E. Solutions and Solubility · Solutions and SolubilityArrhenius Acids and Bases, Hydronium and pH
E3.5 E2.1 A2.2About 70 minutes
Learning goals- I can state the Arrhenius definitions of acids and bases and give examples.
- I can explain the modified Arrhenius theory, using the hydronium ion (H₃O⁺) and bases such as ammonia that react with water.
- I can write equations for the ionization of acids and the reactions of bases with water.
- I can calculate pH from [H₃O⁺] and [H₃O⁺] from pH, with correct significant digits.
Words to know
Arrhenius acid
A substance that produces hydrogen ions (H⁺, more accurately H₃O⁺) in aqueous solution.
Arrhenius base
A substance that produces hydroxide ions (OH⁻) in aqueous solution.
hydronium ion (H₃O⁺)
A water molecule bonded to a hydrogen ion; the form H⁺ takes in water.
modified Arrhenius theory
Acids react with water to form H₃O⁺(aq); bases react with water (or dissociate) to form OH⁻(aq).
pH
pH = −log[H₃O⁺]. Below 7 is acidic, 7 is neutral, above 7 is basic (at 25 °C).
monoprotic / polyprotic acid
An acid that can donate one H⁺ per molecule (HCl) or more than one (H₂SO₄, H₃PO₄).
Sour, slippery and the ions behind them
Lemon juice and vinegar taste sour; soap and drain cleaner feel slippery. In Grade 10 you explained acids with H⁺ ions and bases with OH⁻ ions, used the pH scale, and neutralized acids with bases. This lesson gives that idea a name (the Arrhenius theory), fixes two problems with it, and makes pH a number you can calculate.
Remember from Grades 9 and 10
Acids turn blue litmus red, have pH < 7, react with active metals to produce hydrogen gas and with carbonates to produce CO₂. Bases turn red litmus blue, have pH > 7, and feel slippery. Each pH unit is a factor of 10. Acid + base → salt + water (neutralization). Safety: never taste or touch lab chemicals to test them.
The Arrhenius theory (1887)
The Swedish chemist Svante Arrhenius proposed that some substances break into ions in water (the dissociation and ionization you studied earlier in this unit). He used this to define:
- An acid produces hydrogen ions, H⁺(aq), in water: HCl(aq) → H⁺(aq) + Cl⁻(aq)
- A base produces hydroxide ions, OH⁻(aq), in water: NaOH(s) → Na⁺(aq) + OH⁻(aq)
- Neutralization is H⁺(aq) + OH⁻(aq) → H₂O(l)
His idea was controversial at first, but it explained the conductivity of acid and base solutions and the heat of neutralization, and in 1903 he received the Nobel Prize in Chemistry for his theory of electrolytic dissociation.
Two problems, and the fix
Problem 1: H⁺ is just a proton. A hydrogen atom that loses its only electron is a bare proton, far too reactive to drift around alone. In water it bonds to a lone pair on a water molecule, forming the hydronium ion, H₃O⁺. So acids actually react with water:
HCl(g) + H₂O(l) → H₃O⁺(aq) + Cl⁻(aq)
Problem 2: some bases contain no OH⁻. Ammonia (NH₃) and sodium carbonate make solutions basic even though their formulas have no hydroxide. They react with water to make OH⁻:
NH₃(g) + H₂O(l) ⇌ NH₄⁺(aq) + OH⁻(aq)
CO₃²⁻(aq) + H₂O(l) ⇌ HCO₃⁻(aq) + OH⁻(aq)
(The double arrow ⇌ means the reaction goes only partly; you will see why in the next lesson.)
This updated version is called the modified Arrhenius theory: an acid reacts with water to produce H₃O⁺(aq); a base dissociates or reacts with water to produce OH⁻(aq). Chemists often still write H⁺(aq) as a shorthand for H₃O⁺(aq). In SCH4U you will meet an even broader definition (Brønsted-Lowry).
Acids with more than one hydrogen
HCl and HNO₃ give one H⁺ per molecule: they are monoprotic. Sulfuric acid (H₂SO₄) is diprotic and phosphoric acid (H₃PO₄) is triprotic; they ionize one hydrogen at a time:
H₂SO₄(aq) + H₂O(l) → H₃O⁺(aq) + HSO₄⁻(aq), then HSO₄⁻(aq) + H₂O(l) ⇌ H₃O⁺(aq) + SO₄²⁻(aq)
Only the hydrogens written first in the formula are acidic. Acetic acid, CH₃COOH, is monoprotic: only the H on the O (written last) is released, forming the acetate ion, CH₃COO⁻.
