Lesson 1 · The Mole

🔢 The Mole & Avogadro's Number

Chemists count atoms the way bakers count eggs — by the dozen. Only the chemist's "dozen" is enormous, and it is called the mole.

💡 Why we need the mole

A single drop of water contains more molecules than there are stars in the observable universe. Counting them one at a time is hopeless, so chemists count them in piles of 6.02 × 10²³.

That number is Avogadro's number (N_A), and one pile of it is one mole (mol). A mole is simply a unit for amount of substance — a counting word, exactly like "dozen" or "pair".

1 mol = 6.02 × 10²³ particles

Those particles can be atoms, molecules, ions, or formula units — whichever particle the substance is made of.

A dozen is 12. A mole is 602,000,000,000,000,000,000,000. The mole is just the chemist's dozen, scaled up to where single atoms matter.

⚖️ Molar mass: the bridge between grams and moles

The molar mass of a substance is the mass of exactly one mole of it, measured in grams per mole (g/mol). For any element, the molar mass in g/mol is numerically the same as its atomic mass on the periodic table.

Carbon: atomic mass 12.01 amu → molar mass 12.01 g/mol Water: H₂O = 2(1.01) + 16.00 → molar mass 18.02 g/mol

Molar mass is the conversion factor that lets you jump between the microscopic world of particles and the macroscopic world of the balance.

moles = mass (g) ÷ molar mass (g/mol) mass (g) = moles × molar mass (g/mol)

Every arrow is just a multiplication or a division — no chemistry required.

📝 Worked examples

Example 1 — grams to moles

How many moles are in 36.0 g of water (molar mass 18.0 g/mol)?

moles = 36.0 g ÷ 18.0 g/mol = 2.00 mol

Example 2 — moles to grams

What is the mass of 3.00 mol of carbon dioxide, CO₂ (44.0 g/mol)?

mass = 3.00 mol × 44.0 g/mol = 132 g

Example 3 — moles to particles

How many molecules are in 2.00 mol of methane?

2.00 mol × 6.02 × 10²³ molecules/mol = 1.20 × 10²⁴ molecules

Salt grains, not sand: a mole of marbles would bury Earth kilometres deep. That is exactly why the mole is useful — it turns unweighable numbers of particles into weighable grams.

📝 Worked examples

Example 1 · Particles ↔ moles

One mole is 6.02 × 10²³ particles. How many moles are 3.01 × 10²³ atoms of carbon?

moles = particles ÷ 6.02 × 10²³ = 3.01 × 10²³ ÷ 6.02 × 10²³ = 0.5 mol

Example 2 · Mass ↔ moles

What is the mass of 0.25 mol of water (H₂O, 18 g/mol)?

mass = moles × molar mass = 0.25 mol × 18 g/mol = 4.5 g

Example 3 · Gas volume at STP

At standard temperature and pressure, one mole of any gas occupies 22.4 L.

3 mol of O₂ at STP → 3 × 22.4 = 67.2 L

🌉 The mole bridge

The mole is the bridge that connects the three things you can count or measure:

mass (g) ⇄ moles ⇄ particles ÷ or × molar mass ÷ or × 6.02 × 10²³

To go from mass to particles you always go through moles first.

Remember: 1 mole of iron atoms and 1 mole of water molecules contain the same number of particles, but they have very different masses.

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What a mole counts

One mole of any substance always contains:

A mole is a counting unit, like a dozen, but much bigger.

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Reading molar mass

Magnesium has an atomic mass of 24.3 amu. Its molar mass is:

Molar mass uses the same number as the atomic mass, in grams per mole.

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How many moles are in 36.0 g of water, H₂O? Use a molar mass of 18.0 g/mol.

moles of H₂O = ?

Enter a number, without units.

mol

moles = mass ÷ molar mass: 36.0 ÷ 18.0.

✍️ Type your answer · 4 of 10

What is the mass of 2.00 mol of carbon dioxide, CO₂? Use a molar mass of 44.0 g/mol.

mass of CO₂ = ?

Enter a number, without units.

g

mass = moles × molar mass: 2.00 × 44.0.

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How many moles are in 66.0 g of carbon dioxide, CO₂ (44.0 g/mol)?

moles of CO₂ = ?

Enter a number, without units.

mol

moles = mass ÷ molar mass: 66.0 ÷ 44.0.

✍️ Type your answer · 6 of 10

A sample contains 0.50 mol of helium atoms. Using 6.02 × 10²³ for Avogadro's number, the number of atoms is written as ___ × 10²³.

What number belongs in the blank?

Enter the number that multiplies 1023, to two significant figures.

× 1023 atoms

Half of 6.02, rounded to two significant figures.

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How many in a mole?

How many particles are in one mole of any substance?

This is called Avogadro's number.

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Same number, different mass

Compare 1 mol of Fe atoms with 1 mol of Al atoms. Which statement is true?

A mole counts particles, not grams.

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Water has a molar mass of 18 g/mol.

How many moles are in 9 g of water?

Enter your answer as a decimal or fraction.

mol

moles = mass ÷ molar mass.

✍️ Type your answer · 10 of 10

Carbon dioxide (CO₂) has a molar mass of 44 g/mol.

What is the mass of 0.5 mol of CO₂?

Enter an exact answer, without rounding.

g

mass = moles × molar mass.

📝 Lesson quiz · 5 questions

Question 1 of 5

How many moles are in 88 g of CO₂ (44 g/mol)?

Question 2 of 5

How many molecules are in 2 mol of any molecular substance?

Question 3 of 5

What volume do 2 mol of gas occupy at STP?

Question 4 of 5

What is the mass of 3 mol of O₂ (32 g/mol)?

Question 5 of 5

Which sample contains the most particles?

Lesson 2 · Molar Mass

⚖️ Molar Mass & Percent Composition

A chemical formula is a recipe, and molar mass is the price list. Add up the atoms and you can weigh out any amount of any compound.

🧮 Calculating molar mass from a formula

To find the molar mass of a compound, multiply each element's molar mass by how many atoms of it appear in the formula, then add everything up.

H₂O: 2(1.01 g/mol) + 1(16.00 g/mol) = 2.02 + 16.00 = 18.02 g/mol CaCO₃: 1(40.08) + 1(12.01) + 3(16.00) = 40.08 + 12.01 + 48.00 = 100.09 g/mol

The little numbers in a formula are subscripts, and they multiply only the element they follow. In CaCO₃ the 3 belongs to the oxygen only — there is exactly one calcium and one carbon.

Watch the brackets. In Al(OH)₃ the subscript 3 outside the bracket multiplies everything inside, giving 3 oxygen atoms and 3 hydrogen atoms.

📊 Percent composition by mass

Percent composition tells you what fraction of a compound's total mass comes from each element. It is the tool you use to identify an unknown sample.

% element = (mass of that element in 1 mol ÷ molar mass of compound) × 100

Work with one mole of the compound. Then the "mass of that element" is just its atomic mass times its subscript.

Worked example — percent hydrogen in water

In 1 mol H₂O: mass of H = 2 × 1.01 = 2.02 g total mass = 18.02 g % H = (2.02 ÷ 18.02) × 100 = 11.2%

Compound	Molar mass	% H	% O
H₂O	18.02 g/mol	11.2%	88.8%
H₂O₂	34.02 g/mol	5.9%	94.1%

Same two elements, completely different composition — which is exactly why percent composition can tell the two apart.

⚖️ Atomic masses you can use

Element	Mass	Element	Mass	Element	Mass
H	1.01	Na	22.99	Cl	35.45
C	12.01	Mg	24.31	Ca	40.08
N	14.01	Al	26.98	Fe	55.85
O	16.00	S	32.07	Cu	63.55

All answers in the practice below are rounded to whole numbers, so 18.02 g/mol rounds to 18 g/mol and 44.01 g/mol rounds to 44 g/mol.

🖼️ See it

Percent by mass = mass of the element ÷ molar mass of the compound × 100.

