Some liquids are acids — they taste sour and can be sharp enough to dissolve metal (lemon juice, vinegar, the acid in your stomach). Others are bases (also called alkalis when they dissolve) — they feel soapy and slippery (baking soda, soap, oven cleaner). In between sit neutral substances like pure water. Chemists capture all of this in a single number from 0 to 14 called pH — and, brilliantly, its steps follow the very same "times ten" pattern as the geometric sequences you did in maths.
The three groups:
- Acids — pH less than 7. Sour taste, react with many metals. Examples: lemon (pH ≈ 2), vinegar (≈ 3), fizzy drinks.
- Neutral — pH exactly 7. Pure water.
- Bases / alkalis — pH more than 7. Soapy, slippery feel. Examples: baking soda (≈ 9), soap (≈ 10), oven cleaner (≈ 14).
An indicator is a substance that changes colour depending on pH — it's how you see whether something is an acid or a base.
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
← more acidic · 7 = neutral · more alkaline →. This is the classic universal-indicator rainbow.
Maths connection — pH is a geometric sequence: The pH scale isn't like a ruler where every step is the same size. Every time pH goes down by 1, the acid gets 10 times stronger. So pH 3 is 10× stronger than pH 4, and 100× stronger than pH 5, and 1000× stronger than pH 6. That "multiply by 10 each step" is a geometric sequence with ratio $r = 10$ — exactly what you built in maths Lesson 09. A scale where each step multiplies (instead of adds) is called a logarithmic scale, and now you've met your first one.
Counting the strength (geometric thinking): to compare two acids, count the pH steps between them and raise 10 to that power:
$$\text{strength ratio} = 10^{\,(\text{difference in pH})}$$
Example: from pH 5 to pH 2 is a difference of 3 steps, so the pH 2 acid is $10^3 = 1000$ times stronger.
🔺 The chemist's trick — what's really happening
In the particle view, an acid is a liquid crowded with special "hydrogen" particles ($\text{H}^+$); the lower the pH, the more of them there are — ten times as many for each step down. A base has almost none. When acid meets base they cancel out. Picture the particles and the number line stops being just a rule to memorise.
Neutralisation — acids and bases cancel: mix an acid and a base in the right amounts and they react to make
neutral water + a salt. The pH moves toward 7. This is why:
- Baking soda (base) soothes an acidic bee sting or acid indigestion.
- Toothpaste (mildly basic) neutralises the acids that attack your teeth.
- Farmers add lime (a base) to soil that is too acidic for crops.
🔬 Try It at home — make your own indicator (red cabbage)
- Chop a little red cabbage, cover with hot water, and leave 10 minutes. The water turns purple — that purple juice is a natural pH indicator. Strain out the cabbage.
- Pour a splash of the purple juice into several clear cups.
- Predict first, then add a different household liquid to each: lemon juice, vinegar, water, baking-soda water, soapy water.
- Watch the colours: acids turn it pink/red, neutral stays purple, bases turn it blue/green. You've built the same rainbow as the pH strip above — from a vegetable.
- Explain: the cabbage contains a dye whose shape (and colour) changes with the number of $\text{H}^+$ particles around it.
Worked Examples
Worked Example 1 — reading pH
Mia tests three liquids from the kitchen. Cola reads pH 3, milk reads pH 7, and hand soap reads pH 10. Classify each, and say which is an acid, which is neutral, which is a base.
Cola pH 3 → below 7 → acid (that's the fizzy carbonic and phosphoric acid).
Milk pH 7 → exactly 7 → neutral (roughly).
Soap pH 10 → above 7 → base (that's why it feels slippery).
Worked Example 2 — "how many times stronger?" (geometric)
Lemon juice is about pH 2. Black coffee is about pH 5. How many times more acidic is the lemon juice?
$$\text{difference} = 5 - 2 = 3 \text{ steps}$$
$$\text{strength ratio} = 10^3 = 1000$$
The lemon juice is 1000 times more acidic than the coffee — because each step down the scale multiplies the strength by 10 (a geometric sequence: 10, 100, 1000).
Warm-Up
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Problem 1
Acid, base, or neutral? (a) pH 1, (b) pH 7, (c) pH 12, (d) pH 6, (e) pH 8.5.
classify each →
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Problem 2
Sort these everyday liquids from most acidic to most alkaline: soap (pH 10), lemon juice (pH 2), pure water (pH 7), vinegar (pH 3), baking soda solution (pH 9).
order low → high pH →
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Problem 3
Mia drops red-cabbage indicator into a mystery liquid and it turns bright pink. Is the liquid an acid or a base? What colour would she expect from soapy water?
use the colour rule →
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Problem 4
Fill in the geometric pattern. Going down the pH scale, each step is ×10 stronger: pH 6 → ×1, pH 5 → ×10, pH 4 → ×____, pH 3 → ×____, pH 2 → ×____.