Water itself: neutral
Even pure water contains a tiny number of ions, because water molecules sometimes react with each other:
2 H₂O(l) ⇌ H₃O⁺(aq) + OH⁻(aq)
In pure water at 25 °C, [H₃O⁺] = [OH⁻] = 1.0 × 10⁻⁷ mol/L. A solution is neutral when these are equal, acidic when [H₃O⁺] is larger, and basic when [OH⁻] is larger.
Calculating pH
pH = −log[H₃O⁺] and, going backwards, [H₃O⁺] = 10⁻ᵖᴴ
On a scientific calculator: for pH, press (−), log, then type the concentration. For [H₃O⁺], press 10ˣ (often SHIFT + log) and enter the negative pH.
Significant digits in pH: the number of decimal places in a pH equals the number of significant digits in [H₃O⁺]. For [H₃O⁺] = 0.010 mol/L (two significant digits), pH = 2.00 (two decimal places).
Worked exampleExample 1: pH from concentration
Find the pH of (a) 0.010 mol/L HCl(aq), (b) 0.0025 mol/L HNO₃(aq). Both acids ionize completely, so [H₃O⁺] equals the acid concentration.
- (a) [H₃O⁺] = 0.010 mol/L. pH = −log(0.010) = 2.00. Two significant digits → two decimal places: pH = 2.00.
- (b) [H₃O⁺] = 0.0025 mol/L. pH = −log(0.0025) = 2.602… Two significant digits: pH = 2.60.
Worked exampleExample 2: Concentration from pH
In the 1980s, acid rain in eastern Canada often had a pH in the low 4s, for example 4.25. Unpolluted rain has a pH of about 5.6 (it is naturally slightly acidic because of dissolved carbon dioxide). (a) Find [H₃O⁺] in each. (b) How many times more acidic was the acid rain?
- (a) [H₃O⁺] = 10⁻⁴·²⁵ = 5.6 × 10⁻⁵ mol/L (pH has 2 decimal places → 2 significant digits).
- Clean rain: [H₃O⁺] = 10⁻⁵·⁶ = 3 × 10⁻⁶ mol/L (one decimal place → one significant digit; 2.5 × 10⁻⁶ before rounding).
- (b) Ratio = 10⁻⁴·²⁵ ÷ 10⁻⁵·⁶ = 10¹·³⁵ ≈ 22 times more hydronium.
About 22 times more acidic.
Just for funSome people say the "p" in pH stands for "power" (as in power of ten) and others say "potential." Chemists have argued about it for over a century, which proves that even scientists can be a little acidic sometimes.
Hands-on activityMake a red cabbage pH scale
You need: ¼ of a red cabbage, a pot, water, a sieve, 6 clear glasses, and test liquids: lemon juice, white vinegar, tap water, baking soda dissolved in water, a few drops of dish soap in water, and clear carbonated water. A grown-up does the chopping and boiling.
- A grown-up chops the cabbage, simmers it in about 500 mL of water for 10 minutes, cools it and strains it. The purple liquid is your indicator.
- Put about 50 mL of indicator in each glass. Add a tablespoon of a different test liquid to each. Label the glasses.
- Line them up from most red/pink (acidic) to green/yellow (most basic). Purple is near neutral.
- For each acid, write the equation for its reaction with water, e.g. CH₃COOH(aq) + H₂O(l) ⇌ H₃O⁺(aq) + CH₃COO⁻(aq).
- For baking soda, explain why it is basic using the modified Arrhenius theory (HCO₃⁻ reacts with water to form OH⁻).
What to look for: lemon juice and vinegar turn pink-red, carbonated water turns slightly pink, tap water stays purple or blue-purple, baking soda turns blue-green. You made red cabbage indicator in an earlier grade; this time the focus is explaining each colour with H₃O⁺ and OH⁻. Do not use drain cleaner or bleach, and never mix cleaning products.
Your turn
1State the original Arrhenius definitions of an acid and a base.
Acid: produces H⁺(aq) in water. Base: produces OH⁻(aq) in water.
2Write the equation for nitric acid reacting with water to form hydronium.