📝 Worked examples

Example 1 · Molar mass with brackets

Ca(OH)₂ has one Ca, and the bracket doubles the O and the H.

Ca 1 × 40 = 40 O 2 × 16 = 32 H 2 × 1 = 2 Molar mass = 74 g/mol

Example 2 · Percent composition

What percent of water (18 g/mol) is oxygen?

% O = (mass of O ÷ molar mass) × 100 = (16 ÷ 18) × 100 = 88.9%

Example 3 · Check by adding up

For NaCl (58.5 g/mol): Na = 23 ÷ 58.5 = 39.3% and Cl = 35.5 ÷ 58.5 = 60.7%. The percentages should total 100%.

🧭 Steps to remember

Write the formula and count the atoms of each element.
Multiply each atom count by its atomic mass.
Add them to get the molar mass.
For percent composition, divide the part by the whole and multiply by 100.

Brackets: in Al₂(SO₄)₃ the subscript 3 multiplies everything inside the bracket, giving 3 S and 12 O.

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Subscripts and brackets

How many atoms in total are in one formula unit of Ca(OH)₂?

The 2 outside the brackets doubles both O and H. Then add the Ca.

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Reading a percent composition

Water is 11.2% hydrogen by mass. What is the percentage of oxygen?

The two percentages must add up to 100%.

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Calculate the molar mass of calcium carbonate, CaCO₃, using Ca = 40, C = 12, and O = 16 g/mol.

molar mass of CaCO₃ = ?

Enter a whole number, without units.

g/mol

Add 40 + 12 + 3 × 16.

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How many molecules are in 0.50 mol of water? Express your answer as ___ × 10²³ molecules.

What number belongs in the blank?

Use 6.02 × 1023 for Avogadro's number, to two significant figures.

× 1023 molecules

Multiply 0.50 by 6.02.

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How many moles of oxygen atoms are in 117 g of Al(OH)₃? Use Al = 27, O = 16, H = 1 g/mol.

moles of O atoms = ?

First find the moles of Al(OH)3, then multiply by the oxygen subscript.

mol O

Molar mass of Al(OH)₃ is 27 + 3 × 17 = 78. Find the moles, then × 3.

✍️ Type your answer · 6 of 10

What is the percent by mass of hydrogen in methane, CH₄? Use C = 12 and H = 1 g/mol.

% H by mass = ?

Enter a whole-number percent, without the % sign.

%

Hydrogen mass is 4 × 1 = 4 out of a total of 16.

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Molar mass of CO₂

What is the molar mass of CO₂ (C = 12, O = 16)?

One carbon and two oxygens.

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Percent by mass

What is the percent by mass of carbon in CH₄ (C = 12, H = 1)?

Divide the carbon's mass by the molar mass of CH₄.

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Fe₂O₃ has a molar mass of 160 g/mol (Fe = 56).

What is the percent by mass of iron?

Enter an exact answer, without rounding.

%

There are two Fe atoms, so the iron mass is 2 × 56.

✍️ Type your answer · 10 of 10

Calculate the molar mass of Ca(OH)₂ (Ca = 40, O = 16, H = 1).

What is the molar mass?

Enter an exact answer, without rounding.

g/mol

The bracket means two O and two H.

📝 Lesson quiz · 5 questions

Question 1 of 5

What is the molar mass of H₂SO₄ (H = 1, S = 32, O = 16)?

Question 2 of 5

What is the percent by mass of calcium in CaCO₃ (Ca = 40, C = 12, O = 16)?

Question 3 of 5

What is the molar mass of Al₂(SO₄)₃ (Al = 27, S = 32, O = 16)?

Question 4 of 5

How many moles are in 49 g of H₂SO₄ (98 g/mol)?

Question 5 of 5

Which compound has the greatest percent by mass of oxygen?

Lesson 3 · Formulas

📐 Empirical & Molecular Formulas

Percent composition runs in reverse: give a chemist the mass percentages of a mystery compound and they can rebuild the formula from scratch.

🔄 Two kinds of formula

Every compound has both an empirical formula and a molecular formula, and confusing them is the single most common mistake in this unit.

Empirical formula

The simplest whole-number ratio of atoms in a compound. Glucose's empirical formula is CH₂O.

Molecular formula

The actual number of atoms in one molecule. Glucose's molecular formula is C₆H₁₂O₆.

molecular formula = (empirical formula) × n where n = molar mass ÷ empirical formula mass

Different compounds can share an empirical formula. Formaldehyde (CH₂O), acetic acid (C₂H₄O₂), and glucose (C₆H₁₂O₆) all reduce to CH₂O — yet they behave nothing alike.

📏 The four-step method

Given percent composition by mass, follow the same four steps every time.

Step	What you do	Why
1	Assume a 100 g sample, so each percent becomes grams	Percentages turn into weighable masses
2	Divide each mass by that element's molar mass	Converts grams into moles of atoms
3	Divide every result by the smallest one	Makes the smallest value exactly 1
4	If you get .5 or .33 or .25, multiply all by 2, 3, or 4	Formulas must use whole atoms

Step 4 is not optional. A ratio of 1 : 1.5 must become 2 : 3. Never round 1.5 to 2 — that changes the compound completely.

📝 Worked example — hydrogen peroxide

A compound is 5.9% hydrogen and 94.1% oxygen by mass. Find its empirical formula.

Step 1 In 100 g: 5.9 g H, 94.1 g O Step 2 H: 5.9 ÷ 1.01 = 5.84 mol O: 94.1 ÷ 16.00 = 5.88 mol Step 3 Divide by 5.84: H: 5.84 ÷ 5.84 = 1.00 O: 5.88 ÷ 5.84 = 1.01 Step 4 Already whole numbers. Empirical formula: HO

Hydrogen peroxide's molecular formula is H₂O₂ — exactly twice the empirical formula, which is why the percentages alone can never distinguish HO from H₂O₂ until you also weigh the molecule.

Finding the multiplier from molar mass

Empirical formula CH₂O → empirical mass = 12 + 2(1) + 16 = 30 g/mol Experimental molar mass = 180 g/mol n = 180 ÷ 30 = 6 Molecular formula = (CH₂O)₆ = C₆H₁₂O₆

Quick check: if n comes out to 1.9 or 2.1 instead of a clean 2, your molar mass or your arithmetic has drifted. Real exam problems are designed to land on small whole numbers.

🧮 Hydrates: formulas with water attached

Some ionic compounds crystallise with a fixed number of water molecules trapped in the lattice. The dot in the formula shows this.

CuSO₄ · 5H₂O "copper(II) sulfate pentahydrate" Molar mass = [63.55 + 32.07 + 4(16.00)] + 5(18.02) = 159.62 + 90.10 = 249.72 g/mol

The water is part of the formula, so it counts toward the molar mass and the percent composition.

🖼️ See it

If a ratio is 1 : 1.5, multiply both parts by 2 to get whole numbers.

📝 Worked examples

Example 1 · Empirical formula from percentages

A compound is 40.0% C, 6.7% H and 53.3% O. Assume a 100 g sample.

C: 40.0 g ÷ 12 = 3.33 mol H: 6.7 g ÷ 1 = 6.7 mol O: 53.3 g ÷ 16 = 3.33 mol Divide by the smallest (3.33): C 1 : H 2 : O 1 Empirical formula = CH₂O

Example 2 · Molecular formula

The molar mass is 180 g/mol. The empirical formula mass of CH₂O is 30.

n = 180 ÷ 30 = 6 Molecular formula = (CH₂O)₆ = C₆H₁₂O₆

🧭 Quick method

Turn percentages (or masses) into grams, then into moles.
Divide every mole value by the smallest one.
If you get x.5, double everything (for example 1 : 1.5 becomes 2 : 3).
Molecular formula = empirical formula × (molar mass ÷ empirical mass).

Never round too early: a ratio of 1.33 means × 3, not × 1. Look for thirds (1.33, 1.67) and halves (1.5).

