pH Scale Explained: How to Calculate pH from H+ Concentration

Quick answer: pH measures how many hydrogen ions are in a solution, using the formula pH = -log10[H+]. Below 7 is acidic, exactly 7 is neutral at 25 degrees C, and above 7 is alkaline. Because it is a logarithmic scale, every whole pH unit is a tenfold change, so pH 3 holds ten times more H+ than pH 4.

I lost marks here for an embarrassingly simple reason: I thought "strong acid" and "concentrated acid" meant the same thing. They do not, and one question built on that difference cost me four marks in a mock. Since then I have treated pH as a maths topic that happens to live in chemistry, because once you can run the log calculation both ways, acids and bases stops being vocabulary and starts being something you work out.

Acids and bases: use the proton definition

An acid is a proton (H+) donor and a base is a proton acceptor. That is the Bronsted-Lowry definition, and it is the only one worth carrying around.

When hydrogen chloride dissolves in water:

HCl + H2O -> H3O+ + Cl-

HCl donates a proton, so it is the acid. Water accepts it, so water is the base. What is left behind matters too: Cl- is the conjugate base of HCl, and H3O+ is the conjugate acid of water. A conjugate pair always differs by exactly one H+ — the fastest way to check your pairing.

Water flips roles depending on what it meets. With ammonia, NH3 + H2O -> NH4+ + OH-, water donates the proton, so here water is the acid. A substance that can do both is amphoteric — that word alone is worth a mark. At GCSE and CBSE level you can shortcut this to "an acid releases H+ ions in water", but Cambridge International A-Level and AP Chemistry ask for conjugate pairs by name.

The pH scale is logarithmic, and that changes your answers

pH is not a linear ranking. Each whole unit is a factor of ten in hydrogen ion concentration, so lemon juice at pH 2 does not have slightly more acid than black coffee at pH 5 — it has 10 x 10 x 10 = 1000 times the H+ concentration. Whenever a question asks "how many times more acidic", the answer is 10 raised to the difference in pH.

Two things students get told wrong:

• The scale does not stop at 0 and 14. A 2 mol/dm3 solution of hydrochloric acid gives pH = -log10(2) = -0.30. Negative pH is real.
• Neutral means [H+] equals [OH-], not "exactly 7". pH 7 is neutral only at 25 degrees C.

Worked example: calculating pH in both directions

Here is the method I use every time.

Example A: find the pH of 0.050 mol/dm3 hydrochloric acid.

1. Decide strong or weak. HCl is strong, so it dissociates completely.
2. Count protons per molecule. HCl is monoprotic, so one H+.
3. Therefore [H+] = 0.050 mol/dm3.
4. pH = -log10(0.050) = 1.30.

Example B: go backwards. A solution has pH 2.70, so find [H+]. Rearrange to [H+] = 10^(-pH), giving 10^(-2.70) = 2.0 x 10^-3 mol/dm3. On a calculator that is the shift-log or 10^x button, not the log button.

Example C: the sulfuric acid trap. Find the pH of 0.050 mol/dm3 sulfuric acid. H2SO4 is diprotic, so you take two H+ per molecule. [H+] = 2 x 0.050 = 0.100 mol/dm3, and pH = -log10(0.100) = 1.00. Skip step 2 and you write 1.30 and lose the mark.

Example D: what dilution does. Dilute that 0.050 mol/dm3 HCl ten times to 0.0050 mol/dm3. pH = -log10(0.0050) = 2.30, so the pH rose by exactly 1.00. Dilute a hundredfold and it rises by exactly 2 — a free sanity check on any dilution question.

Two habits worth building. Give pH to two decimal places, since that is what mark schemes expect. And check your calculator is on log base 10, not ln, which quietly turns 1.30 into 3.00. If a calculation will not come out, put the numbers into our step-by-step explainer and ask for the rearrangement, not the answer.

Strong versus weak is not concentrated versus dilute

Strong and weak describe how completely an acid ionises. Concentrated and dilute describe how much acid there is per unit volume. They are independent, and confusing them is the commonest error in this topic.

A strong acid ionises fully, so it takes a one-way arrow: HCl -> H+ + Cl-. A weak acid sets up an equilibrium, so CH3COOH is in equilibrium with H+ + CH3COO-, and only about one molecule in a hundred has given up its proton at any moment.