HNO₃(aq) + H₂O(l) → H₃O⁺(aq) + NO₃⁻(aq)
3Ammonia has no OH⁻ in its formula. Explain, with an equation, why it is a base.
It reacts with water to produce OH⁻: NH₃(g) + H₂O(l) ⇌ NH₄⁺(aq) + OH⁻(aq).
4Find the pH of 0.15 mol/L HCl.
5Find [H₃O⁺] for a solution with pH 2.40.
10⁻²·⁴⁰ = 4.0 × 10⁻³ mol/L.
6A lake has pH 6.80. Is it acidic, neutral or basic? Find [H₃O⁺].
Slightly acidic (below 7). [H₃O⁺] = 10⁻⁶·⁸⁰ = 1.6 × 10⁻⁷ mol/L.
7Which hydrogen in acetic acid, CH₃COOH, is acidic?
The H written last, bonded to oxygen (in –COOH). The three H atoms on carbon are not released.
More practice: warm-up
1What is the formula of the hydronium ion?
2[H₃O⁺] = 1.0 × 10⁻³ mol/L. pH?
3What are [H₃O⁺] and [OH⁻] in pure water at 25 °C?
4Is H₂SO₄ monoprotic or diprotic?
5Who proposed the original theory of acids and bases based on ions in water?
More practice: on your own
1Find the pH of 0.50 mol/L HBr (a strong acid).
2A soft drink has pH 3.50 and orange juice has pH 3.80. Which is more acidic, and by what factor?
The soft drink, by 10^(3.80 − 3.50) = 10^0.30 ≈ 2.0 times.
3Explain why a solution of sodium carbonate is basic.
Carbonate ions react with water to form OH⁻: CO₃²⁻(aq) + H₂O(l) ⇌ HCO₃⁻(aq) + OH⁻(aq), so [OH⁻] > [H₃O⁺].
4Explain what was wrong with writing H⁺(aq) in the original theory, and how the modified theory fixes it.
H⁺ is a bare proton and cannot exist alone in water; it bonds to a water molecule. The modified theory writes it as H₃O⁺(aq), formed when an acid reacts with water.
5A 0.020 mol/L H₂SO₄ solution is assumed (for this question) to release both hydrogens completely. Estimate its pH.
[H₃O⁺] ≈ 2 × 0.020 = 0.040 mol/L; pH ≈ −log(0.040) = 1.40. (In reality the second ionization is incomplete, so the true pH is a little higher.)
Challenge
110.0 mL of 0.10 mol/L HCl is diluted to 1.00 L. Find the new pH and explain why diluting an acid raises its pH.
c₂ = (0.10)(10.0 mL) ÷ 1000 mL = 0.0010 mol/L; pH = 3.00 (up from 1.00). Dilution lowers [H₃O⁺], and lower [H₃O⁺] means higher pH.
2Extension (SCH4U preview): at 25 °C, [H₃O⁺] × [OH⁻] = 1.0 × 10⁻¹⁴. Find [H₃O⁺] and the pH of 0.010 mol/L NaOH.
[OH⁻] = 0.010; [H₃O⁺] = 1.0 × 10⁻¹⁴ ÷ 0.010 = 1.0 × 10⁻¹² mol/L; pH = 12.00.
3Could a solution have a pH below 0? Explain using the definition.
Yes. If [H₃O⁺] is greater than 1 mol/L (e.g. 2.0 mol/L HCl), pH = −log(2.0) = −0.30. The 0 to 14 range covers most solutions but is not a strict limit.
Quiz
1. According to the modified Arrhenius theory, an acid
3. The pH of 0.0010 mol/L HCl is
4. A solution has pH 9. It is
5. pH 2 has how many times more H₃O⁺ than pH 5?
Big idea (E3.5): acids produce H₃O⁺ and bases produce OH⁻ in water; pH = −log[H₃O⁺] measures acidity.
How to help: Ask your teen to explain why baking soda or ammonia is basic even though neither 'has OH'. Practise the calculator steps for pH together, and check the rule 'decimal places in pH = significant digits in concentration'.
Common difficulties:
- Forgetting the negative sign in pH = −log[H₃O⁺].
- Thinking a bigger pH means more acidic (it is the opposite).
- Treating the H atoms on carbon in acetic acid as acidic.
- Calculator entry errors with 10ˣ.
Safety: a grown-up should cut and boil the cabbage. Do not use strong cleaners (drain cleaner, oven cleaner, bleach) for testing, and never mix cleaning products.