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SEC G3 Combined Science Chemistry component K326/K328

C4: Chemical Calculations

Move between formulae, equations, moles, masses, gas volumes, limiting reactants, and concentration with ratios visible.

Reviewed for the 2027 cohort on 19 July 2026. The official syllabus remains authoritative for assessable wording and paper details.

Download this chapter PDF

Core notes

Chemical calculations preserve atoms, charge, and reacting ratios from formula construction through equations, moles, gas volumes, and concentrations.

Formulae and equations

Use correct element symbols and formulae. Determine a molecular formula from atom ratios, and determine an ionic formula by balancing total positive and negative charge. The required skills include writing the symbols and formulae named in the syllabus, ionic and molecular formulae, and balanced equations from the information supplied.

A balanced chemical equation conserves each element. Use (s) for solid, (l) for liquid, (g) for gas, and (aq) for a substance dissolved in water. For example, $\ce{HCl(aq) + NaOH(aq) -> NaCl(aq) + H2O(l)}$ becomes the net ionic equation $\ce{H+(aq) + OH-(aq) -> H2O(l)}$ after unchanged spectator ions are removed. Both atoms and total charge must be conserved.

Relative masses and moles

Relative atomic mass, Ar, is the weighted average mass of an atom of an element compared with one twelfth of the mass of a carbon-12 atom. Relative molecular mass or relative formula mass, Mr, is the dimensionless sum of all constituent Ar values. Molar mass M has the same numerical value but carries units of g/mol.

One mole contains the Avogadro constant, $6.02\times10^{23}$ , of specified particles. Convert a measured mass to moles before using an equation's coefficient ratio.

Reacting quantities and solutions

At room temperature and pressure, one mole of gas occupies $\pu{24 dm3}$ . A limiting reactant is consumed first and determines the maximum amount of product.

Solution concentration may be expressed in $\pu{mol.dm-3}$ or $\pu{g.dm-3}$ . Convert $\pu{cm3}$ to $\pu{dm3}$ before molar calculations. Percentage yield and percentage purity calculations are outside this Combined requirement.

Core symbols and formulae used in Combined Chemistry

Know the symbols and formulae named throughout the official syllabus. This table is a compact reference, not a substitute for deducing formulae from atom ratios or ion charges.

Group	Names	Symbols or formulae
Common elements	hydrogen, carbon, nitrogen, oxygen, chlorine, bromine, iodine, lithium, sodium, potassium, calcium, magnesium, aluminium, zinc, iron, lead, copper, silver, argon	H, C, N, O, Cl, Br, I, Li, Na, K, Ca, Mg, Al, Zn, Fe, Pb, Cu, Ag, Ar
Common ions	hydrogen, hydroxide, ammonium, aluminium, calcium, copper(II), iron(II), iron(III), zinc, carbonate, chloride, nitrate, sulfate	$\ce{H+}$ , $\ce{OH-}$ , $\ce{NH4+}$ , $\ce{Al^3+}$ , $\ce{Ca^2+}$ , $\ce{Cu^2+}$ , $\ce{Fe^2+}$ , $\ce{Fe^3+}$ , $\ce{Zn^2+}$ , $\ce{CO3^2-}$ , $\ce{Cl-}$ , $\ce{NO3-}$ , $\ce{SO4^2-}$
Common molecules and reagents	hydrogen, oxygen, chlorine, water, ammonia, carbon dioxide, sulfur dioxide, hydrochloric acid, sodium hydroxide, calcium hydroxide, silver nitrate, barium nitrate, potassium manganate(VII), potassium iodide	$\ce{H2}$ , $\ce{O2}$ , $\ce{Cl2}$ , $\ce{H2O}$ , $\ce{NH3}$ , $\ce{CO2}$ , $\ce{SO2}$ , $\ce{HCl}$ , $\ce{NaOH}$ , $\ce{Ca(OH)2}$ , $\ce{AgNO3}$ , $\ce{Ba(NO3)2}$ , $\ce{KMnO4}$ , $\ce{KI}$

Formulae and relationships

Relationship	Use
$n=\dfrac{m}{M}$	Convert mass to amount in moles.
$n=cV$	Relate moles, molar concentration, and volume in $\pu{dm3}$ .
$V_{\text{gas}}=24n$	Find gas volume in $\pu{dm3}$ at room temperature and pressure.
$\text{mass concentration}=\dfrac{\text{mass of solute}}{\text{solution volume}}$	Relate concentration in $\pu{g.dm-3}$ , solute mass in $\pu{g}$ , and solution volume in $\pu{dm3}$ .

