The Chemical Equation and How to Balance It
Every time you light the stove in the kitchen, the methane in the gas reacts with the oxygen in the air and turns into carbon dioxide and water vapor. That transformation is written as a chemical equation: a short sentence made of formulas that tells you exactly what goes in and what comes out. And for it to tell the story correctly, it has to be balanced.
Reactants and products
When you mix vinegar and baking soda in a glass, it fizzes intensely: the white powder disappears and a new gas is released. How do we represent, in an orderly way, which substances we had at the start and which ones appeared?
When lighting a gas ring on a cooker, methane ($\text{CH}4$) reacts with oxygen in the air and turns into carbon dioxide and water vapour. The diagram shows the…
When lighting a gas ring on a cooker, methane ($\text{CH}_4$) reacts with oxygen in the air and turns into carbon dioxide and water vapour. The diagram shows the particles of each substance:
Identify the reactants and products of this reaction.
Complete the sentence with the missing words: 'In a chemical equation, the substances that are transformed are called $\dots$ and are written to the $\dots$ of the…
Complete the sentence with the missing words: 'In a chemical equation, the substances that are transformed are called $\dots$ and are written to the $\dots$ of the arrow; the new substances formed are called $\dots$ and are written to the $\dots$.'
Nadia says: 'When paper burns, matter disappears because the ash weighs much less than the original paper.' Is she right? Reason your answer considering all the…
Nadia says: 'When paper burns, matter disappears because the ash weighs much less than the original paper.' Is she right? Reason your answer considering all the substances involved and formed, including gases.
Subscripts and coefficients: they are not the same thing
To count the atoms in a formula with a coefficient, multiply: the coefficient times the subscript of each element. In $2\ \text{H}_2\text{O}$ there are $2 \times 2 = 4$ hydrogen atoms and $2 \times 1 = 2$ oxygen atoms.
Read equation $\text{N}2 + 3\ \text{H}2 \rightarrow 2\ \text{NH}3$ carefully and explain in your own words what it tells us: how many molecules of each substance react…
Read equation $\text{N}_2 + 3\ \text{H}_2 \rightarrow 2\ \text{NH}_3$ carefully and explain in your own words what it tells us: how many molecules of each substance react and how many molecules are formed.
What does the subscript $2$ in $\text{H}2$ mean? And the coefficient $2$ in front of $2\ \text{H}2\text{O}$? Explain in your own words the difference between a subscript…
What does the subscript $2$ in $\text{H}_2$ mean? And the coefficient $2$ in front of $2\ \text{H}_2\text{O}$? Explain in your own words the difference between a subscript and a coefficient.
How many atoms of each element are there in total in $3\ \text{CO}2$? And in $2\ \text{H}2\text{O}$? The figure shows these molecules: Explain how atoms are counted when…
How many atoms of each element are there in total in $3\ \text{CO}_2$? And in $2\ \text{H}_2\text{O}$? The figure shows these molecules:
Explain how atoms are counted when a formula has a coefficient in front of it.
To 'balance' the equation $\text{H}2 + \text{O}2 \rightarrow \text{H}2\text{O}$, a student changes the product and writes…
To 'balance' the equation $\text{H}_2 + \text{O}_2 \rightarrow \text{H}_2\text{O}$, a student changes the product and writes $\text{H}_2 + \text{O}_2 \rightarrow \text{H}_2\text{O}_2$. Explain why this trick is not allowed: what substance $\text{H}_2\text{O}_2$ actually is and what changing a subscript in a formula means.
Why we have to balance: the conservation of mass
If you burn $16\text{ g}$ of methane with $64\text{ g}$ of oxygen in a closed container, the scale reads $80\text{ g}$ before and after. How is it shown, at the scale of atoms, that no mass is gained or lost?
That is the law of conservation of mass (Lavoisier): in a reaction, the total mass of the reactants equals the total mass of the products. The reason: atoms are neither created nor destroyed, they are only rearranged into different molecules.
This explains cases that seem to be deceiving us. When you burn a piece of paper, the ash weighs less, but the paper also combines with oxygen from the air and forms gases (carbon dioxide and water vapor) that escape. If you weighed everything, gases included, the mass would be the same. A candle on a scale works the same way: in open air the gases escape and the reading goes down; under a closed bell jar nothing escapes and the reading barely changes. Matter never just "disappears."
