Stoichiometry: Formulae, Equations and Reacting Masses
Recipe Master: Count Like a Chemist 🧪
Introduction
1. Introduction
Alright, let's talk stoichiometry. Sounds like a final-boss word, but it's basically chemistry's version of a recipe: how much of this do I mix to get that much of the other thing? Bakers do it with cups; at Core, chemists do it with formulae, equations and relative masses.
Here's the cheat code for the whole chapter: atoms are only ever rearranged, so mass is conserved and every mass in a reaction scales together. Lock that in and every Core calculation is simple proportion (no moles needed). This is your fast refresh, not the full textbook: one key idea per topic, one quick worked example, and the exact move the marker wants. Let's count like a chemist! 🧪
Here's the cheat code for the whole chapter: atoms are only ever rearranged, so mass is conserved and every mass in a reaction scales together. Lock that in and every Core calculation is simple proportion (no moles needed). This is your fast refresh, not the full textbook: one key idea per topic, one quick worked example, and the exact move the marker wants. Let's count like a chemist! 🧪
2. Writing Chemical Formulae
A formula just says which atoms and how many. The little number sticks to the symbol right before it, so is two H and one O. An ionic compound has no molecules, so its formula is the ratio of ions: is one magnesium ion for every two chloride ions. Learn the common groups by formula and charge: hydroxide , nitrate , carbonate , sulfate , sulfite , ammonium . The molecular formula is the number and type of different atoms in one molecule. Given a model or a diagram, deduce the formula by counting each type of atom (count balls, never sticks).
Key idea🔑 Key idea: Ionic formula = ratio of ions. Molecular formula = number and type of atoms in one molecule. From a model: count each type of atom, then write the counts as subscripts. 🎯
Worked example
Worked Example: A Formula from a Model
Worked Example: Count the Balls 🧲
A ball-and-stick model shows one black ball joined by single sticks to four white balls. The key says black = carbon, white = hydrogen. What is the formula?
- 1Count the balls: 1 black (carbon) and 4 white (hydrogen). The sticks are bonds, so they're not counted.
- 2Write carbon first, with the counts as subscripts: (methane).
So the formula is , not : the small number goes after the element it counts. ✅
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3. Counting Atoms in a Formula
When you count atoms, the only thing that catches people out is the brackets. A number outside a bracket multiplies everything inside it, not just the first atom. So in , that little 2 doubles the whole group: both the nitrogen and all four hydrogens. Split the formula into "the bracket bit" and "the rest", count each, then add. Easy marks once you slow down.
Key idea🔑 Key idea: A subscript outside a bracket multiplies every atom inside it. Count the bracketed group first, then the rest, then add. 🧮
Worked example
Worked Example: Atoms in Ammonium Sulfate
Worked Example: Two Blocks, One Total 🧱
How many atoms in total are in one formula unit of ammonium sulfate, ?
- 1Do the bracket first. is two ammonium groups; each is 1 N + 4 H = 5 atoms, so two of them is 10 atoms (2 N, 8 H).
- 2Now the rest. is 1 S + 4 O = 5 atoms. Add the two blocks.
15 atoms in total (but only 4 different elements). 🔥
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Answer
4. Balancing Equations
A balanced equation is just a promise that no atoms vanish: the same number of each element on both sides. You make it balance by changing the big numbers in front only, never the little subscripts (that would change the actual substance). And don't forget state symbols when they're asked for: solid, liquid, gas, dissolved in water.
Key idea🔑 Key idea: Balance with the big front numbers, never the subscripts. Then add state symbols , , , where needed. ⚡
Worked example
Worked Example: Potassium Plus Oxygen
Worked Example: Balance It Out 🔥
Potassium reacts with oxygen to form potassium oxide, . Balance the equation.
- 1Write the formulae first (oxygen is ): . Oxygen is unbalanced (2 on the left, 1 on the right), so put a 2 in front of .
- 2Now there are 4 potassium on the right, so put a 4 in front of potassium on the left.
Both sides: 4 K, 2 O. Balanced. ✅
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Answer
5. Relative Atomic Mass
Atoms are way too tiny to weigh one at a time, so chemists compare everything to a carbon-12 atom (set at exactly 12). The relative atomic mass () is the average mass of an element's atoms. It's an average because most elements come as a mix of isotopes (same element, different masses), and the average leans toward whichever isotope is more common, like a class average being pulled towards the bigger group. That's why chlorine's is 35.5 and not a tidy whole number.
Key idea🔑 Key idea: is the average isotope mass on the carbon-12 scale. It lies between the isotope masses, closer to the more abundant one. 🎯
Worked example
Worked Example: The Mass of Boron
Worked Example: Lean Toward the Common One 🧪
Boron has two isotopes, of mass 10 and 11. The heavier one (mass 11) is more common. Which is the most likely : 10.0, 10.2, 10.8 or 11.0?
- 1The average has to be between 10 and 11, so rule out 10.0 and 11.0 (those are the pure isotopes).
- 2The heavier isotope (mass 11) is more common, so the average gets pulled up above the half-way value of 10.5. Only 10.8 fits.