Worked examples

Example 1: How many moles are in $\pu{25.0 cm3}$ of $\pu{0.200 mol.dm-3}$ sodium hydroxide?

Convert $\pu{25.0 cm3}$ to $\pu{0.0250 dm3}$ .
Use $n=cV$ .
Calculate $0.200 \times 0.0250=\pu{0.00500 mol}$ .

Answer: $5.00 \times 10^{-3}\,\pu{mol}$ .

Example 2: Magnesium burns according to $\ce{2Mg + O2 -> 2MgO}$ . How many moles of oxygen react with $\pu{0.30 mol}$ magnesium?

Read the balanced coefficient ratio $\ce{Mg}:\ce{O2}$ as $2:1$ .
Multiply $\pu{0.30 mol}$ $\ce{Mg}$ by $1/2$ .
Keep the reacting substance named in the answer.

Answer: $\pu{0.15 mol}$ of oxygen.

Example 3: Calculate the mass of magnesium oxide formed from $\pu{0.20 mol}$ $\ce{MgO}$ . Take $M(\ce{MgO})=\pu{40.3 g.mol-1}$ .

Use $m=nM$ .
Calculate $0.20 \times 40.3\,\pu{g}$ .
Round to the precision supported by the data.

Answer: $\pu{8.1 g}$ of magnesium oxide.

Example 4: At r.t.p., what volume is occupied by $\pu{0.125 mol}$ carbon dioxide?

Use $\pu{24 dm3.mol-1}$ only because r.t.p. is stated.
Calculate $0.125 \times 24\,\pu{dm3}$ .
Attach the gas-volume unit.

Answer: $\pu{3.00 dm3}$ of carbon dioxide.

Example 5: For $\ce{2H2 + O2 -> 2H2O}$ , $\pu{3.0 mol}$ $\ce{H2}$ reacts with $\pu{1.0 mol}$ $\ce{O2}$ . Identify the limiting reactant and amount of water formed.

The equation needs $\pu{2 mol}$ $\ce{H2}$ for $\pu{1 mol}$ $\ce{O2}$ .
Only $\pu{2.0 mol}$ of the $\pu{3.0 mol}$ $\ce{H2}$ are needed, so $\ce{O2}$ is consumed first.
The $1:2$ ratio from $\ce{O2}$ to $\ce{H2O}$ gives $\pu{2.0 mol}$ $\ce{H2O}$ .

Answer: Oxygen is limiting and $\pu{2.0 mol}$ water forms.

Example 6: $\pu{25.0 cm3}$ of $\pu{0.100 mol.dm-3}$ acid reacts exactly with $\pu{20.0 cm3}$ alkali in a $1:1$ mole ratio. Find the alkali concentration.

Find acid moles: $0.100 \times 0.0250=\pu{0.00250 mol}$ .
Use the $1:1$ ratio, so alkali moles are also $\pu{0.00250 mol}$ .
Divide by $\pu{0.0200 dm3}$ to obtain the concentration.

Answer: $\pu{0.125 mol.dm-3}$ .

Example 7: A solution contains $\pu{6.0 g}$ sodium chloride in $\pu{250 cm3}$ of solution. Find its concentration in $\pu{g.dm-3}$ .

Convert $\pu{250 cm3}$ to $\pu{0.250 dm3}$ .
Divide the solute mass by the solution volume in $\pu{dm3}$ .
Calculate $\dfrac{6.0}{0.250}$ and attach the concentration unit.

Answer: $\pu{24 g.dm-3}$ .

Chapter checkpoint

Use these three moves to organise the topic before attempting a mixed or practical question.

Explain Formulae and equations with the named terms, evidence, and causal links kept distinct.
Use Relative masses and moles to interpret the evidence given and justify each conclusion.
Apply Reacting quantities and solutions to a new example, then check the conclusion against the information given.

Official outcome coverage

K326 C4: 10 mapped outcomes, references C4.1(a), C4.1(b), C4.1(c), C4.1(d), C4.1(e), C4.2(a), C4.2(b), C4.2(c), C4.2(d), C4.2(e). Check the official K326 syllabus.