When the system is closed, you can use conservation directly: $12\text{ g}$ of carbon + $32\text{ g}$ of oxygen give $12 + 32 = 44\text{ g}$ of carbon dioxide.
Move the coefficients until the table says "balanced" for every element. Notice that hydrogen and oxygen do not balance at the same time with the same number.
Why must chemical equations be balanced before using them? Name the law on which balancing is based and explain it in a simple sentence about what happens to atoms in a…
Why must chemical equations be balanced before using them? Name the law on which balancing is based and explain it in a simple sentence about what happens to atoms in a reaction.
Count the hydrogen and oxygen atoms on each side of equation $\text{H}2 + \text{O}2 \rightarrow \text{H}2\text{O}$, represented with particles in the figure, and state,…
Count the hydrogen and oxygen atoms on each side of equation $\text{H}_2 + \text{O}_2 \rightarrow \text{H}_2\text{O}$, represented with particles in the figure, and state, without changing it yet, whether it is balanced or not. Justify your answer.
In a closed container, $12\ \text{g}$ of carbon are completely burned with $32\ \text{g}$ of oxygen, forming carbon dioxide. The diagram represents the closed container…
In a closed container, $12\ \text{g}$ of carbon are completely burned with $32\ \text{g}$ of oxygen, forming carbon dioxide. The diagram represents the closed container before and after the reaction:
What mass of carbon dioxide is obtained? Which law allows you to state this without needing to weigh it?
In a closed container, $10\ \text{g}$ of a substance A react completely with $5\ \text{g}$ of a substance B to produce $12\ \text{g}$ of a substance C together with a…
In a closed container, $10\ \text{g}$ of a substance A react completely with $5\ \text{g}$ of a substance B to produce $12\ \text{g}$ of a substance C together with a certain mass of a substance D. The diagram summarises the known masses:
- a) What mass of D has been formed?
- b) Justify your calculation by stating the law you applied.
We place a lit candle on a precision balance in two situations: a) In the open air: the reading on the balance decreases as the candle is consumed. b) Inside an airtight…
We place a lit candle on a precision balance in two situations:
- a) In the open air: the reading on the balance decreases as the candle is consumed.
- b) Inside an airtight glass bell jar: the reading barely changes.
The figure shows the two set-ups:
Explain both results using the law of conservation of mass, and reason whether matter really 'disappears' in either case.
Balancing by trial and error
Balance the equation for the formation of water by inspection: $\text{H}2 + \text{O}2 \rightarrow \text{H}2\text{O}$. Write the coefficients needed for each substance.
Balance the equation for the formation of water by inspection: $\text{H}_2 + \text{O}_2 \rightarrow \text{H}_2\text{O}$. Write the coefficients needed for each substance.
The natural gas in many homes is methane. Balance its combustion by inspection: $\text{CH}4 + \text{O}2 \rightarrow \text{CO}2 + \text{H}2\text{O}$. State the…
The natural gas in many homes is methane. Balance its combustion by inspection: $\text{CH}_4 + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O}$. State the coefficients in the order in which the substances appear.
Ammonia is manufactured industrially from nitrogen and hydrogen and then used to make fertilisers. Balance the equation: $\text{N}2 + \text{H}2 \rightarrow \text{NH}3$.
Ammonia is manufactured industrially from nitrogen and hydrogen and then used to make fertilisers. Balance the equation: $\text{N}_2 + \text{H}_2 \rightarrow \text{NH}_3$.
The magnesium in sparklers and fireworks burns with a very intense white light, forming magnesium oxide. Balance the equation:…
The magnesium in sparklers and fireworks burns with a very intense white light, forming magnesium oxide. Balance the equation: $\text{Mg} + \text{O}_2 \rightarrow \text{MgO}$.
When iron rusts completely, iron(III) oxide is formed. Balance the equation: $\text{Fe} + \text{O}2 \rightarrow \text{Fe}2\text{O}3$. Then check by counting the atoms of…
When iron rusts completely, iron(III) oxide is formed. Balance the equation: $\text{Fe} + \text{O}_2 \rightarrow \text{Fe}_2\text{O}_3$. Then check by counting the atoms of each element on both sides.