So the most likely relative atomic mass is 10.8. ✅
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Answer
6. Relative Formula Mass
Once you know the of each element, the relative molecular (or formula) mass is just the total mass of all the atoms in the formula. Add them up. The one thing that trips everyone is brackets: a number outside a bracket multiplies everything inside it, so has two oxygens and two hydrogens, not just two oxygens.
Key idea🔑 Key idea: = sum of all the values in the formula. A bracket number multiplies every atom inside the bracket. 🧱
Worked example
Worked Example: Calcium Hydroxide
Worked Example: Don't Drop the Bracket 👀
Find the relative formula mass of calcium hydroxide, . (: Ca = 40, O = 16, H = 1.)
- 1The 2 outside the bracket doubles both the O and the H. So you've got 1 Ca, 2 O, 2 H.
- 2Add the masses.
So . Forget the bracket and you'd wrongly get 57 or 58. 🚧
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Answer
7. Conservation of Mass
In any reaction, atoms just get rearranged, never created or destroyed. So the total mass of products equals the total mass of reactants. If mass looks like it changed, a gas snuck in or escaped: burning magnesium gets heavier (grabs oxygen from the air), a heated carbonate gets lighter (lets carbon dioxide escape). And because a reaction is fixed, if you scale the amounts up or down, every mass scales by the same factor, so you can answer loads of questions with simple proportion.
Key idea🔑 Key idea: Mass of products = mass of reactants, always. Scale a fixed reaction up or down and every mass scales together. ⚖️
Worked example
Worked Example: Burning Magnesium by Proportion
Worked Example: Scale It Down 🪙
48 g of magnesium burns to form 80 g of magnesium oxide. What mass of magnesium oxide forms from 24 g of magnesium?
- 1Compare the magnesium: 24 g is a half of 48 g.
- 2So you make a half of the product.
40 g of magnesium oxide. No moles needed, just proportion. ✅
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Answer
8. Units of Concentration
A solution's concentration is how much solute is dissolved in a fixed volume. At Core the one thing to learn is the statement: concentration can be measured in g/dm³ or mol/dm³. g/dm³ is the mass of solute, in grams, in each 1 dm³ of solution. mol/dm³ is the amount of solute in moles in each 1 dm³; at Core you only need to recognise that unit and know what it measures, not calculate with it. And 1 dm³ = 1 litre = 1000 cm³.
Key idea🔑 Key idea: Concentration is measured in g/dm³ or mol/dm³. Solute unit on top, volume (dm³) underneath. 🎯
Worked example
Worked Example: Which Unit?
Worked Example: Solute Over Volume 💧
Which are the units of a concentration measured in moles: dm³/mol, g/dm, cm/g or mol/dm³?
- 1Concentration is solute per volume, so the solute unit goes on top: measured in moles, the top is mol. That leaves dm³/mol or mol/dm³, and dm³/mol is upside down.
- 2g/dm and cm/g don't use moles, and dm and cm are lengths, not volumes.
So the answer is mol/dm³. ✅
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9. Reading a Concentration in g/dm³
A concentration in g/dm³ tells you how many grams sit in each dm³. So 12 g of salt dissolved to make 2 dm³ of solution is g in each dm³: 6 g/dm³. It's the same sharing-out idea as proportion. To compare two solutions, put both into g/dm³ first. Never compare total masses: a big volume can hold more salt in total and still be more dilute.
Key idea🔑 Key idea: g/dm³ = grams ÷ dm³ of solution. Compare concentrations, never total masses. 🔬
Worked example
Worked Example: Which Solution Is Stronger?
Worked Example: Same Unit First 💎
Solution J has 12 g of a salt in 2 dm³ of solution. Solution K has 15 g of the same salt in 5 dm³. State each concentration in g/dm³ and say which is more concentrated.
- 1J: g/dm³. K: g/dm³.
- 26 is bigger than 3, so J is more concentrated, even though K has more salt in total. 💎
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10. Reacting Masses from an Equation
At Core, reacting-mass calculations do not use moles: they're simple proportion. From a balanced equation, multiply each relative mass by its big balancing number to get a mass line in grams. For (Mg = 24, = 32, MgO = 40): 48 g Mg + 32 g O₂ → 80 g MgO. Then find the scale factor from the same substance (new mass ÷ mass-line mass) and multiply the other mass by it. Check: less in means less out, and the masses add up.
Key idea🔑 Key idea: Mass line = balancing number × relative mass. Scale factor = new ÷ reference (same substance). Multiply. No moles at Core. 🧮
Worked example
Worked Example: Magnesium to Magnesium Oxide
Worked Example: Mass to Mass 🔥
. The of magnesium is 24 and the of magnesium oxide is 40. What mass of magnesium oxide forms from 9.6 g of magnesium?
- 1Mass line: magnesium g; magnesium oxide g. So 48 g Mg → 80 g MgO.
- 2Scale factor: . Mass of magnesium oxide g.
16.0 g of magnesium oxide. Check: oxygen used is g, and g. 🎯
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