Acids, Bases & pH — Reference Sheet

Two Definitions of Acids and Bases

Chemistry uses two definitions side by side. The Arrhenius definition came first and works well for water solutions. The Bronsted-Lowry definition is broader and is the one used for most reaction mechanisms, including reactions that don't involve water at all.

Model	Acid is defined as	Base is defined as	Scope
Arrhenius	A substance that increases [H⁺] (or [H₃O⁺]) when dissolved in water	A substance that increases [OH⁻] when dissolved in water	Aqueous solutions only
Bronsted-Lowry	A proton (H⁺) donor	A proton (H⁺) acceptor	Any solvent, gas phase, non-aqueous reactions

Example: HCl(g) + NH₃(g) → NH₄Cl(s). Neither reactant is in water, so the Arrhenius definition can't even apply here. But HCl is still donating a proton to NH₃, so Bronsted-Lowry calls HCl the acid and NH₃ the base.

Conjugate pairs

Every Bronsted-Lowry acid has a conjugate base (what's left after it donates H⁺), and every base has a conjugate acid (what forms after it accepts H⁺). HF (acid) donates a proton to become F⁻ (its conjugate base). H₂O (base) accepts that proton to become H₃O⁺ (its conjugate acid).

Strong vs. Weak Acids and Bases

"Strong" and "weak" describe how completely a substance ionizes in water, not how concentrated or how corrosive it is. A strong acid dissociates essentially 100%. A weak acid only partially ionizes, leaving most of the molecules intact in an equilibrium with their ions.

Category	Examples	Behavior in water
Strong acids	HCl, HBr, HI, HNO₃, H₂SO₄, HClO₄	Ionize completely: HCl → H⁺ + Cl⁻ (one-way arrow)
Weak acids	CH₃COOH (acetic), HF, HNO₂, H₂CO₃, HCN	Partial equilibrium: CH₃COOH ⇌ H⁺ + CH₃COO⁻
Strong bases	Group 1 hydroxides (LiOH, NaOH, KOH), Ca(OH)₂, Sr(OH)₂, Ba(OH)₂	Ionize completely: NaOH → Na⁺ + OH⁻
Weak bases	NH₃, amines (e.g. CH₃NH₂)	Partial equilibrium: NH₃ + H₂O ⇌ NH₄⁺ + OH⁻

Strong is not the same as concentrated

A concentrated weak acid can have a higher [H⁺] than a dilute strong acid, but "strong" only describes the fraction that ionizes. 12 M acetic acid (weak) is still mostly molecular CH₃COOH at equilibrium, yet its [H⁺] (about 0.015 M) beats that of 0.001 M HCl (strong), which is 100% ionized but only 0.001 M. Don't confuse strong/weak with concentrated/dilute — they're independent properties.

The pH and pOH Scale

pH measures how acidic or basic a water solution is, on a scale that (at 25°C) usually runs from 0 to 14. Because the scale is logarithmic, each whole-number step is a 10× change in [H⁺]. A solution of pH 3 has 10 times more H⁺ than pH 4, and 100 times more than pH 5.

pH range	Classification	[H⁺] vs [OH⁻]
pH < 7	Acidic	[H⁺] > [OH⁻]
pH = 7	Neutral (pure water, 25°C)	[H⁺] = [OH⁻] = 1.0 × 10⁻⁷ M
pH > 7	Basic (alkaline)	[H⁺] < [OH⁻]

pH 7 is only neutral at 25°C

Neutral means [H⁺] = [OH⁻], not "pH equals 7" by definition. Water's self-ionization shifts with temperature, so neutral pH drifts slightly off 7 at other temperatures. For a high school course, treat pH 7 = neutral at standard conditions (25°C) unless a problem tells you otherwise.

Calculating pH, pOH, and Kw

The core formulas convert between hydrogen-ion concentration and pH, and between pH and pOH. All three hold at 25°C for dilute aqueous solutions.

Quantity	Formula	Notes
pH	pH = −log[H⁺]	[H⁺] in mol/L
[H⁺] from pH	[H⁺] = 10⁻ᵖᴴ	Inverse of the pH formula
pOH	pOH = −log[OH⁻]	[OH⁻] in mol/L
pH + pOH	pH + pOH = 14.00	At 25°C only
Kw (water's ion-product constant)	Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴	At 25°C; use this if you're given one concentration and need the other

Worked example: a solution has [H⁺] = 2.5 × 10⁻⁵ M. pH = −log(2.5 × 10⁻⁵) = 4.60. Since pH < 7, the solution is acidic. Its pOH = 14.00 − 4.60 = 9.40.