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Empirical vs molecular

An empirical formula shows the:

Empirical means the simplest ratio, like CH₂O for glucose.

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Messy mole ratios

A calculation gives a mole ratio of 1 : 1.5. The empirical formula is:

Multiply both sides of the ratio by 2 to get whole numbers.

✍️ Type your answer · 3 of 11

Benzene has the molecular formula C₆H₆. Use C = 12 and H = 1 g/mol.

molar mass of C₆H₆ = ?

Enter a whole number, without units.

g/mol

Add 6 × 12 and 6 × 1.

✍️ Type your answer · 4 of 11

Glucose has the molecular formula C₆H₁₂O₆. Use C = 12, H = 1, and O = 16 g/mol.

molar mass of C₆H₁₂O₆ = ?

Enter a whole number, without units.

g/mol

Add 6 × 12, 12 × 1 and 6 × 16.

✍️ Type your answer · 5 of 11

A 100 g sample of a compound contains 2.5 g of hydrogen. Use H = 1 g/mol.

How many moles of H atoms are in the sample?

Enter a number, without units.

mol H

moles = mass ÷ molar mass: 2.5 ÷ 1.

✍️ Type your answer · 6 of 11

A 100 g sample contains 2.5 g of hydrogen and 35.0 g of nitrogen (the remaining mass is oxygen). Use H = 1 and N = 14 g/mol.

In the empirical formula N_aH_b, what is the value of a? Use only the H and N data.

Find the moles of each, then divide both by the smaller value.

(N subscript)

N: 35.0 ÷ 14 = 2.5 mol. Divide both mole amounts by the smaller one.

✍️ Type your answer · 7 of 11

A compound has the empirical formula CH₂O and an experimental molar mass of 180 g/mol.

What is n, the multiplier applied to the empirical formula? (Use C = 12, H = 1, O = 16 g/mol.)

Enter a whole number.

n

The empirical mass of CH₂O is 30. How many 30s make 180?

✏️ Quick check · 8 of 11

Simplest ratio

What is the empirical formula of C₆H₁₂O₆?

Find the largest number that divides 6, 12 and 6.

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Reduce it

What is the empirical formula of N₂O₄?

Divide both subscripts by their common factor.

✍️ Type your answer · 10 of 11

A compound contains 12 g of carbon and 4 g of hydrogen (C = 12, H = 1).

How many hydrogen atoms are there for each carbon atom?

Enter an exact answer, without rounding.

Convert each mass to moles, then compare.

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The empirical formula is CH₂ (mass 14). The molar mass of the compound is 42 g/mol.

What is n in (CH₂)ₙ?

Enter an exact answer, without rounding.

Divide the molar mass by the empirical mass.

📝 Lesson quiz · 5 questions

Question 1 of 5

What is the empirical formula of C₄H₈?

Question 2 of 5

A compound has empirical formula CH₂O and molar mass 60 g/mol. What is its molecular formula?

Question 3 of 5

A sample has 2 mol of H for every 1 mol of O. What is its empirical formula?

Question 4 of 5

Which of these is already an empirical formula?

Question 5 of 5

Benzene has the empirical formula CH (13 g/mol) and a molar mass of 78 g/mol. What is its molecular formula?

Lesson 4 · Stoichiometry

🧮 Stoichiometry & Limiting Reactants

A balanced equation is a recipe with exact proportions. Stoichiometry is the arithmetic that turns those proportions into grams you can actually weigh.

⚗ The balanced equation is the recipe

Coefficients tell you the ratio in which particles react. The equation below says two hydrogen molecules react with one oxygen molecule to make two water molecules — and that same 2 : 1 : 2 ratio works in moles.

2H₂ + O₂ → 2H₂O

2 molecules H₂ + 1 molecule O₂ → 2 molecules H₂O 2 dozen H₂ + 1 dozen O₂ → 2 dozen H₂O 2 mol H₂ + 1 mol O₂ → 2 mol H₂O

Coefficients count moles, never grams. You cannot read masses straight off a balanced equation — you must convert grams into moles first.

🔄 The only pathway that works

Every stoichiometry problem follows the same three-step road. There is no shortcut that skips the middle.

Never convert grams of A directly to grams of B. The mole ratio only exists between moles, because coefficients count particles, not mass.

📝 Worked example

How many grams of water form when 4.0 g of hydrogen burns in excess oxygen? (H₂ = 2.0, H₂O = 18.0 g/mol)

Equation: 2H₂ + O₂ → 2H₂O Mole ratio: 2 mol H₂ → 2 mol H₂O, so 1 : 1 Step 1 moles H₂ = 4.0 g ÷ 2.0 g/mol = 2.0 mol Step 2 moles H₂O = 2.0 mol H₂ × (2 ÷ 2) = 2.0 mol Step 3 mass H₂O = 2.0 mol × 18.0 g/mol = 36 g

The same three steps work for every reaction, no matter how complicated the equation looks.

🚫 Limiting reactants

In the real world you rarely mix reactants in exactly the right ratio. The reactant that runs out first is the limiting reactant, and it decides how much product you can make. The leftover reactant is in excess.

Limiting reactant

Runs out first. It caps the amount of product and is completely used up.

Excess reactant

Left over when the reaction stops. Some of it never reacts at all.

How to find it

Convert every reactant's mass to moles.
Divide each reactant's moles by its coefficient in the balanced equation.
The smallest result is the limiting reactant.

10 g H₂ (5 mol) + 32 g O₂ (1 mol) Equation: 2H₂ + O₂ → 2H₂O H₂: 5 ÷ 2 = 2.5 O₂: 1 ÷ 1 = 1.0 ← smaller O₂ is limiting; H₂ is in excess. Product is capped by O₂: 1 mol O₂ → 2 mol H₂O = 36 g.

Bigger mass does not mean limiting. Here 10 g of hydrogen is less than 32 g of oxygen, yet oxygen is the one that runs out — you must always compare moles, adjusted by coefficients.

📝 Worked examples

Example 1 · Mole ratios

2H₂ + O₂ → 2H₂O. The coefficients give the mole ratio H₂ : O₂ : H₂O = 2 : 1 : 2.

3 mol H₂ → 3 mol H₂O (ratio 2 : 2) 3 mol H₂ needs 1.5 mol O₂ (ratio 2 : 1)

Example 2 · Mass to mass

How many grams of water form from 4 g of H₂ (2 g/mol)? Water is 18 g/mol.

4 g H₂ ÷ 2 = 2 mol H₂ 2 mol H₂ → 2 mol H₂O 2 mol × 18 g/mol = 36 g H₂O

Example 3 · Limiting reactant

You have 2 mol H₂ and 2 mol O₂. The reaction needs 2 : 1.

2 mol H₂ needs only 1 mol O₂ → O₂ is in excess H₂ runs out first → H₂ is the LIMITING reactant Product: 2 mol H₂O

📌 Percent yield

The theoretical yield is what the maths predicts. The actual yield is what you really collect. Real reactions rarely give 100%.

percent yield = (actual ÷ theoretical) × 100

Always convert to moles before using the ratio. Coefficients compare moles, not grams.

✏️ Quick check · 1 of 11

What coefficients mean

In 2H₂ + O₂ → 2H₂O, the coefficients directly tell you the ratio of:

Coefficients count particles, which is the same as counting moles.

✏️ Quick check · 2 of 11

Finding the limit

The limiting reactant in a reaction is the one that:

Like making sandwiches: whatever runs out first decides how many you can make.

✍️ Type your answer · 3 of 11

Aluminium reacts with hydrochloric acid: 2Al + 6HCl → 2AlCl₃ + 3H₂. You start with 2.0 mol of Al and plenty of acid.

How many moles of H₂ can form?

Use the mole ratio from the balanced equation.

mol H2

2 Al gives 3 H₂, so 2.0 mol Al gives…

✍️ Type your answer · 4 of 11

Propane burns by the equation C₃H₈ + 5O₂ → 3CO₂ + 4H₂O. You burn 1.0 mol of propane in excess oxygen. Use CO₂ = 44 g/mol.