The butane in gas cylinders, $\text{C}4\text{H}{10}$, burns with oxygen in the air, forming carbon dioxide and water. a) Balance the equation:…
The butane in gas cylinders, $\text{C}_4\text{H}_{10}$, burns with oxygen in the air, forming carbon dioxide and water.
- a) Balance the equation: $\text{C}_4\text{H}_{10} + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O}$.
- b) Verify, by counting the carbon, hydrogen and oxygen atoms on both sides, that your balanced equation satisfies the conservation of atoms.
Hydrogen peroxide from the first-aid kit, $\text{H}2\text{O}2$, gradually decomposes into water and oxygen. a) Balance the equation:…
Hydrogen peroxide from the first-aid kit, $\text{H}_2\text{O}_2$, gradually decomposes into water and oxygen.
- a) Balance the equation: $\text{H}_2\text{O}_2 \rightarrow \text{H}_2\text{O} + \text{O}_2$.
- b) The bottle of hydrogen peroxide states that it should be kept tightly closed and in a cool, dark place. Relate these instructions to the reaction above and explain what would happen if they were not followed.
What the coefficients mean once balanced
A chemical reaction is not simply mixing. When you mix, the substances stay the same. In a reaction, the bonds in the reactant molecules break, the same atoms regroup in a different way, and they form new molecules, the products. Since no atom appears or disappears, the total number of each element and the mass stay the same.
The balanced equation for the combustion of methane is $\text{CH}4 + 2\ \text{O}2 \rightarrow \text{CO}2 + 2\ \text{H}2\text{O}$. If $5$ methane molecules are burned: a)…
The balanced equation for the combustion of methane is $\text{CH}_4 + 2\ \text{O}_2 \rightarrow \text{CO}_2 + 2\ \text{H}_2\text{O}$. If $5$ methane molecules are burned:
- a) How many oxygen molecules are consumed?
- b) How many carbon dioxide molecules and how many water molecules are formed?
The thin layer that protects aircraft aluminum parts from corrosion is formed when the metal reacts with oxygen in the air. a) Balance the equation:…
The thin layer that protects aircraft aluminum parts from corrosion is formed when the metal reacts with oxygen in the air.
- a) Balance the equation: $\text{Al} + \text{O}_2 \rightarrow \text{Al}_2\text{O}_3$.
- b) Explain why, when balancing by inspection, it is advisable to start with an element that appears in only one substance on each side of the arrow.
The balanced equation for the formation of water is $2\ \text{H}2 + \text{O}2 \rightarrow 2\ \text{H}2\text{O}$. Someone suggests dividing all coefficients by two and…
The balanced equation for the formation of water is $2\ \text{H}_2 + \text{O}_2 \rightarrow 2\ \text{H}_2\text{O}$. Someone suggests dividing all coefficients by two and writing $\text{H}_2 + \frac{1}{2}\ \text{O}_2 \rightarrow \text{H}_2\text{O}$.
- a) Would conservation of atoms still hold?
- b) What is the problem with referring to 'half a molecule' of oxygen?
- c) Justify why, by convention, the coefficients of a balanced equation are the simplest possible integers.
Explain, using the particle model, exactly what happens to atoms in a chemical reaction: what happens to the atoms of the reactants, why their total number does not…
Explain, using the particle model, exactly what happens to atoms in a chemical reaction: what happens to the atoms of the reactants, why their total number does not change, and how a chemical reaction differs from simply mixing substances. Illustrate your explanation with the reaction of hydrogen with oxygen to form water, represented using particles in the figure:
Some rockets use hydrogen as fuel, which burns with oxygen to form water vapour. a) Write the equation for the reaction and balance it. b) If $100$ hydrogen molecules…
Some rockets use hydrogen as fuel, which burns with oxygen to form water vapour.
- a) Write the equation for the reaction and balance it.
- b) If $100$ hydrogen molecules are burned in a ground test, how many oxygen molecules are consumed and how many water molecules are formed?
- c) How many hydrogen atoms are there in total before the reaction? And after? Relate your answer to the law of conservation.
Back to the beginning: the combustion of the methane in your stove is written with the balanced equation $\text{CH}_4 + 2\ \text{O}_2 \rightarrow \text{CO}_2 + 2\ \text{H}_2\text{O}$: for every molecule of methane you need exactly two molecules of oxygen from the air to get one of carbon dioxide and two of water vapor.