Chemistry · Intermediate

Balancing Equations
Study Guide

A complete study system covering conservation of mass, metal reactivity, solubility, organic reactions, and 35 mixed drills — from easy to advanced.

⏱ 40-min session 35 drills + 10 advanced 3 deep-dive concepts Review loop included
Study System · Step 1
Your 40-Minute Session Plan
Follow this plan once before doing the drills — it tells you what to study, in what order, and why interleaving works better than cramming.
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Learn
Read the session plan. Understand the concepts before you drill.
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Practice
Work through 25 mixed drills. Mark got it / missed honestly.
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Review
All missed questions land here. Re-attempt until they're clear.
Why interleaving works Mixing different question types forces your brain to figure out which strategy to use, not just apply one on autopilot. It's harder in the moment — but research shows it produces much stronger long-term memory.
Expand each block for full concept notes
Study System · Step 2
25 Mixed Practice Drills
Work through these in order. Don't skip ahead to the answer — try each one first. Mark yourself honestly: that's how the review loop helps you.
Progress0 / 25 answered
Study System · Challenge
Advanced Drills
These questions are harder because they require deeper understanding, not just pattern-matching. Expect multi-step reasoning, explain-why questions, and tricky distractors.
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Exam-style challenge questions
Mix of: predict the products · will/won't react · explain why · tricky balancing · mixed-concept reasoning
Advanced progress0 / 10 answered
Study System · Step 3
Mastery Loop
Every question you marked "missed it" reappears here. Re-attempt until your review list is empty. Then wait 24 hours and try again — that spacing interval is where real learning happens.
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answered
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got it ✓
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to review
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accuracy
Mastery tip For every question you missed, don't just check the answer — identify where your thinking went wrong. Was it: wrong atom count? Wrong balancing order? Forgot a polyatomic ion unit? Misidentified reaction type? Fix the root cause, not just the answer.
Questions to re-attempt
Chemistry Deep Dive · Concept 1 of 3
Metal Reactivity & Displacement Reactions
Learn how to predict which metal will displace another, why some metals are more reactive, and how the activity series connects to electron behaviour.
Key concepts — click any to expand
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Core idea
What is the activity series actually ranking?
The activity series ranks metals by how eagerly they give away electrons to become positive ions. Potassium at the top is desperate to lose electrons — it reacts explosively with water. Gold at the bottom barely reacts with anything. The series is not arbitrary: it reflects the underlying atomic structure of each element.

The key property being measured is how tightly the atom holds its outer electrons. Metals high on the series have outer electrons far from the nucleus and loosely held — easy to remove. Metals low on the series hold their electrons tightly. This energy difference is captured as electrode potential: a higher metal has a more negative electrode potential, meaning it "wants" to oxidise.
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How it works
How does displacement actually happen?
When you place zinc metal into copper sulfate solution, you're asking: which metal is more stable as an ion here? Zinc ions (Zn²⁺) are more stable in solution than copper ions (Cu²⁺). So zinc dissolves — giving away 2 electrons — and copper ions pick those electrons up and plate out as solid copper metal.

The more reactive metal always displaces the less reactive one. Never the other way around. The driving force is the difference in electrode potential: a bigger gap in the series means more energy is released and the reaction happens faster and more completely. Zn + CuSO₄ → ZnSO₄ + Cu   (Zn is above Cu in the series ✓)
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Why it matters
Why does hydrogen appear in the middle?
Hydrogen is included as a reference point, not a metal. It helps you predict acid reactions: any metal above H will displace hydrogen from dilute acid, producing H₂ gas. Metals below H — like copper, silver, gold — cannot do this.

That's why you can dissolve iron in dilute HCl (Fe is above H) but you can't dissolve copper in it (Cu is below H). In exams, if you're asked "does this metal react with dilute acid?", just check whether it's above or below H in the series. Fe + 2HCl → FeCl₂ + H₂ ↑   (Fe above H ✓) Cu + HCl → no reaction   (Cu below H ✗)
Common mistake
Writing a displacement reaction backwards
Students often write a reaction where a less reactive metal displaces a more reactive one — e.g. copper displacing zinc from zinc sulfate. This never happens. The reaction would need to run uphill energetically — it's thermodynamically forbidden.