What mass of CO₂ is produced?

Find the moles of CO2 first, then convert to grams.

g CO2

1 mol of propane gives 3 mol of CO₂. Multiply by 44.

✍️ Type your answer · 5 of 11

Heating potassium chlorate decomposes it: 2KClO₃ → 2KCl + 3O₂. A student heats 2.0 mol of KClO₃. Use O₂ = 32 g/mol.

What mass of oxygen gas is released?

Enter a whole number of grams.

g O2

2 mol of KClO₃ gives 3 mol of O₂. Multiply by 32.

✍️ Type your answer · 6 of 11

4.0 g of H₂ (2.0 mol) reacts with 32.0 g of O₂ (1.0 mol): 2H₂ + O₂ → 2H₂O.

How many moles of H₂O form?

Divide each reactant's moles by its coefficient to check which one limits.

mol H2O

Both reactants divide to 1.0, so neither is left over. 2 H₂ gives 2 H₂O.

✍️ Type your answer · 7 of 11

Hydrogen peroxide decomposes: 2H₂O₂ → 2H₂O + O₂. You decompose 34 g of H₂O₂. Use H₂O₂ = 34 g/mol and O₂ = 32 g/mol.

What is the theoretical mass of O₂ produced?

Enter a whole number of grams.

g O2

34 g is 1 mol of H₂O₂, which gives half a mole of O₂.

✏️ Quick check · 8 of 11

Use the ratio

N₂ + 3H₂ → 2NH₃. How many moles of NH₃ form from 3 mol of N₂ (with plenty of H₂)?

Compare the coefficients of N₂ and NH₃.

✏️ Quick check · 9 of 11

Which is limiting?

The limiting reactant is the one that:

Think about which ingredient you run out of first.

✍️ Type your answer · 10 of 11

2H₂ + O₂ → 2H₂O.

How many moles of O₂ are needed to react completely with 4 mol of H₂?

Enter an exact answer, without rounding.

mol O₂

Divide the H₂ moles by 2.

✍️ Type your answer · 11 of 11

The theoretical yield is 10 g and you collect 8 g.

What is the percent yield?

Enter an exact answer, without rounding.

%

Divide actual by theoretical.

📝 Lesson quiz · 5 questions

Question 1 of 5

2Na + Cl₂ → 2NaCl. How many moles of NaCl form from 4 mol of Na?

Question 2 of 5

CH₄ + 2O₂ → CO₂ + 2H₂O. How many moles of O₂ burn 3 mol of CH₄?

Question 3 of 5

You have 5 mol H₂ and 1 mol O₂ for 2H₂ + O₂ → 2H₂O. What is the limiting reactant?

Question 4 of 5

A reaction has a theoretical yield of 25 g and an actual yield of 20 g. What is the percent yield?

Question 5 of 5

C + O₂ → CO₂. How many grams of CO₂ form from 12 g of C (C = 12, CO₂ = 44)?

Lesson 5 · Periodic Table

📊 Periodic Trends & Ion Formation

The periodic table is not a poster to memorise — it is a map that lets you predict how any element will behave before you ever touch it.

🗺 Groups, periods, and valence electrons

The table is arranged by increasing atomic number, and its shape comes directly from electron arrangement. Elements fall into groups (vertical columns) and periods (horizontal rows).

Group (column)

Elements share the same number of valence electrons, so they behave alike chemically.

Period (row)

Elements share the same number of occupied electron shells, so their sizes follow a pattern.

For main-group elements: valence electrons = the group number's last digit

Group	1	2	13	14	15	16	17	18
Valence e⁻	1	2	3	4	5	6	7	8
Ion formed	1+	2+	3+	varies	3−	2−	1−	none

📉 Three trends worth knowing

All three trends come from the same two competing forces: the pull of the nucleus, and the shielding of inner shells.

Trend	Left → right across a period	Top → bottom down a group
Atomic radius	Decreases — the nucleus pulls harder	Increases — more shells added
Ionisation energy	Increases — electrons held tighter	Decreases — outer electrons are far away
Electronegativity	Increases — stronger pull on shared electrons	Decreases — weaker pull on shared electrons

Why radius shrinks across a period: each step adds a proton to the nucleus and an electron to the same outer shell. More pull, no extra shielding — so the whole electron cloud is drawn in tighter.

⚡ How ions form

Atoms react to reach a stable, full outer shell — the octet rule. Metals lose electrons and become positive cations; non-metals gain electrons and become negative anions.

Sodium (group 1, 1 valence e⁻) → loses 1 → Na⁺ Magnesium (group 2, 2 valence e⁻) → loses 2 → Mg²⁺ Oxygen (group 16, 6 valence e⁻) → gains 2 → O²⁻ Chlorine (group 17, 7 valence e⁻) → gains 1 → Cl⁻

Notice the pattern: elements close to a full shell gain electrons; elements with just a few valence electrons lose them. Group 18 already has a full shell, so it barely reacts at all.

Writing formulas by balancing charge

In an ionic compound the total positive charge must equal the total negative charge. That single rule gives you every formula.

Al³⁺ and O²⁻: charge needed: 3+ × 2 = 6+ 2⁻ × 3 = 6⁻ ratio: 2 aluminium ions to 3 oxide ions formula: Al₂O₃ Ca²⁺ and Cl⁻: Ca²⁺ × 1 = 2+ Cl⁻ × 2 = 2⁻ formula: CaCl₂

Naming rule: the metal keeps its name and the non-metal takes an -ide ending. Al₂O₃ is aluminium oxide; CaCl₂ is calcium chloride.

📝 Worked examples

Example 1 · Forming ions

Na (11 p, 11 e⁻) loses 1 e⁻ → Na⁺ (11 p, 10 e⁻) Cl (17 p, 17 e⁻) gains 1 e⁻ → Cl⁻ (17 p, 18 e⁻) O (8 p, 8 e⁻) gains 2 e⁻ → O²⁻ (8 p, 10 e⁻)

Metals tend to lose electrons (forming cations). Non-metals tend to gain electrons (forming anions).

Example 2 · Predict the charge from the group

Group 1 → 1+, Group 2 → 2+, Group 13 → 3+, Group 16 → 2−, Group 17 → 1−.

📈 Trends to know

Down a group

Atomic radius increases. Ionisation energy decreases.

Across a period →

Atomic radius decreases. Ionisation energy increases.

Ions vs. atoms: a cation is smaller than its atom (fewer electrons, but the same number of protons pulling on them). An anion is larger (more electrons repel each other).

✏️ Quick check · 1 of 11

Who forms positive ions?

Which kind of element forms a positive ion (cation)?

Atoms that lose electrons become positive.

✏️ Quick check · 2 of 11

Why atoms shrink

Atomic radius decreases from left to right across a period because:

More protons pull the same shells in tighter.

✍️ Type your answer · 3 of 11

Arsenic sits in group 15 of the periodic table.

How many valence electrons does an arsenic atom have?

For main-group elements, valence electrons = the last digit of the group number.

valence e−

Take the last digit of 15.

✍️ Type your answer · 4 of 11

Oxygen is in group 16, so it has 6 valence electrons.

How many electrons must an oxygen atom gain to reach a full outer shell?

A full outer shell holds 8 electrons.

electrons gained

Take 6 from 8.

✍️ Type your answer · 5 of 11

Aluminium is in group 13.

What is the magnitude of the charge on the ion aluminium forms? (Enter the number only — for Al³⁺ enter 3.)

Metals in group 13 lose three electrons.

charge magnitude

Group 13 has three outer electrons to lose.

✍️ Type your answer · 6 of 11

Calcium (group 2) reacts with chlorine (group 17) to form an ionic compound with the formula CaCl_x.

What is the value of x? (Balance the charges: Ca²⁺ and Cl⁻.)