Sig figs in log math

For pH and pOH, only the digits AFTER the decimal point count as significant figures — they come from the mantissa of the log, not the exponent. [H⁺] = 2.5 × 10⁻⁵ M (2 sig figs) gives pH = 4.60 (2 decimal places, not 2 total digits). Reporting pH = 4.6021... overstates your precision.

Neutralization Reactions

When an acid and a base react, the H⁺ from the acid combines with the OH⁻ from the base to form water, and the leftover ions combine into a salt. The general pattern is: acid + base → salt + water.

Example 1 (monoprotic): HCl + NaOH → NaCl + H₂O Example 2 (needs balancing): H₂SO₄ + Ca(OH)₂ → CaSO₄ + 2 H₂O — the 2 in front of H₂O balances the 2 OH⁻ groups Ca(OH)₂ provides.

Quantity	Formula	Use
Titration (monoprotic acid + monoprotic base)	MₐVₐ = M_bV_b	Find an unknown concentration or volume at the equivalence point
Titration (general)	MₐVₐnₐ = M_bV_bn_b	n = number of acidic H⁺ or basic OH⁻ per formula unit (e.g. n = 2 for H₂SO₄)

Worked example: 25.0 mL of HCl is exactly neutralized by 30.0 mL of 0.100 M NaOH. Find the HCl concentration. MₐVₐ = M_bV_b → Mₐ(25.0 mL) = (0.100 M)(30.0 mL) → Mₐ = 0.120 M.

The equivalence point vs. the endpoint

The equivalence point is where moles of acid exactly equal moles of base (by stoichiometry). The endpoint is where the indicator visibly changes color during a titration. A well-chosen indicator makes these nearly identical, but they aren't defined the same way — don't use the words interchangeably on a lab report.

Common Acid-Base Indicators

An indicator is a weak acid or base whose molecular form and ionized form are different colors. Which color you see depends on the pH of the solution relative to the indicator's transition range.

Indicator	Color (acidic)	Color (basic)	Approximate transition pH range
Litmus	Red	Blue	4.5 – 8.3
Phenolphthalein	Colorless	Pink/magenta	8.2 – 10.0
Methyl orange	Red	Yellow	3.1 – 4.4
Bromothymol blue	Yellow	Blue	6.0 – 7.6
Universal indicator	Red (low pH) through green (neutral) to purple (high pH)	—	0 – 14 (full range)

Picking an indicator for a titration

Choose an indicator whose color-change range brackets the expected equivalence-point pH, not necessarily pH 7. A strong-acid/weak-base titration has an acidic equivalence point (below 7), so methyl orange works better there than phenolphthalein.

Try It Yourself

Download ph-lab-samples.csvph-lab-samples.csv

Eight solution samples, each with a measured hydrogen-ion or hydroxide-ion concentration, so you can practice both directions of the pH / pOH / Kw math on this sheet.

Open it in Google Sheets or Excel

The concentration column uses scientific notation like 2.5e-3, which spreadsheets read correctly as 2.5 × 10⁻³. You'll also need a calculator with a log button, or a spreadsheet's LOG10 function, since pH = −log[H⁺].

1. A solution has [H⁺] = 1.0 × 10⁻⁴ M. What is its pH, and is it acidic, basic, or neutral? 2. A solution has a pH of 9.00. What is [H⁺], and what is [OH⁻]? 3. Write the balanced neutralization equation for phosphoric acid (H₃PO₄) reacting with sodium hydroxide (NaOH) to form water and a salt. Using ph-lab-samples.csv: 4. For each sample, find the pH. If a row lists [OH⁻] instead of [H⁺], find pOH first (pOH = −log[OH⁻]), then use pH + pOH = 14.00 to get pH. Round every pH and pOH to 2 decimal places. 5. Classify each sample as acidic, basic, or neutral from your pH values. 6. Rank all 8 samples from most acidic (lowest pH) to most basic (highest pH). 7. For the ammonia cleaner sample (S7), use Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ to calculate [H⁺]. Round your answer to 2 significant figures.