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CDS Chemistry · Mole Concept and Stoichiometry

Balancing Equations and Reacting Amounts

Balancing a chemical equation by counting atoms, then reading it as a mole ratio to find how much reacts, how much forms, and which reactant runs out first.

All Mole Concept and Stoichiometry notes

Why this matters

Five CDS questions, three of them from the 2018 papers. Two ask for a balanced equation; three use a balanced equation's mole ratio, one of them HARD (which fuel gives the most hydrogen per gram).

Concept 1 of 2: Balancing a chemical equation

Atoms are neither made nor destroyed in a reaction (conservation of mass), so every element must have the same number of atoms on both sides. Balance by changing the numbers in front of formulas, never the subscripts inside them.

Definition

The method:

  • Write the skeleton equation with correct formulas.
  • Balance the element in the most complex formula first, then the others; leave H and O (or free elements) for last.
  • Change only the coefficients, never the subscripts.
  • Check every element at the end.

Conservation of atoms

∑atoms of each element (reactants)=∑atoms of that element (products)\sum \text{atoms of each element (reactants)} = \sum \text{atoms of that element (products)}

Worked example

Balance: Al + O₂ → Al₂O₃.
Practice this conceptself-check · 3 quick reps

The same idea in a real exam question:

CDS · 2023 · CDS (II) 2023 — General Knowledge · Q10Easy

Example 1 · Mole Concept and Stoichiometry · Stoichiometry and Laws of Chemical Combination

Which one of the following equations is the balanced chemical equation for the given reaction ? Fe+H2O→Fe3O4+H2\mathrm{Fe} + \mathrm{H_2O} \rightarrow \mathrm{Fe_3O_4} + \mathrm{H_2}

Re-check the first element after fixing the second

In Fe + Cl₂ → FeCl₃, fixing chlorine to 3Cl₂ → 2FeCl₃ puts 2 Fe on the right, so the iron must go back to 2Fe: 2Fe + 3Cl₂ → 2FeCl₃.

Never change a subscript

Changing H₂O to H₂O₂ to balance oxygen makes a different substance (hydrogen peroxide). Only the numbers in front of formulas may change.
Drill 1 more on balancing a chemical equation

Concept 2 of 2: Mole ratios and the limiting reactant

A balanced equation is a recipe in moles. Its coefficients tell you how many moles react and form. If you have more of one reactant than the recipe needs, the other one runs out first and decides how much product you get.

Definition

The steps:

  • Read the coefficients as mole ratios.
  • For each reactant, work out how much it needs of the other. The one that runs out is the limiting reactant; it fixes the amount of product.
  • To compare yields per gram, divide moles of product by the mass of reactant used.

Mole ratio from coefficients

aA+bB→cC:nC=ca nAaA + bB \rightarrow cC: \qquad n_C = \frac{c}{a}\, n_A

Worked example

In N₂ + 3H₂ → 2NH₃, 2 mol of N₂ is mixed with 3 mol of H₂. Which is limiting, and how much NH₃ forms?
Practice this conceptself-check · 3 quick reps

The same idea in a real exam question:

CDS · 2022 · CDS (I) 2022 — General Knowledge · Q7Moderate

Example 2 · Mole Concept and Stoichiometry · Stoichiometry and Laws of Chemical Combination

The number of moles of oxygen gas used in the complete combustion of 1 mole of glucose is :

The reactant in excess does not set the yield

In CH₄ + ½O₂ → CO + 2H₂ with 3 mol CH₄ and 1 mol O₂, the methane would need 1.5 mol O₂, so oxygen is limiting: 1 mol O₂ reacts with 2 mol CH₄ and gives 2 mol CO.

Mass is conserved, moles need not be

In 2H₂ + O₂ → 2H₂O, three moles of gas give two moles of water, yet the mass on both sides is the same (36 g). Conservation applies to mass and atoms, not to the number of moles.

Per gram means divide by mass

To find which reaction gives the most product per gram, divide the moles of product by the reactant's molar mass. A larger coefficient does not mean more per gram if the reactant is heavy.
Drill 2 more on mole ratios and the limiting reactant

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (2)

  • Balancing a chemical equation

    Conservation of atoms

    ∑atoms of each element (reactants)=∑atoms of that element (products)\sum \text{atoms of each element (reactants)} = \sum \text{atoms of that element (products)}
  • Mole ratios and the limiting reactant

    Mole ratio from coefficients

    aA+bB→cC:nC=ca nAaA + bB \rightarrow cC: \qquad n_C = \frac{c}{a}\, n_A

Watch out for (5)

Test yourself on a real paper

Sit a past CDS paper, timed and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.

Sit a CDS past paperDrill all 5 questions