Enter a whole number.

x

One Ca²⁺ needs enough Cl⁻ ions to cancel a charge of 2+.

✍️ Type your answer · 7 of 11

Aluminium oxide has the formula Al_yO₃. Aluminium forms Al³⁺ and oxygen forms O²⁻.

What is the value of y?

Total positive charge must equal total negative charge.

y

Three O²⁻ ions give 6−. How many Al³⁺ make 6+?

✏️ Quick check · 8 of 11

Predict the ion

Magnesium is in Group 2. What ion does it form?

Metals lose electrons.

✏️ Quick check · 9 of 11

Biggest atom

Which atom has the largest atomic radius?

Look for the element lowest in the same group.

✍️ Type your answer · 10 of 11

A sulfide ion is S²⁻. Sulfur has 16 protons.

How many electrons does S²⁻ have?

Enter an exact answer, without rounding.

A 2− charge means two extra electrons.

✍️ Type your answer · 11 of 11

An aluminium ion is Al³⁺. Aluminium has 13 protons.

How many electrons does Al³⁺ have?

Enter an exact answer, without rounding.

A 3+ charge means three electrons were lost.

📝 Lesson quiz · 5 questions

Question 1 of 5

Which of these has the highest first ionisation energy?

Question 2 of 5

Elements in Group 17 form ions with what charge?

Question 3 of 5

How does the radius of F⁻ compare with a neutral F atom?

Question 4 of 5

Why do elements in the same group behave similarly?

Question 5 of 5

Which alkali metal is most reactive?

Lesson 6 · Bonding

🤝 Bonding, Electronegativity & Shapes

Whether two atoms share, steal, or split electrons comes down to one number — and once you know the shape of a molecule, you can predict almost everything it does.

⚖️ One scale explains every bond

Electronegativity measures how strongly an atom pulls on shared electrons. Fluorine is the champion at 4.0; caesium sits near the bottom at 0.7. Compare the two values and you can classify the bond without any further work.

Electronegativity difference	Bond type	What the electrons do
Less than 0.5	Nonpolar covalent	Shared essentially equally
0.5 to 1.7	Polar covalent	Shared, but pulled toward the more electronegative atom
Greater than 1.7	Ionic	Transferred completely from one atom to the other

H–Cl: 3.2 − 2.2 = 1.0 → polar covalent Na–Cl: 3.2 − 0.9 = 2.3 → ionic Cl–Cl: 3.2 − 3.2 = 0.0 → nonpolar covalent

The scale is a continuum, not a set of boxes. Bonds near the 1.7 boundary show a mix of both behaviours — the categories are a convenience, not a law of nature.

Watch the threshold. H–F has ΔEN = 4.0 − 2.2 = 1.8, which sits just above 1.7. By the rule of thumb you could call it ionic, but H–F is in fact the classic polar covalent bond — electrons shifted far toward fluorine, not handed over. So do not treat 1.7 as a sharp border: H–F is polar covalent, while NaCl at ΔEN = 2.3 really is ionic.

📐 Drawing Lewis structures

A Lewis structure shows valence electrons as dots. Bonding pairs sit between atoms; lone pairs stay on one atom.

The four-step routine

Count the total valence electrons in the molecule.
Put the least electronegative atom in the centre (never hydrogen).
Connect atoms with single bonds, then complete each outer atom's octet.
Place any leftover electrons on the central atom; form double bonds if the centre is short.

Doubles are common, triples are rare. C, N, and O frequently form double bonds. If your structure leaves the central atom short of an octet, convert a lone pair from a neighbouring atom into a second bond.

📏 VSEPR: electrons decide the shape

Electron pairs repel each other, so they spread out as far apart as possible. That single idea — VSEPR — predicts the shape of every molecule once you know how many electron domains surround the central atom.

Domains	Bonds	Lone pairs	Shape	Example
2	2	0	Linear	CO₂, BeCl₂
3	3	0	Trigonal planar	BF₃
4	4	0	Tetrahedral	CH₄
4	3	1	Trigonal pyramidal	NH₃
4	2	2	Bent	H₂O

Count domains, not just bonds. A double bond still counts as one domain. Lone pairs push harder than bonding pairs, which is why water is bent at roughly 104.5° rather than the perfect 109.5° of methane.

🌊 Why shape matters

Shape and bond polarity together decide whether a whole molecule is polar — having a slightly positive end and a slightly negative end.

H₂O: polar bonds + bent shape → the pulls do NOT cancel → polar molecule CO₂: polar bonds + linear shape → the two pulls cancel exactly → nonpolar molecule

This is why water dissolves salts so well, why it has such a high boiling point, and why ice floats. Symmetry can switch polarity off entirely.

Conducts electricity

Ionic compounds when melted or dissolved, because the ions are free to move.

Does not conduct

Solid ionic crystals, and most covalent molecular substances, because nothing is free to carry charge.

📝 Worked examples

Example 1 · Bond type from electronegativity

Electronegativities: H 2.2, C 2.6, N 3.0, O 3.4, Cl 3.2, Na 0.9. Subtract to get ΔEN.

Cl–Cl: 3.2 − 3.2 = 0.0 → nonpolar covalent H–Cl: 3.2 − 2.2 = 1.0 → polar covalent Na–Cl: 3.2 − 0.9 = 2.3 → ionic

Rule of thumb: ΔEN < 0.4 nonpolar, 0.4 to 1.7 polar covalent, > 1.7 ionic.

Example 2 · Molecular shapes (VSEPR)

CO₂ 2 bonds, 0 lone pairs → linear H₂O 2 bonds, 2 lone pairs → bent NH₃ 3 bonds, 1 lone pair → trigonal pyramidal CH₄ 4 bonds, 0 lone pairs → tetrahedral

📌 Shape depends on lone pairs too

Electron pairs (bonding and lone) repel each other and spread out as far as possible. Lone pairs take up space, which is why water is bent rather than linear.

Polar molecule? It needs polar bonds and an asymmetrical shape. CO₂ has polar bonds but is symmetrical and linear, so the pulls cancel and the molecule is nonpolar.

✏️ Quick check · 1 of 11

Classifying a bond

Two atoms have an electronegativity difference of 1.2. The bond between them is:

Below about 0.4 is nonpolar and above about 1.8 is ionic. Where is 1.2?

✏️ Quick check · 2 of 11

Symmetry and polarity

CO₂ is a nonpolar molecule even though each C=O bond is polar. Why?

Two equal pulls in opposite directions cancel out.

✍️ Type your answer · 3 of 11

Hydrogen has an electronegativity of 2.2 and fluorine has 4.0.

What is the electronegativity difference in the H–F bond?

Give the difference to one decimal place.

difference

Subtract: 4.0 − 2.2.

✍️ Type your answer · 4 of 11

Lithium has an electronegativity of 1.0 and chlorine has 3.2.

What is the electronegativity difference in the Li–Cl bond?

Give the difference to one decimal place.

difference

Subtract: 3.2 − 1.0.

✍️ Type your answer · 5 of 11

In carbon dioxide, the central carbon is double-bonded to each oxygen: O=C=O.

How many electron domains surround the central carbon atom?

A double bond counts as one domain.

domains

Count the groups of electrons around carbon: one per double bond.

✍️ Type your answer · 6 of 11

Methane, CH₄, has a central carbon bonded to four hydrogen atoms and no lone pairs on the carbon.

How many electron domains surround the central carbon?

Enter a whole number.

domains

Four bonds, no lone pairs.

✍️ Type your answer · 7 of 11

Ammonia, NH₃, has a central nitrogen with three bonds and one lone pair, giving it a trigonal pyramidal shape.

How many lone pairs are on the central nitrogen atom?

Enter a whole number.

lone pairs

Nitrogen has 5 outer electrons and uses 3 of them in bonds.

✏️ Quick check · 8 of 11

Ionic or covalent?

What type of bond forms between sodium (0.9) and chlorine (3.2)?

Subtract the electronegativities.