K328 C4: 10 mapped outcomes, references C4.1(a), C4.1(b), C4.1(c), C4.1(d), C4.1(e), C4.2(a), C4.2(b), C4.2(c), C4.2(d), C4.2(e). Check the official K328 syllabus.

The outcome wording is not reproduced here. The relevant official syllabus remains authoritative for exact assessable scope.

Practical and data connection

Process pipette, burette, gas-volume, mass or concentration data from a quantitative experiment. Record burette readings to the expected precision, obtain concordant titres when instructed, balance the equation first, show units at every conversion, and report a precision supported by the apparatus.

Continue to O-Level Chemistry practical resources.

Exam traps and retrieval check

Avoid these traps

Balancing an equation by changing formula subscripts.
Using $\pu{cm3}$ directly with $\pu{mol.dm-3}$ .
Choosing an excess reactant as the product-limiting quantity.

Check from memory

What must an ionic formula balance?

Total positive and negative charge.

What gas volume represents one mole at r.t.p.?

$\pu{24 dm3}$ .

What does the limiting reactant control?

The maximum product amount.

Official Combined Science scope

This shared Combined Chemistry owner serves both K326 and K328. Formulae, equations, relative masses, moles, reacting quantities, limiting reactants, and solution concentration without percentage yield, percentage purity, gas-law calculations, or gas molar volumes away from room temperature and pressure.

Loading blog content…

SEC G3 Combined Science Chemistry component K326/K328

C4: Chemical Calculations

Move between formulae, equations, moles, masses, gas volumes, limiting reactants, and concentration with ratios visible.

Reviewed for the 2027 cohort on 19 July 2026. The official syllabus remains authoritative for assessable wording and paper details.

Download this chapter PDF

Core notes

Chemical calculations preserve atoms, charge, and reacting ratios from formula construction through equations, moles, gas volumes, and concentrations.

Formulae and equations

Relative masses and moles

One mole contains the Avogadro constant, $6.02\times10^{23}$ , of specified particles. Convert a measured mass to moles before using an equation's coefficient ratio.

Reacting quantities and solutions

At room temperature and pressure, one mole of gas occupies $\pu{24 dm3}$ . A limiting reactant is consumed first and determines the maximum amount of product.

Core symbols and formulae used in Combined Chemistry

Know the symbols and formulae named throughout the official syllabus. This table is a compact reference, not a substitute for deducing formulae from atom ratios or ion charges.

Group	Names	Symbols or formulae
Common elements	hydrogen, carbon, nitrogen, oxygen, chlorine, bromine, iodine, lithium, sodium, potassium, calcium, magnesium, aluminium, zinc, iron, lead, copper, silver, argon	H, C, N, O, Cl, Br, I, Li, Na, K, Ca, Mg, Al, Zn, Fe, Pb, Cu, Ag, Ar
Common ions	hydrogen, hydroxide, ammonium, aluminium, calcium, copper(II), iron(II), iron(III), zinc, carbonate, chloride, nitrate, sulfate	$\ce{H+}$ , $\ce{OH-}$ , $\ce{NH4+}$ , $\ce{Al^3+}$ , $\ce{Ca^2+}$ , $\ce{Cu^2+}$ , $\ce{Fe^2+}$ , $\ce{Fe^3+}$ , $\ce{Zn^2+}$ , $\ce{CO3^2-}$ , $\ce{Cl-}$ , $\ce{NO3-}$ , $\ce{SO4^2-}$
Common molecules and reagents	hydrogen, oxygen, chlorine, water, ammonia, carbon dioxide, sulfur dioxide, hydrochloric acid, sodium hydroxide, calcium hydroxide, silver nitrate, barium nitrate, potassium manganate(VII), potassium iodide	$\ce{H2}$ , $\ce{O2}$ , $\ce{Cl2}$ , $\ce{H2O}$ , $\ce{NH3}$ , $\ce{CO2}$ , $\ce{SO2}$ , $\ce{HCl}$ , $\ce{NaOH}$ , $\ce{Ca(OH)2}$ , $\ce{AgNO3}$ , $\ce{Ba(NO3)2}$ , $\ce{KMnO4}$ , $\ce{KI}$

Formulae and relationships

Relationship	Use
$n=\dfrac{m}{M}$	Convert mass to amount in moles.
$n=cV$	Relate moles, molar concentration, and volume in $\pu{dm3}$ .
$V_{\text{gas}}=24n$	Find gas volume in $\pu{dm3}$ at room temperature and pressure.
$\text{mass concentration}=\dfrac{\text{mass of solute}}{\text{solution volume}}$	Relate concentration in $\pu{g.dm-3}$ , solute mass in $\pu{g}$ , and solution volume in $\pu{dm3}$ .

