
Example: HCl + NaOH → NaCl + H₂O
Example: H₂SO₄ + 2 KOH → K₂SO₄ + 2 H₂O
At the molecular level, the H⁺ from the acid combines with the OH⁻ from the base to form H₂O. The remaining cation (from the base) and anion (from the acid) form the salt.
Why neutralization happens
H⁺ + OH⁻ → H₂O has a huge driving force. The bond between H⁺ and OH⁻ to form water is energetically very favorable, so acids and bases combine readily when given the chance. Neutralization is exothermic.
10. Titration math
| Formula / quantity | Variables | Units | Notes |
|---|---|---|---|
| MAVA = MBVB (Table T) | M = molarity; V = volume | M in mol/L; V in mL or L (must match) | Valid when mole ratio acid:base is 1:1 |
| Molarity | M = mol solute / L solution | mol/L | Concentration of titrant or analyte |
| Equivalence point | moles H⁺ = moles OH⁻ | — | The stoichiometric point (calculated) |
| Endpoint | indicator color change | — | What you observe — should match equivalence |
| pH at eq. (strong / strong) | — | — | pH = 7 |
| pH at eq. (weak acid / strong base) | — | — | pH > 7 → use phenolphthalein (Table M) |
Titration is a procedure for finding the unknown concentration of an acid or base by reacting it carefully with a solution of known concentration until neutralization.
The titration formula (Reference Table T):
MaVa = MbVb
where Ma = molarity of acid, Va = volume of acid, Mb = molarity of base, Vb = volume of base.
When the formula works as written
MaVa = MbVb directly works only when the acid and base react in a 1:1 ratio (one H⁺ per OH⁻). HCl + NaOH is 1:1; H₂SO₄ + NaOH is 1:2 and needs adjustment. For NYS Regents-level Part B titration problems, 1:1 is almost always assumed. Units must match on both sides (mL and mL, or L and L).
Worked example
What is the molarity of an HCl solution if 25.0 mL is neutralized by 30.0 mL of 0.500 M NaOH?
MaVa = MbVb
(Ma)(25.0 mL) = (0.500 M)(30.0 mL)
Ma = (0.500)(30.0) / 25.0
Ma = 0.600 M HCl
11. Salts
A salt is an ionic compound formed from the cation of a base and the anion of an acid (other than H⁺ and OH⁻). NaCl is the classic example: Na⁺ comes from NaOH and Cl⁻ comes from HCl.
- Many salts are soluble in water and dissociate into ions (electrolytes).
- Some salt solutions are not pH 7. Salts of strong acid + strong base are neutral. Salts of weak acid + strong base are basic. Salts of strong acid + weak base are acidic. This is called hydrolysis.
Key terms
| Arrhenius acid | Substance that releases H⁺ in aqueous solution. |
| Arrhenius base | Substance that releases OH⁻ in aqueous solution. |
| Brønsted-Lowry acid | Proton donor (H⁺ donor). |
| Brønsted-Lowry base | Proton acceptor (H⁺ acceptor). |
| Conjugate acid-base pair | Two species differing by one H⁺. After an acid donates H⁺, the remainder is its conjugate base. |
| pH | −log[H⁺]; scale of 0 to 14 measuring acidity. |
| Indicator | Substance that changes color over a specific pH range (Table M). |
| Neutralization | Acid + base reaction producing salt + water. Exothermic. |
| Titration | Procedure for finding an unknown concentration by careful neutralization. |
| Electrolyte | Substance that produces ions in solution, making it conduct electricity. |
| Strong acid/base | Ionizes completely in water. |
| Weak acid/base | Ionizes only partially in water. |
| Salt | Ionic compound made of the cation of a base and anion of an acid. |
Practice questions
Q1. According to the Brønsted-Lowry theory, an acid is a substance that:
Answer: (1) donates a proton. A Brønsted-Lowry acid is a proton (H⁺) donor. A Brønsted-Lowry base is a proton acceptor. Electron donation/acceptance describes redox chemistry, not acid-base chemistry.
Q2. A solution with a pH of 3 contains how many times more H⁺ ions than a solution with a pH of 6?
Answer: (4) 1000. The pH scale is logarithmic. Each decrease of 1 unit of pH means 10 times more H⁺. Going from pH 6 to pH 3 is a decrease of 3 units, so the H⁺ concentration is 10 × 10 × 10 = 1000 times greater.
Q3. Which equation represents a neutralization reaction?
Answer: (2) HCl + NaOH → NaCl + H₂O. Neutralization is acid + base → salt + water. Option 1 is single replacement. Option 3 is decomposition (electrolysis of water). Option 4 is also decomposition.
Q4. (Part B-2) A student titrates 20.0 mL of an HCl solution with 0.250 M NaOH. It takes 32.0 mL of NaOH to reach the endpoint. (a) Calculate the molarity of the HCl. Show all work and units. (b) Suggest an appropriate indicator from Table M for this titration, and justify your choice.
Sample full-credit response:
(a) Calculation:
Using MaVa = MbVb (from Table T, 1:1 ratio for
HCl + NaOH):
(Ma)(20.0 mL) = (0.250 M)(32.0 mL)
Ma = (0.250 × 32.0) / 20.0
Ma = 0.400 M HCl
(b) Indicator choice: Bromothymol blue is appropriate because it changes
color between pH 6.0 and 7.6, which brackets the endpoint of a strong acid–strong base
titration (pH = 7). Phenolphthalein is also commonly used for this kind of titration; its
color change near pH 8–10 occurs very close to the endpoint with strong acid and strong
base. The choice depends on which color change is easier to see. Methyl orange would not
be appropriate because its range (3.1–4.4) is too acidic; the titration would be stopped
well before neutralization.
Q5. (Part C) Compare strong acids and weak acids in terms of: (a) the meaning of "strong" and "weak," (b) the degree of ionization in water, (c) electrical conductivity of equal-molarity solutions, and (d) pH of equal-molarity solutions. Give one example of each.
Sample full-credit response:
(a) Meaning of strong and weak: Strength refers to how completely an acid
ionizes (dissociates) in water. It is independent of concentration. A 0.001 M strong acid
is still strong; a 12 M weak acid is still weak.
(b) Degree of ionization: A strong acid ionizes essentially 100 percent
in water; nearly every molecule donates its proton. A weak acid ionizes only partially;
most of the molecules remain undissociated in solution, with an equilibrium between the
ionized and un-ionized forms.
(c) Conductivity: At the same molarity, a strong acid solution conducts
electricity much better than a weak acid solution. This is because the strong acid produces
more ions per liter (it is a stronger electrolyte). Conductivity is a direct measure of
free ion concentration.
(d) pH: At the same molarity, a strong acid solution has a lower (more
acidic) pH than a weak acid solution, because it produces more H⁺ ions per liter. For
example, 0.10 M HCl has a pH near 1, while 0.10 M CH₃COOH (a weak acid) has a pH near 2.9.
Examples: Strong acid: HCl (hydrochloric acid). Weak acid: CH₃COOH
(ethanoic acid, vinegar).