✏️ Quick check · 9 of 11

Name the shape

What is the shape of a methane (CH₄) molecule?

Count bonding pairs and lone pairs on carbon.

✍️ Type your answer · 10 of 11

Carbon is 2.6 and oxygen is 3.4.

What is the electronegativity difference for a C–O bond?

Enter an exact answer, without rounding.

Subtract the smaller from the larger.

✍️ Type your answer · 11 of 11

The central oxygen in H₂O has 2 bonds and some lone pairs. Oxygen has 6 valence electrons.

How many lone pairs does oxygen have in H₂O?

Enter an exact answer, without rounding.

6 valence electrons − 2 used in bonds = 4 left over. Each pair is 2 electrons.

📝 Lesson quiz · 5 questions

Question 1 of 5

What type of bond is O–H (O 3.4, H 2.2)?

Question 2 of 5

What is the shape of H₂O?

Question 3 of 5

What is the shape of CO₂?

Question 4 of 5

Which molecule is nonpolar?

Question 5 of 5

What is the shape of NH₃?

Lesson 7 · Solutions

🧪 Solutions & Molarity

"Concentrated" is a feeling, not a number. Molarity turns it into something you can calculate, measure, and reproduce exactly.

🧪 Solute, solvent, solution

A solution is a homogeneous mixture. The substance present in the smaller amount is the solute; the substance doing the dissolving is the solvent. In salt water, salt is the solute and water is the solvent.

When an ionic solid dissolves, the polar water molecules pull the crystal apart and surround each ion — a process called dissociation.

NaCl(s) → Na⁺(aq) + Cl⁻(aq) CaCl₂(s) → Ca²⁺(aq) + 2Cl⁻(aq)

Notice the second equation: one formula unit of calcium chloride releases three ions, because of its 1 : 2 ratio. Counting ions correctly matters constantly in this unit.

"(aq)" means dissolved in water. Free-moving ions are exactly why salt water conducts electricity while solid salt does not.

📊 Molarity: concentration as a number

Molarity (M) is the number of moles of solute dissolved in exactly one litre of solution. It is the standard way chemists describe concentration.

M = moles of solute ÷ litres of solution

moles = M × V V = moles ÷ M

Litres of solution, not litres of solvent. You dissolve the solute and then fill the flask up to the mark. Adding 1 L of water to a solute does not reliably give 1 L of solution.

Worked example — mass to molarity

What is the molarity of a solution made by dissolving 5.85 g of NaCl in enough water to make 500 mL of solution? (NaCl = 58.5 g/mol)

Step 1 moles NaCl = 5.85 g ÷ 58.5 g/mol = 0.100 mol Step 2 volume = 500 mL = 0.500 L Step 3 M = 0.100 mol ÷ 0.500 L = 0.200 M

The unit always ends up as mol/L, sometimes written mol dm⁻³.

💧 Dilution

Adding water changes the volume but not the number of moles of solute. That fact gives the most useful shortcut in the whole unit:

M₁V₁ = M₂V₂

where state 1 is the concentrated stock solution and state 2 is the diluted result. Any consistent volume unit works, as long as both sides match.

How much 12.0 M stock HCl makes 250 mL of 1.50 M HCl? M₁V₁ = M₂V₂ (12.0)(V₁) = (1.50)(250 mL) V₁ = 375 ÷ 12.0 V₁ = 31.3 mL

Sanity check: diluting always needs less stock solution than the final volume. If your answer is bigger than V₂, you have flipped the ratio.

🌊 Solubility and precipitates

Solubility is the maximum amount of solute that dissolves in a given amount of solvent at a given temperature. When two solutions are mixed and an insoluble product forms, that solid is called a precipitate.

Rule	Usually soluble	Exceptions
Group 1 and ammonium salts	Always soluble	None
Nitrates	Always soluble	None
Halides (Cl⁻, Br⁻, I⁻)	Soluble	Ag⁺, Pb²⁺
Sulfates	Soluble	Ba²⁺, Pb²⁺, Ca²⁺
Carbonates, hydroxides	Mostly insoluble	Group 1, NH₄⁺

AgNO₃(aq) + NaCl(aq) → AgCl(s) + NaNO₃(aq) ↑ AgCl is the precipitate

🖼️ See it

Always convert millilitres to litres by dividing by 1000 before using the formula M = n ÷ V.

📝 Worked examples

Example 1 · Calculate molarity

2 mol of NaCl are dissolved to make 4 L of solution.

M = moles ÷ litres = 2 ÷ 4 = 0.5 M

Example 2 · From mass

What is the molarity of 58.5 g NaCl (58.5 g/mol) in 1 L?

moles = 58.5 ÷ 58.5 = 1 mol M = 1 mol ÷ 1 L = 1 M

Example 3 · Dilution

When you add water, the amount of solute stays the same: M₁V₁ = M₂V₂.

2 M × 0.1 L = M₂ × 0.5 L M₂ = 0.2 ÷ 0.5 = 0.4 M

📌 Key vocabulary

Solute — what dissolves (e.g. salt).
Solvent — what does the dissolving (e.g. water).
Molarity (M) — moles of solute per litre of solution.

Units! Convert mL to L (divide by 1000) before calculating molarity. 250 mL = 0.25 L.

✏️ Quick check · 1 of 11

Naming the parts

In a salt-water solution, the salt is the:

The solute is the substance that dissolves.

✏️ Quick check · 2 of 11

What molarity means

A concentration of 2.0 M means the solution contains:

M means moles of solute per litre of the whole solution.

✍️ Type your answer · 3 of 11

A solution contains 2.0 mol of solute dissolved in enough water to make 4.0 L of solution.

What is the molarity?

Enter a number to two decimal places, without units.

M

Molarity = moles ÷ litres: 2.0 ÷ 4.0.

✍️ Type your answer · 4 of 11

Hydrochloric acid is often supplied at 0.100 M. A student measures out 50.0 mL of it.

How many moles of HCl are in that 50.0 mL?

Convert millilitres to litres first: 50.0 mL = 0.0500 L.

mol HCl

moles = M × V: 0.100 × 0.0500.

✍️ Type your answer · 5 of 11

You need 500.0 mL of a 0.500 M sodium hydroxide solution. Use NaOH = 40.0 g/mol.

What mass of solid NaOH must you dissolve?

moles = M × V (in litres), then mass = moles × molar mass.

g NaOH

moles = 0.500 × 0.5000 L, then multiply by 40.0.

✍️ Type your answer · 6 of 11

You want 300 mL of a 1.0 M solution, starting from a 6.0 M stock solution. Use M₁V₁ = M₂V₂.

What volume of stock solution do you need?

Volumes may stay in millilitres as long as both sides match. Enter a whole number.

mL stock

6.0 × V₁ = 1.0 × 300.

✍️ Type your answer · 7 of 11

Potassium sulfate dissolves as K₂SO₄(s) → 2K⁺(aq) + SO₄²⁻(aq).

How many potassium ions are released per formula unit?

Read the subscript on potassium in the formula.

K+ ions

The subscript on K in K₂SO₄.

✏️ Quick check · 8 of 11

Units

What are the units of molarity?

M stands for moles per litre.

✏️ Quick check · 9 of 11

Solute or solvent?

In salt water, the salt is the:

Which one is doing the dissolving?

✍️ Type your answer · 10 of 11

3 mol of KCl are dissolved to make 1.5 L of solution.

What is the molarity?

Enter an exact answer, without rounding.

M

M = moles ÷ litres.

✍️ Type your answer · 11 of 11

Dilute 50 mL of 6 M acid to a final volume of 300 mL. Use M₁V₁ = M₂V₂.

What is the new molarity?

Enter an exact answer, without rounding.

M

You can leave the volumes in mL as long as both use the same unit.

📝 Lesson quiz · 5 questions

Question 1 of 5

How many moles are in 2.5 L of a 0.4 M solution?