Always check: is the element you're adding higher in the series than the dissolved metal? If not, write "no reaction". This check takes two seconds and prevents a common exam error.
The series ranks
How strongly each metal "wants" to lose electrons
Displacement rule
A metal displaces another only if it sits higher in the series
The H₂ benchmark
Metals above H react with dilute acids — below H, they don't
Click a metal bar to see its displacement power and periodic position
↑ more reactive (loses e⁻ eagerly) less reactive (holds e⁻ tightly) ↓
Halogens — the same idea, but gaining electrons
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Core idea
Halogens are the mirror image of metals
Metals compete to lose electrons. Halogens compete to gain electrons. The most reactive halogen (F₂) grabs electrons from any other halide ion. The least reactive (I₂) barely holds onto the electrons it already has.

The trend runs down Group 17 of the periodic table — as atomic radius increases, the nucleus is farther from the outer shell and attracts incoming electrons less strongly. So reactivity decreases going down (F > Cl > Br > I), which is the opposite of what happens with alkali metals.
Exam shortcut
The colour-change test for halogen displacement
Add Cl₂ water to a solution containing Br⁻ or I⁻, then shake with cyclohexane (an organic layer). The organic layer turns:
  • Orange — Br₂ has been displaced from Br⁻
  • Violet/purple — I₂ has been displaced from I⁻
This colour change is your observable proof that displacement occurred. In exams, the question will often ask you to describe what you see — give the colour and what it means.
Period 2 · Group 17
F₂
Fluorine
strongest oxidiser
Most electronegative element. Displaces Cl⁻, Br⁻, I⁻.
Period 3 · Group 17
Cl₂
Chlorine
displaces Br⁻, I⁻
Smaller atom than Br — nucleus pulls electrons more strongly.
Period 4 · Group 17
Br₂
Bromine
displaces I⁻ only
Larger atom — weaker pull on incoming electrons.
Period 5 · Group 17
I₂
Iodine
weakest — can't displace
Largest atom — electrons too far from nucleus to attract new ones.
Chemistry Deep Dive · Concept 2 of 3
Solubility, Ksp & Precipitation Reactions
Understand from first principles why some ionic compounds dissolve and others don't — and how to predict whether mixing two solutions will produce a solid precipitate.
Why precipitates form
Lattice energy of the solid beats hydration energy keeping ions dissolved
The Ksp idea
Tiny Ksp = almost no ions can coexist in solution — solid forms immediately
The test
If [A⁺][B⁻] exceeds Ksp, precipitation starts at once
Build your understanding — click each step to expand
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Step 1
What does "solubility" actually mean?
When an ionic solid dissolves in water, it breaks apart into positive and negative ions. Water molecules surround each ion — this is called hydration — and pull the crystal lattice apart. A compound is soluble if this process releases enough energy to break the lattice.

Two forces are in competition: the lattice energy (how tightly the crystal holds itself together) and the hydration energy (how strongly water molecules attract the freed ions). If hydration wins → the compound dissolves. If lattice energy wins → the compound is insoluble.
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Step 2
What is a saturated solution?
As you keep dissolving a salt, at some point the solution becomes saturated: ions are re-joining the crystal just as fast as they're leaving it. This is a dynamic equilibrium — both processes (dissolving and crystallising) happen simultaneously at equal rates.

The solution looks still, but at the molecular level there's constant activity. You can't dissolve any more solid past this point — adding more just makes the undissolved pile at the bottom bigger.
saturated solution
A⁺
B⁻
A⁺
B⁻
Ions float freely in equilibrium with solid at the bottom. Adding more ions tips the balance — solid forms.
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Step 3
What is Ksp and what does it actually measure?
The solubility product constant (Ksp) is the equilibrium constant for the dissolving reaction at saturation. For a compound AB → A⁺ + B⁻: Ksp = [A⁺] × [B⁻]   (at equilibrium / saturation) It is a fixed number for each compound at a given temperature. A very small Ksp (like 10⁻¹⁰) means almost no ions can coexist dissolved — the compound is extremely insoluble. A large Ksp means lots of ions can dissolve freely.