Worked examples

Example 1: How many moles are in $\pu{25.0 cm3}$ of $\pu{0.200 mol.dm-3}$ sodium hydroxide?

Convert $\pu{25.0 cm3}$ to $\pu{0.0250 dm3}$ .
Use $n=cV$ .
Calculate $0.200 \times 0.0250=\pu{0.00500 mol}$ .

Answer: $5.00 \times 10^{-3}\,\pu{mol}$ .

Example 2: Magnesium burns according to $\ce{2Mg + O2 -> 2MgO}$ . How many moles of oxygen react with $\pu{0.30 mol}$ magnesium?

Read the balanced coefficient ratio $\ce{Mg}:\ce{O2}$ as $2:1$ .
Multiply $\pu{0.30 mol}$ $\ce{Mg}$ by $1/2$ .
Keep the reacting substance named in the answer.

Answer: $\pu{0.15 mol}$ of oxygen.

Example 3: Calculate the mass of magnesium oxide formed from $\pu{0.20 mol}$ $\ce{MgO}$ . Take $M(\ce{MgO})=\pu{40.3 g.mol-1}$ .

Use $m=nM$ .
Calculate $0.20 \times 40.3\,\pu{g}$ .
Round to the precision supported by the data.

Answer: $\pu{8.1 g}$ of magnesium oxide.

Example 4: At r.t.p., what volume is occupied by $\pu{0.125 mol}$ carbon dioxide?

Use $\pu{24 dm3.mol-1}$ only because r.t.p. is stated.
Calculate $0.125 \times 24\,\pu{dm3}$ .
Attach the gas-volume unit.

Answer: $\pu{3.00 dm3}$ of carbon dioxide.

Example 5: For $\ce{2H2 + O2 -> 2H2O}$ , $\pu{3.0 mol}$ $\ce{H2}$ reacts with $\pu{1.0 mol}$ $\ce{O2}$ . Identify the limiting reactant and amount of water formed.

The equation needs $\pu{2 mol}$ $\ce{H2}$ for $\pu{1 mol}$ $\ce{O2}$ .
Only $\pu{2.0 mol}$ of the $\pu{3.0 mol}$ $\ce{H2}$ are needed, so $\ce{O2}$ is consumed first.
The $1:2$ ratio from $\ce{O2}$ to $\ce{H2O}$ gives $\pu{2.0 mol}$ $\ce{H2O}$ .

Answer: Oxygen is limiting and $\pu{2.0 mol}$ water forms.

Example 6: $\pu{25.0 cm3}$ of $\pu{0.100 mol.dm-3}$ acid reacts exactly with $\pu{20.0 cm3}$ alkali in a $1:1$ mole ratio. Find the alkali concentration.

Find acid moles: $0.100 \times 0.0250=\pu{0.00250 mol}$ .
Use the $1:1$ ratio, so alkali moles are also $\pu{0.00250 mol}$ .
Divide by $\pu{0.0200 dm3}$ to obtain the concentration.

Answer: $\pu{0.125 mol.dm-3}$ .

Example 7: A solution contains $\pu{6.0 g}$ sodium chloride in $\pu{250 cm3}$ of solution. Find its concentration in $\pu{g.dm-3}$ .

Convert $\pu{250 cm3}$ to $\pu{0.250 dm3}$ .
Divide the solute mass by the solution volume in $\pu{dm3}$ .
Calculate $\dfrac{6.0}{0.250}$ and attach the concentration unit.

Answer: $\pu{24 g.dm-3}$ .

Chapter checkpoint

Use these three moves to organise the topic before attempting a mixed or practical question.