Question 2 of 5

What mass of NaOH (40 g/mol) is needed to make 0.5 L of 1 M solution?

Question 3 of 5

What is the molarity of 49 g of H₂SO₄ (98 g/mol) in 0.5 L?

Question 4 of 5

Which solution is the most concentrated?

Question 5 of 5

100 mL of 2 M solution is diluted to 0.5 M. What is the final volume?

Lesson 8 · Acids & Bases

🍋 Acids, Bases & pH

Every acid–base story is really a story about one ion. Follow the hydrogen ion and the whole pH scale makes sense.

🧪 Defining acids and bases

The simplest definitions focus on what each substance releases when it dissolves in water.

Acid

Releases hydrogen ions, H⁺, in water. Also called a proton donor. Example: HCl → H⁺ + Cl⁻.

Base

Releases hydroxide ions, OH⁻, in water. Also called a proton acceptor. Example: NaOH → Na⁺ + OH⁻.

A sharper definition: a Brønsted–Lowry acid donates a proton and a base accepts one. This explains why ammonia, which contains no OH⁻ at all, still behaves as a base.

📊 Strong versus weak

The word "strong" has nothing to do with concentration. It describes how completely a substance ionises in water.

Type	Ionisation in water	Examples
Strong acid	Complete — every molecule splits apart	HCl, HNO₃, H₂SO₄
Weak acid	Partial — most molecules stay intact	CH₃COOH, H₂CO₃
Strong base	Complete	NaOH, KOH
Weak base	Partial	NH₃

Because HCl ionises completely, a 0.010 M solution of HCl has [H⁺] = 0.010 M exactly. A weak acid of the same concentration would give far fewer hydrogen ions.

🌈 The pH scale

pH measures the concentration of hydrogen ions on a logarithmic — that is, powers-of-ten — scale. Each whole step is a tenfold change, not a small nudge.

pH = −log[H⁺] and [H⁺] = 10^−pH

Logarithm warning: pH 3 is not "a bit more acidic" than pH 5 — it is one hundred times more acidic, because the difference is two powers of ten.

⚖️ Neutralisation

When an acid meets a base they cancel each other out, producing a salt and water. This is a neutralisation reaction.

acid + base → salt + water

HCl + NaOH → NaCl + H₂O Balance the ions, not just the atoms: H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O ↑ two hydroxide ions needed per sulfuric acid

In a titration, you use this reaction to find an unknown concentration: add base from a burette until the indicator changes colour, then use the mole ratio.

Watch the subscripts. H₂SO₄ has two acidic hydrogens, so it needs two moles of NaOH per mole of acid. Forgetting this is the classic titration error.

📝 Worked examples

Example 1 · pH from concentration

pH = −log[H⁺]. For powers of ten the pH is just the positive exponent.

[H⁺] = 1 × 10⁻³ M → pH = 3 [H⁺] = 1 × 10⁻¹¹ M → pH = 11

Example 2 · pH and pOH

At 25 °C, pH + pOH = 14.

pH = 11 → pOH = 14 − 11 = 3 [OH⁻] = 1 × 10⁻³ M

Example 3 · Neutralisation

HCl + NaOH → NaCl + H₂O acid + base → salt + water

📌 The pH scale is logarithmic

Each pH step is a factor of 10. A solution at pH 3 is 10 times more acidic than pH 4, and 100 times more acidic than pH 5.

pH < 7

Acidic. More H⁺ than OH⁻.

pH > 7

Basic. More OH⁻ than H⁺.

✏️ Quick check · 1 of 11

Strong vs concentrated

Calling an acid "strong" means it:

Strong is about how much it breaks into ions, not how much is dissolved.

✏️ Quick check · 2 of 11

Following the ions

In the Brønsted–Lowry model, a base is a substance that:

Acids give protons; bases take them.

✍️ Type your answer · 3 of 11

A solution has a hydrogen ion concentration of 1 × 10⁻³ M.

What is its pH?

Use pH = −log[H+]. Enter a whole number.

pH

pH is the power of ten without the minus sign.

✍️ Type your answer · 4 of 11

A solution has a pH of 3.

What is the hydrogen ion concentration, in mol/L?

Use [H+] = 10−pH. Enter a decimal, not a fraction.

mol/L

10⁻³ is one thousandth.

✍️ Type your answer · 5 of 11

A solution has a hydrogen ion concentration of 1 × 10⁻⁸ M.

What is its pH?

A pH above 7 means the solution is basic. Enter a whole number.

pH

pH is the power of ten without the minus sign.

✍️ Type your answer · 6 of 11

Sulfuric acid is neutralised by sodium hydroxide: H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O. You have 0.50 mol of H₂SO₄.

How many moles of NaOH are needed to neutralise it completely?

Read the coefficients in the balanced equation.

mol NaOH

1 H₂SO₄ needs 2 NaOH.

✍️ Type your answer · 7 of 11

Barium hydroxide is neutralised by hydrochloric acid: 2HCl + Ba(OH)₂ → BaCl₂ + 2H₂O. You have 0.25 mol of Ba(OH)₂.

How many moles of HCl are needed?

Enter a decimal, without units.

mol HCl

1 Ba(OH)₂ needs 2 HCl.

✏️ Quick check · 8 of 11

Find the pH

A solution has [H⁺] = 1 × 10⁻⁵ M. What is its pH?

For 1 × 10⁻ⁿ, the pH is n.

✏️ Quick check · 9 of 11

Acid or base?

A solution has a pH of 9. It is:

Neutral is pH 7.

✍️ Type your answer · 10 of 11

A solution has pH 4.

What is its pOH?

Enter an exact answer, without rounding.

The two always add to 14 at 25 °C.

✍️ Type your answer · 11 of 11

Compare a solution with pH 3 to one with pH 5.

How many times more acidic is the pH 3 solution?

Enter an exact answer, without rounding.

Each pH unit is a factor of 10.

📝 Lesson quiz · 5 questions

Question 1 of 5

What is the pH of 0.01 M HCl (a strong acid)?

Question 2 of 5

Neutralisation reactions between an acid and a base produce:

Question 3 of 5

How much more acidic is pH 2 than pH 4?

Question 4 of 5

A solution has pOH = 3. What is [OH⁻]?

Question 5 of 5

Which of these is a strong base?

Lesson 9 · Energy & Equilibrium

🔥 Energy, Rates & Equilibrium

Reactions can release energy or soak it up, run fast or crawl, and finish completely or settle into a balance. This lesson covers all three.

⚖️ Exothermic and endothermic

Every reaction either releases energy to the surroundings or absorbs energy from them. The energy change is called enthalpy, written ΔH.

Exothermic ΔH negative

Releases heat; the surroundings get warmer. Combustion and respiration are exothermic.

Endothermic ΔH positive

Absorbs heat; the surroundings get colder. Photosynthesis and melting ice are endothermic.

CH₄ + 2O₂ → CO₂ + 2H₂O ΔH = −890 kJ/mol (exothermic) CaCO₃ → CaO + CO₂ ΔH = +178 kJ/mol (endothermic)

The reason is bond energy: breaking bonds costs energy, forming new bonds releases it. If the new bonds are stronger overall, the reaction is exothermic.

📈 Reading an energy diagram

An energy diagram shows the energy of the reactants and products, and the activation energy — the hill that must be climbed before anything can happen.

Exothermic

Endothermic

Catalysts lower the hill, not the floor. A catalyst reduces the activation energy so the reaction goes faster, but it cannot change the energy difference between reactants and products — so ΔH stays exactly the same.

🌡️ Measuring heat: calorimetry

When a reaction warms up a known mass of water, you can calculate the energy released directly.

q = m × c × ΔT

where m is the mass in grams, c is the specific heat capacity (4.18 J/g°C for water), and ΔT is the temperature change.

100 g of water warms from 20.0 °C to 30.0 °C. q = (100 g)(4.18 J/g°C)(10.0 °C) = 4180 J = 4.18 kJ

Molar enthalpy divides that energy by the moles that reacted, giving kJ/mol. That is how a value like ΔH = −890 kJ/mol for methane is measured experimentally.