Think of it this way: Ksp is the maximum "ion budget" a solution can hold before the solid starts forming. Exceed the budget and the solid crystallises immediately.
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Step 4
Why do precipitates form when you mix two solutions?
When you mix two solutions containing different ions, you suddenly have all four types of ions in the same solution. For every possible cation–anion pair, the system checks: does [A⁺] × [B⁻] exceed Ksp for that compound?

If yes → the solution is "supersaturated" with respect to that compound → it immediately precipitates out as solid to bring concentrations back below Ksp. With very insoluble compounds (tiny Ksp), this happens the instant the two solutions touch. Ag⁺ + Cl⁻ → AgCl ↓   Ksp(AgCl) ≈ 1.8×10⁻¹⁰ — extremely insoluble
Exam shortcut
The "will it precipitate?" test — step by step
  1. Write out all ions present after mixing both solutions.
  2. List every possible cation–anion combination.
  3. For each pair: is that compound soluble or insoluble? (Use solubility rules below.)
  4. If any combination is insoluble → precipitation occurs. Write the net ionic equation.
  5. Key insight: you don't need to know the exact Ksp value — the solubility rules encode which combinations are "too insoluble" in practice.
Common mistake
Ksp is not the same as solubility
Ksp measures the equilibrium ion product. Solubility is how much of the compound actually dissolves (in mol/L). They're related but not the same thing — you can't directly compare Ksp values across compounds with different formulas (like AB vs A₂B) without doing the maths first. A compound with a higher Ksp is generally more soluble, but this breaks down when the formulas differ.
Solubility rules — quick reference
Always soluble Insoluble (precipitates) Exceptions apply
Will it precipitate? — interactive checker

Mix any cation and anion below. The checker applies solubility rules and explains the result.

Cation: Anion:
Select ions above to check.
Chemistry Deep Dive · Concept 3 of 3
Core Organic Reactions: Alkanes, Alcohols & Esters
Understand the three main organic families you'll encounter, what makes them chemically different, and how to balance and predict their key reactions.
The three families — know these first
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Foundation
What makes organic families different from each other?
Organic molecules are all built around carbon chains. The key difference between families is the functional group — the part of the molecule that determines how it reacts. You don't need to memorise the whole molecule; spot the functional group and you know the reaction type.
Alkanes CₙH₂ₙ₊₂
Pure carbon–hydrogen chains with only single bonds. No functional group — completely non-polar. Methane, ethane, propane, butane...
Spot it: only C and H, single bonds everywhere
Alcohols –OH group
Alkane chain with one –OH (hydroxyl) group. This one oxygen atom changes how the molecule burns. Ethanol (C₂H₅OH) is the key example.
Spot it: formula ends in –OH
Esters –COO– linkage
Formed from carboxylic acid + alcohol. The –COO– linkage gives esters their fruity smell. Esterification is reversible.
Spot it: two O atoms, –COO– in the middle
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Golden rule
The order for balancing organic combustion: C → H → O
For any hydrocarbon or oxygen-containing organic compound burning in oxygen, always follow this order:
  1. Balance C first — each C atom produces one CO₂
  2. Balance H next — every 2 H atoms produce one H₂O
  3. Balance O last — count all O atoms needed on the right, subtract any O in the fuel, divide by 2 for O₂
  4. Clear any fractions by multiplying all coefficients by 2
O is always last because it appears in both products (CO₂ and H₂O) and can only be fixed once you know how many of each product you need.
Key trick — very commonly tested
Why alcohols need special oxygen accounting
An alcohol molecule already contains one oxygen atom (in the –OH group). That oxygen ends up in the products (CO₂ or H₂O). So when you calculate how much O₂ you need to add from outside, you must subtract 1 for the oxygen already present in the alcohol.

Forgetting this subtraction is one of the most common mistakes in organic balancing — it gives you one too many O₂ on the left. C₂H₅OH + 3O₂ → 2CO₂ + 3H₂O
O needed on right: 4+3=7. O in alcohol: 1. Extra O needed: 6 → 3O₂ ✓
Reaction types — click to expand each one
O₂ coefficient calculator
Molecule
n (carbons)