10, 100, 1000, … →
Core Problems
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Problem 5
Stomach acid is about pH 1. Orange juice is about pH 4. Using $10^{(\text{difference in pH})}$: how many times more acidic is stomach acid than orange juice?
difference $= 4 - 1 = ?$
count steps → 10 to that power →
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Problem 6
A stable's soil is measured at pH 5 (too acidic for good grazing grass). Grass grows best around pH 7. (a) How many pH steps must the soil rise? (b) Each step means the acidity is divided by 10 — by what total factor must the acidity drop to reach pH 7? (c) The farmer adds lime, a base. Explain in one sentence why adding a base raises the pH.
steps → 10^steps → why base raises pH →
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Problem 7
Mia tests rainwater at three cities on her travels and records the pH:
| City | Rain pH |
|---|
| Clean mountain air (Alps) | 6 |
| City with some pollution | 5 |
| Heavily polluted valley | 4 |
(a) Which rain is the most acidic? (b) How many times more acidic is the polluted-valley rain than the Alps rain? (c) "Acid rain" damages stone statues and leaves. Which reading should worry a city most?
compare → 10^(difference) → interpret →
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Problem 8
Mia is stung by a wasp (wasp stings are alkaline, around pH 9). She has two things nearby: vinegar (pH 3, acidic) and baking-soda paste (pH 9, alkaline). (a) Which should she dab on the sting to neutralise it, and why? (b) What does "neutralise" mean in terms of the pH number? (c) In the particle view, what happens to the extra particles when acid meets base?
choose the opposite → define neutralise → particles cancel →
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Problem 9 Challenge
An acid at pH 2 is 100,000 times more acidic than a certain base. (a) Using $10^{(\text{difference})} = 100{,}000$, how many pH steps apart are they? (b) What is the pH of the base? (c) Is your answer an acid, neutral, or a base — does that make sense with the word "base" in the question?
100000 = 10^? → add steps to pH 2 → classify →
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Problem 10 Open
Using only red-cabbage indicator and things in a kitchen, design an experiment to rank five household liquids from most acidic to most alkaline without ever tasting or touching them. Describe how you'd build a colour "key" to read off an approximate pH, what you'd keep the same for a fair test, and one liquid whose result you genuinely can't predict. There's no single right answer — explain your reasoning.
your indicator experiment + colour key →
Show answers
Problem 1
(a) acid · (b) neutral · (c) base · (d) acid (just below 7) · (e) base.
Problem 2
Most acidic → most alkaline: lemon juice (2), vinegar (3), pure water (7), baking soda (9), soap (10).
Problem 3
Pink means it's an acid. Soapy water is a base, so the indicator would turn blue/green.
Problem 4
pH 4 → ×100, pH 3 → ×1000, pH 2 → ×10000. (Each step multiplies by 10: a geometric sequence with $r = 10$.)
Problem 5
Difference $= 4 - 1 = 3$ steps, so $10^3 = 1000$ times more acidic.
Problem 6
(a) 2 steps (from pH 5 to pH 7). (b) $10^2 = 100$ — the acidity must drop to $\tfrac{1}{100}$ of its value. (c) A base cancels acid particles ($\text{H}^+$), so adding it removes acidity and pushes the pH up toward 7.
Problem 7
(a) The polluted valley (pH 4) is most acidic — lowest pH. (b) Difference $= 6 - 4 = 2$ steps → $10^2 = 100$ times more acidic than the Alps rain. (c) The polluted valley (pH 4) — the most acidic rain does the most damage to stone and plants.
Problem 8
(a) Vinegar (acid) — the sting is alkaline, so an acid neutralises it (opposites cancel). (b) "Neutralise" means moving the pH toward 7. (c) The acid's extra $\text{H}^+$ particles react with the base's particles and cancel out, forming water (+ a salt).
Problem 9
(a) $100{,}000 = 10^5$, so 5 steps apart. (b) pH $= 2 + 5 = 7$. (c) pH 7 is neutral, not a base — so the puzzle's wording is a little loose: pure water at pH 7 is $10^5$ times less acidic than a pH 2 acid, but it's neutral rather than a true base. (A real base would need pH above 7, i.e. more than 5 steps.)
Problem 10
Open answer. A strong design: make a colour key first by adding indicator to knowns (lemon = pink acid, water = purple neutral, baking soda = blue base), then add the same amount of indicator to the same volume of each mystery liquid in identical clear cups, and match colours to the key. Keep amount of indicator, volume, cup, and lighting the same. A genuinely uncertain one is fine to name (e.g. milk or fruit juice, which sit close to the middle).
Chemistry arc — off to a strong start! 🧪
You've built the three pillars of chemistry: what matter is (particles), how mixtures come apart (separation), and how substances react (acids & bases). And every step tied back to maths — heating-curve graphs, concentration ratios, and a pH scale that's really a geometric sequence. Next in the arc: atoms, elements, and the periodic table — the "alphabet" all these particles are written in.