Explain Formulae and equations with the named terms, evidence, and causal links kept distinct.
Use Relative masses and moles to interpret the evidence given and justify each conclusion.
Apply Reacting quantities and solutions to a new example, then check the conclusion against the information given.

Official outcome coverage

K326 C4: 10 mapped outcomes, references C4.1(a), C4.1(b), C4.1(c), C4.1(d), C4.1(e), C4.2(a), C4.2(b), C4.2(c), C4.2(d), C4.2(e). Check the official K326 syllabus.

K328 C4: 10 mapped outcomes, references C4.1(a), C4.1(b), C4.1(c), C4.1(d), C4.1(e), C4.2(a), C4.2(b), C4.2(c), C4.2(d), C4.2(e). Check the official K328 syllabus.

The outcome wording is not reproduced here. The relevant official syllabus remains authoritative for exact assessable scope.

Practical and data connection

Continue to O-Level Chemistry practical resources.

Exam traps and retrieval check

Avoid these traps

Balancing an equation by changing formula subscripts.
Using $\pu{cm3}$ directly with $\pu{mol.dm-3}$ .
Choosing an excess reactant as the product-limiting quantity.

Check from memory

What must an ionic formula balance?

Total positive and negative charge.

What gas volume represents one mole at r.t.p.?

$\pu{24 dm3}$ .

What does the limiting reactant control?

The maximum product amount.

Core notes

Formulae and equations

Relative masses and moles

Reacting quantities and solutions

Core symbols and formulae used in Combined Chemistry

Formulae and relationships

Worked examples

Example 1: How many moles are in 25.0 cm3\pu{25.0 cm3}25.0 cm3 of 0.200 mol ⋅ dm−3\pu{0.200 mol.dm-3}0.200 mol⋅dm−3 sodium hydroxide?

Example 2: Magnesium burns according to 2 Mg+OX2→2 MgO\ce{2Mg + O2 -> 2MgO}2Mg+OX2​​2MgO. How many moles of oxygen react with 0.30 mol\pu{0.30 mol}0.30 mol magnesium?

Example 3: Calculate the mass of magnesium oxide formed from 0.20 mol\pu{0.20 mol}0.20 mol MgO\ce{MgO}MgO. Take M(MgO)=40.3 g ⋅ mol−1M(\ce{MgO})=\pu{40.3 g.mol-1}M(MgO)=40.3 g⋅mol−1.

Example 4: At r.t.p., what volume is occupied by 0.125 mol\pu{0.125 mol}0.125 mol carbon dioxide?

Example 5: For 2 HX2+OX2→2 HX2O\ce{2H2 + O2 -> 2H2O}2HX2​+OX2​​2HX2​O, 3.0 mol\pu{3.0 mol}3.0 mol HX2\ce{H2}HX2​ reacts with 1.0 mol\pu{1.0 mol}1.0 mol OX2\ce{O2}OX2​. Identify the limiting reactant and amount of water formed.

Example 6: 25.0 cm3\pu{25.0 cm3}25.0 cm3 of 0.100 mol ⋅ dm−3\pu{0.100 mol.dm-3}0.100 mol⋅dm−3 acid reacts exactly with 20.0 cm3\pu{20.0 cm3}20.0 cm3 alkali in a 1:11:11:1 mole ratio. Find the alkali concentration.

Example 7: A solution contains 6.0 g\pu{6.0 g}6.0 g sodium chloride in 250 cm3\pu{250 cm3}250 cm3 of solution. Find its concentration in g ⋅ dm−3\pu{g.dm-3}g⋅dm−3.

Chapter checkpoint

Official outcome coverage

Practical and data connection

Exam traps and retrieval check

Avoid these traps

Check from memory

Official Combined Science scope

Core notes

Formulae and equations

Relative masses and moles

Reacting quantities and solutions

Core symbols and formulae used in Combined Chemistry

Formulae and relationships

Worked examples

Example 1: How many moles are in 25.0 cm3\pu{25.0 cm3}25.0 cm3 of 0.200 mol ⋅ dm−3\pu{0.200 mol.dm-3}0.200 mol⋅dm−3 sodium hydroxide?

Example 2: Magnesium burns according to 2 Mg+OX2→2 MgO\ce{2Mg + O2 -> 2MgO}2Mg+OX2​​2MgO. How many moles of oxygen react with 0.30 mol\pu{0.30 mol}0.30 mol magnesium?

