Chemical change

Quantitative chemistry

Mole ratios from a balanced equation. Limiting reagent. Concentration c = n/V.

CAPS

Grade 11 · Physical Sciences (Chemistry) · Chemical change

Chemistry is Physical Sciences Paper 2.

  • The paper

    Grade 11 Paper 2 covers the mole, concentration, stoichiometry, energy change, types of reaction, and the start of chemical systems.

  • Working

    Balance before you use a mole ratio. Show n = mM or c = nV with units. An IUPAC name needs the number on the functional group. A reaction that is not balanced cannot support a stoichiometric answer.

  • The relation

    c = nV. Concentration in mol·dm⁻³

  • How a marker reads it

    Convert cm³ to dm³ before multiplying. Forgetting1000 makes c a thousand times too small.

Paper 2 is 150 marks. Tables of ions and the data sheet are part of the exam. Significant figures follow the data you were given.

particle

Diagram

Worked example

25 cm³ of 0.10 mol·dm⁻³ HCl is needed to neutralise 20 cm³ of NaOH. Find c(NaOH).

Before any working — hunt first

Given

Numbers and units already in the sentence: 25 cm³ · 0.10 mol·dm⁻³ · 20 cm³. Copy each one into a column. A name without a number is not given.

Missing

After you copy the given, the letter that still has no number is missing. The paper is pointing at: c(NaOH). Circle that word — that is the missing variable.

Find

We are required to find: c(NaOH). Write that as a symbol on the left, with a question mark, before you touch a formula.

Calculate

Write c = nV with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives c(NaOH).

Simplified approach

n = c V (in dm³). 1:1 ratio from HCl + NaOH → NaCl + H₂O, so n(NaOH) = n(HCl).

Culture note

A titration in a KZN school lab with phenolphthalein turning from pink to colourless — this is that sum.

Formulas

c=nV

Concentration in mol·dm⁻³

Exam tricks you must know

These are the moves markers look for — not shortcuts that skip the method, but the habits that earn the method mark.

  • Never change a subscript to balance — only coefficients

    How:The given formula is a substance. Fe₂O₃ is not FeO. Count atoms on each side. Put a number in front (coefficient) until both sides match. Changing a subscript invents a different compound and zeros the question.

    When to use it:Balancing equations and mole-ratio questions.

Step 1 / 6

Convert cm³ to dm³

V(HCl)=251000=0.025 dm³. V(NaOH)=0.020 dm³.

Diagram
Diagram
V=0.025 dm³

Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

4. Step-by-step working

  1. 01

    Convert cm³ to dm³

    V(HCl)=251000=0.025 dm³. V(NaOH)=0.020 dm³.

    V=0.025 dm³
  2. 02

    Moles of HCl

    n=c V=0.10×0.025=0.0025 mol. Ratio 1:1 so n(NaOH)=0.0025 mol.

    n=0.0025 mol
  3. 03

    Concentration of NaOH

    c=nV=0.00250.020=0.125 mol·dm⁻³.

    c=0.125 mol·dm⁻³

More worked examples

Board walkthroughs on this topic. Open one, copy the working, then try the next.

Example 1 / 20

2H₂ + O₂ → 2H₂O. A learner mixes 2.0 mol of H₂ with 2.0 mol of O₂. Which reagent is limiting, and how many moles of water form?

4. Step-by-step working

  1. 01

    Write the formula

    The equation uses 2 mol of H₂ for every 1 mol of O₂.

    2 H₂ : 1 O₂
  2. 02

    Divide

    H₂: 2.02=1.0. O₂: 2.01=2.0. The smaller result is H₂, so hydrogen runs out first.

    2.02=1.0
  3. 03

    Multiply

    One complete reaction uses 2.0 mol H₂ and 1.0 mol O₂ and makes 2.0 mol of water.

    n(H₂O)=2.0 mol
  4. 04

    Subtract

    Oxygen left=2.0−1.0=1.0 mol.

    2.0−1.0=1.0

How we got there

Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

Explain in another language · 11

1. What is the question asking?

Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: 2H₂ + O₂ → 2H₂O. A learner mixes 2.0 mol of H₂ with 2.0 mol of O₂. Which reagent is limiting, and how many moles of water form?

In other words — as if you have never seen this before

If you have never seen this before: Divide each amount by its coefficient. The smaller result is the limiting reagent. The other reagent is left over. We will name a method in words, write the formula with no numbers, then substitute one line at a time.

2. What do we already know?

2.0 mol H₂ and 2.0 mol O₂. Equation ratio is 2 mol H₂ per 1 mol O₂.

3. Which method — and why this one?

Divide each amount by its coefficient. The smaller result is the limiting reagent. The other reagent is left over.

4. Step-by-step working

  1. 01 / 07

    Write the formula

    The equation uses 2 mol of H₂ for every 1 mol of O₂.

    2 H₂ : 1 O₂

    Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

  2. 02 / 07

    Divide

    H₂: 2.02=1.0. O₂: 2.01=2.0. The smaller result is H₂, so hydrogen runs out first.

    2.02=1.0

    Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

  3. 03 / 07

    Multiply

    One complete reaction uses 2.0 mol H₂ and 1.0 mol O₂ and makes 2.0 mol of water.

    n(H₂O)=2.0 mol

    Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

  4. 04 / 07

    Subtract

    Oxygen left=2.0−1.0=1.0 mol.

    2.0−1.0=1.0

    Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

  5. 05 / 07

    Step G — Sense-check the size

    Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.

    Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.

  6. 06 / 07

    Step F — Box the answer with its unit

    H₂ is limiting. 2.0 mol of water forms. 1.0 mol of O₂ is left.

    Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.

  7. 07 / 07

    Step H — What the marker is looking for

    On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.

    Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

5. The answer

H₂ is limiting. 2.0 mol of water forms. 1.0 mol of O₂ is left.

Copy onto your answer sheet — in this order

Formula: 2 H₂ : 1 O₂

Answer: H₂ is limiting. 2.0 mol of water forms. 1.0 mol of O₂ is left.

6. Check it like a marker

Having equal moles does not mean neither is limiting. The equation does not use them 1:1.

7. A trap first-timers fall into

First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”

Ntsako · fx-991ZA PLUS. Tap to calculate.