The numbers make it obvious. For 0.10 mol/dm3 hydrochloric acid, [H+] = 0.10 and pH = 1.00. For 0.10 mol/dm3 ethanoic acid, with Ka = 1.7 x 10^-5, use [H+] = sqrt(Ka x concentration) = sqrt(1.7 x 10^-5 x 0.10) = 1.3 x 10^-3 mol/dm3, giving pH = 2.88. Identical concentration, pH nearly two units apart, purely because of dissociation.

Mark-scheme wording matters. Write "partially dissociates", and add "the position of equilibrium lies to the left" if you can. Saying a weak acid "does not dissolve well" scores zero, because dissolving and dissociating are different things.

Finding the pH of an alkali

You cannot put an alkali's concentration straight into the pH formula, because it needs H+ and you have been given OH-. Route it through the ionic product of water:

Kw = [H+][OH-] = 1.0 x 10^-14 at 25 degrees C

Worked example: find the pH of 0.10 mol/dm3 sodium hydroxide. NaOH is a strong base, so [OH-] = 0.10. Rearranging Kw gives [H+] = (1.0 x 10^-14) / 0.10 = 1.0 x 10^-13 mol/dm3, so pH = 13.00.

The shortcut: pOH = -log10(0.10) = 1.00, and since pH + pOH = 14, pH = 13.00.

Built-in check: if an alkali comes out below pH 7, you skipped the Kw step and fed [OH-] into the acid formula. Sodium hydroxide is never pH 1.

Measuring pH without losing practical marks

Universal indicator gives an approximate whole-number pH from a colour chart. A pH probe gives a number to one or two decimal places, which is why it is the right answer whenever a question asks how to improve accuracy.

For titrations, universal indicator is wrong because it changes colour gradually across a wide range, so there is no sharp end point. You need one indicator whose colour change falls inside the vertical part of the titration curve:

• Strong acid with strong alkali: methyl orange or phenolphthalein both work.
• Weak acid with strong alkali: phenolphthalein, changing between pH 8.3 and 10.
• Strong acid with weak alkali: methyl orange, changing between pH 3.1 and 4.4.
• Weak acid with weak alkali: no indicator is suitable, so use a pH probe.

Methyl orange is red in acid and yellow in alkali. Phenolphthalein is colourless in acid and pink in alkali. I keep these four lines as a deck on flashcards because they appear in almost every practical paper.

Test yourself

1. Calculate the pH of 0.020 mol/dm3 nitric acid, to two decimal places.
2. A solution has pH 11.40. Calculate [H+] and [OH-] at 25 degrees C.
3. Explain why 0.10 mol/dm3 hydrochloric acid has a lower pH than ethanoic acid at the same concentration.

Quick answers:

1. Nitric acid is strong and monoprotic, so [H+] = 0.020 and pH = -log10(0.020) = 1.70.
2. [H+] = 10^(-11.40) = 4.0 x 10^-12, so [OH-] = (1.0 x 10^-14) / (4.0 x 10^-12) = 2.5 x 10^-3 mol/dm3. Check it with pOH = 14 - 11.40 = 2.60.
3. Hydrochloric acid dissociates completely, so [H+] is the full 0.10 mol/dm3. Ethanoic acid only partially dissociates, so its [H+] is lower and its pH higher.

If those felt slow, generate a set on quiz or work through more calculations on the chemistry hub.

FAQ

Can pH really be negative or above 14?

Yes. Hydrochloric acid at 2 mol/dm3 gives pH -0.30, and concentrated sodium hydroxide can exceed 14. The 0 to 14 range is a convention covering dilute school-lab solutions, not a limit in the maths.

Why is pure water only pH 7 at 25 degrees C?

Because Kw changes with temperature. Heat water and it self-ionises more, so [H+] rises and pH falls below 7. It is still neutral, because [H+] and [OH-] remain equal. Neutral means equal concentrations, not the number 7.

Do I need logarithms for GCSE and CBSE chemistry?

Generally no. AQA, Edexcel, OCR and CBSE mostly want acidic, neutral or alkaline, the tenfold rule and indicator colours. The log calculations, Ka and Kw belong to Cambridge International A-Level and AP Chemistry.

Why does diluting an acid never push it past pH 7?

Each tenfold dilution adds 1 to the pH, but you are only removing H+, never adding OH-. As you approach pH 7 the water's own ionisation takes over and holds the value there. Dilution gets you close to neutral, never alkaline.

In short: pH = -log10[H+], every unit is a factor of ten, and the reverse is [H+] = 10^(-pH). Check whether the acid is strong or weak before you touch the formula, count the protons each molecule releases, and route any alkali through Kw before you take a log. Get those three checks in order and pH becomes some of the most reliable marks on the paper.