Example 3: Calculate the mass of magnesium oxide formed from 0.20 mol\pu{0.20 mol}0.20 mol MgO\ce{MgO}MgO. Take M(MgO)=40.3 g ⋅ mol−1M(\ce{MgO})=\pu{40.3 g.mol-1}M(MgO)=40.3 g⋅mol−1.

Example 4: At r.t.p., what volume is occupied by 0.125 mol\pu{0.125 mol}0.125 mol carbon dioxide?

Example 5: For 2 HX2+OX2→2 HX2O\ce{2H2 + O2 -> 2H2O}2HX2​+OX2​​2HX2​O, 3.0 mol\pu{3.0 mol}3.0 mol HX2\ce{H2}HX2​ reacts with 1.0 mol\pu{1.0 mol}1.0 mol OX2\ce{O2}OX2​. Identify the limiting reactant and amount of water formed.

Example 6: 25.0 cm3\pu{25.0 cm3}25.0 cm3 of 0.100 mol ⋅ dm−3\pu{0.100 mol.dm-3}0.100 mol⋅dm−3 acid reacts exactly with 20.0 cm3\pu{20.0 cm3}20.0 cm3 alkali in a 1:11:11:1 mole ratio. Find the alkali concentration.

Example 7: A solution contains 6.0 g\pu{6.0 g}6.0 g sodium chloride in 250 cm3\pu{250 cm3}250 cm3 of solution. Find its concentration in g ⋅ dm−3\pu{g.dm-3}g⋅dm−3.

Chapter checkpoint

Official outcome coverage

Practical and data connection

Exam traps and retrieval check

Avoid these traps

Check from memory

Official Combined Science scope

Example 1: How many moles are in $\pu{25.0 cm3}$ of $\pu{0.200 mol.dm-3}$ sodium hydroxide?

Example 2: Magnesium burns according to $\ce{2Mg + O2 -> 2MgO}$ . How many moles of oxygen react with $\pu{0.30 mol}$ magnesium?

Example 3: Calculate the mass of magnesium oxide formed from $\pu{0.20 mol}$ $\ce{MgO}$ . Take $M(\ce{MgO})=\pu{40.3 g.mol-1}$ .

Example 4: At r.t.p., what volume is occupied by $\pu{0.125 mol}$ carbon dioxide?

Example 5: For $\ce{2H2 + O2 -> 2H2O}$ , $\pu{3.0 mol}$ $\ce{H2}$ reacts with $\pu{1.0 mol}$ $\ce{O2}$ . Identify the limiting reactant and amount of water formed.

Example 6: $\pu{25.0 cm3}$ of $\pu{0.100 mol.dm-3}$ acid reacts exactly with $\pu{20.0 cm3}$ alkali in a $1:1$ mole ratio. Find the alkali concentration.

Example 7: A solution contains $\pu{6.0 g}$ sodium chloride in $\pu{250 cm3}$ of solution. Find its concentration in $\pu{g.dm-3}$ .

Example 1: How many moles are in $\pu{25.0 cm3}$ of $\pu{0.200 mol.dm-3}$ sodium hydroxide?

Example 2: Magnesium burns according to $\ce{2Mg + O2 -> 2MgO}$ . How many moles of oxygen react with $\pu{0.30 mol}$ magnesium?

Example 3: Calculate the mass of magnesium oxide formed from $\pu{0.20 mol}$ $\ce{MgO}$ . Take $M(\ce{MgO})=\pu{40.3 g.mol-1}$ .

Example 4: At r.t.p., what volume is occupied by $\pu{0.125 mol}$ carbon dioxide?

Example 5: For $\ce{2H2 + O2 -> 2H2O}$ , $\pu{3.0 mol}$ $\ce{H2}$ reacts with $\pu{1.0 mol}$ $\ce{O2}$ . Identify the limiting reactant and amount of water formed.

Example 6: $\pu{25.0 cm3}$ of $\pu{0.100 mol.dm-3}$ acid reacts exactly with $\pu{20.0 cm3}$ alkali in a $1:1$ mole ratio. Find the alkali concentration.

Example 7: A solution contains $\pu{6.0 g}$ sodium chloride in $\pu{250 cm3}$ of solution. Find its concentration in $\pu{g.dm-3}$ .