⚡ What controls reaction rate

Particles only react when they collide with enough energy and the right orientation. Anything that increases the number or the energy of collisions speeds the reaction up.

Change	Effect on rate	Why
Increase temperature	Faster	Particles move faster, so more collisions exceed E_a
Increase concentration	Faster	More particles in the same space, so more collisions
Increase surface area	Faster	More exposed particles available to collide
Add a catalyst	Faster	Lowers the activation energy barrier
Decrease temperature	Slower	Fewer collisions reach E_a

Powdered calcium carbonate reacts far faster than the same mass of marble chips in acid — same chemistry, much more surface area.

⚖️ Reversible reactions and equilibrium

Some reactions can run in both directions. Initially only the forward reaction is fast, but as products build up the reverse reaction speeds up too. Eventually the two rates become equal and the amounts stop changing.

N₂ + 3H₂ ⇌ 2NH₃

The double arrow means the reaction is reversible. At dynamic equilibrium the forward and reverse reactions are still happening — both rates are simply equal, so the concentrations look frozen.

Dynamic, not dead. At equilibrium the reaction has not stopped. Individual molecules are still reacting in both directions at exactly the same rate.

Le Chatelier's principle

If you disturb a system at equilibrium, it shifts in the direction that partly undoes your change.

Change you make	Direction the equilibrium shifts
Add more reactant	Toward products (forward)
Remove a product as it forms	Toward products (forward)
Add more product	Toward reactants (reverse)
Raise the temperature (exothermic forward)	Toward reactants (reverse)
Increase pressure on a gas reaction	Toward the side with fewer gas molecules

For N₂ + 3H₂ ⇌ 2NH₃, the left side has 4 gas molecules and the right has 2. Increasing pressure therefore pushes the equilibrium toward ammonia.

📝 Worked examples

Example 1 · Heat absorbed

q = m × c × ΔT. For 50 g of water (c = 4.18 J/g°C) heated by 10 °C:

q = 50 × 4.18 × 10 = 2090 J

Example 2 · Exothermic vs. endothermic

Reactants 500 kJ → Products 350 kJ ΔH = products − reactants = −150 kJ Negative ΔH = exothermic (heat released)

Example 3 · Le Chatelier's principle

For N₂ + 3H₂ ⇌ 2NH₃, adding more N₂ stresses the system, so it shifts right to use up the extra N₂.

📌 What speeds a reaction up?

Higher temperature — particles move faster and collide harder.
Higher concentration — more collisions per second.
Greater surface area — more particles exposed (powder beats a lump).
A catalyst — lowers the activation energy and is not used up.

At equilibrium the forward and reverse rates are equal. The amounts stay constant, but the reactions have not stopped.

✏️ Quick check · 1 of 12

Reading ΔH

A reaction has ΔH = −890 kJ/mol. This reaction is:

Negative ΔH means energy leaves the reaction.

✏️ Quick check · 2 of 12

What a catalyst does

A catalyst speeds up a reaction by:

It provides an easier path with a lower energy hill.

✏️ Quick check · 3 of 12

Speeding up a reaction

Which change would make a reaction between two solutions go faster?

Faster particles collide more often and with more energy.

✏️ Quick check · 4 of 12

Dynamic equilibrium

At dynamic equilibrium:

Both reactions keep going at the same speed.

✏️ Quick check · 5 of 12

Shifting the balance

For N₂ + 3H₂ ⇌ 2NH₃, what happens if you add more N₂?

The system uses up the extra N₂ by making more product.

✍️ Type your answer · 6 of 12

100 g of water warms by 10.0 °C. The specific heat capacity of water is 4.18 J/g°C.

How much energy was absorbed, in kilojoules?

Use q = mcΔT, then convert joules to kilojoules. Give your answer to two decimal places.

kJ

q = 100 × 4.18 × 10.0 J. Divide by 1000 for kJ.

✍️ Type your answer · 7 of 12

Dissolving 25.0 g of a salt (molar mass 100.0 g/mol) in water releases 5.00 kJ of heat.

What is the magnitude of the molar enthalpy change, in kJ/mol?

First find moles = mass ÷ molar mass, then divide the energy by the moles.

kJ/mol

moles = 25.0 ÷ 100.0. Then 5.00 kJ ÷ moles.

✍️ Type your answer · 8 of 12

50.0 g of water warms by 10.0 °C during a reaction. The specific heat capacity of water is 4.18 J/g°C.

How much energy did the water absorb, in kilojoules?

Use q = mcΔT, then convert joules to kilojoules. Give your answer to two decimal places.

kJ

q = 50.0 × 4.18 × 10.0 J. Divide by 1000 for kJ.

✏️ Quick check · 9 of 12

What does a catalyst do?

A catalyst speeds up a reaction by:

It is not used up.

✏️ Quick check · 10 of 12

Exothermic

In an exothermic reaction:

Exo means exit.

✍️ Type your answer · 11 of 12

Use q = m × c × ΔT with c = 4.18 J/g°C.

How much heat (in J) warms 100 g of water by 5 °C?

Enter an exact answer, without rounding.

J

Multiply 100 × 4.18 × 5.

✍️ Type your answer · 12 of 12

Reactants have 500 kJ of energy and products have 350 kJ.

What is ΔH (products − reactants)?

Enter an exact answer, without rounding.

kJ

Subtract reactants from products.

📝 Lesson quiz · 5 questions

Question 1 of 5

Raising the temperature usually makes a reaction go:

Question 2 of 5

N₂ + 3H₂ ⇌ 2NH₃. If more N₂ is added, the equilibrium shifts:

Question 3 of 5

At equilibrium:

Question 4 of 5

Why does powdered zinc react faster than a lump?

Question 5 of 5

An endothermic reaction:

Final Challenge

🏆 19-Question Challenge Quiz

One question from every topic you just learned. Pick an answer for each question, then hit Check My Answers.

Q1 · The Mole

How many moles are in 36 g of water? (H₂O = 18 g/mol)

Q2 · Molar Mass

What is the molar mass of CO₂? (C = 12, O = 16 g/mol)

Q3 · Formulas

A compound is 1.0 mol C, 2.0 mol H, and 1.0 mol O. Its empirical formula is:

Q4 · Stoichiometry

In 2H₂ + O₂ → 2H₂O, how many moles of H₂O form from 3.0 mol of H₂ with excess O₂?

Q5 · Periodic Trends

Which element has the largest atomic radius?

Q6 · Bonding

An electronegativity difference of 2.1 between two atoms produces which bond type?

Q7 · Solutions

What is the molarity of a solution containing 2.0 mol of solute in 4.0 L of solution?

Q8 · Acids & Bases

How many times more acidic is a solution of pH 3 than one of pH 5?

Q9 · Thermochemistry

A reaction that releases heat to the surroundings has:

Q10 · Equilibrium

At dynamic equilibrium, the forward and reverse reaction rates are:

Q11 · The Mole & Avogadro's Number

Which sample contains the most particles?

Q12 · Molar Mass & Percent Composition

Which compound has the greatest percent by mass of oxygen?

Q13 · Empirical & Molecular Formulas

Benzene has the empirical formula CH (13 g/mol) and a molar mass of 78 g/mol. What is its molecular formula?

Q14 · Stoichiometry & Limiting Reactants

C + O₂ → CO₂. How many grams of CO₂ form from 12 g of C (C = 12, CO₂ = 44)?

Q15 · Periodic Trends & Ion Formation

Which alkali metal is most reactive?

Q16 · Bonding, Electronegativity & Shapes

What is the shape of NH₃?

Q17 · Solutions & Molarity

100 mL of 2 M solution is diluted to 0.5 M. What is the final volume?

Q18 · Acids, Bases & pH

Which of these is a strong base?

Q19 · Energy, Rates & Equilibrium

An endothermic reaction: