Balancing Chemical Equations
In your kitchen at home, the LP gas in the stove burns and the flame heats the tortillas. If you could weigh all the gas, all the oxygen, and everything that comes out (CO₂ and water vapor), the total mass would be the same. How do you write that in a chemical equation, and how do you know the equation is "balanced"?
Conservation of atoms: coefficients and subscripts
If you burn $10\ \text{g}$ of steel wool inside a sealed flask on a scale, the needle doesn't move. On an open dish, the residue weighs more because it picks up oxygen from the air. Matter doesn't appear out of nowhere: everything that goes in and comes out is accounted for.
To tell whether an equation is balanced, count the atoms of each element on both sides: the coefficient multiplies all the subscripts in its formula. For example, $4\ \text{Al} + 3\ \text{O}_2 \rightarrow 2\ \text{Al}_2\text{O}_3$ has $4$ Al and $6$ O on the left, and $2 \times 2 = 4$ Al and $2 \times 3 = 6$ O on the right.
Count the atoms of each element on both sides of equation $\text{CH}4 + \text{O}2 \rightarrow \text{CO}2 + \text{H}2\text{O}$, as it is written. The figure shows it…
Count the atoms of each element on both sides of equation $\text{CH}_4 + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O}$, as it is written. The figure shows it using the particle model:
Reason whether it is balanced or not. If it is not, state which elements fail.
The thin layer that protects the aluminum parts of an aeroplane from the air is aluminum oxide. The figure shows the particles involved: Check, by counting the atoms of…
The thin layer that protects the aluminum parts of an aeroplane from the air is aluminum oxide. The figure shows the particles involved:
Check, by counting the atoms of each element on both sides, whether this equation is balanced: $4\ \text{Al} + 3\ \text{O}_2 \rightarrow 2\ \text{Al}_2\text{O}_3$.
Balancing by trial and error
In simple equations it's enough to "keep trying," but with three or four substances an order helps so you don't undo what you've already done.
Hydrochloric acid is obtained industrially by reacting gaseous hydrogen and chlorine. Balance the equation: $\text{H}2 + \text{Cl}2 \rightarrow \text{HCl}$.
Hydrochloric acid is obtained industrially by reacting gaseous hydrogen and chlorine. Balance the equation: $\text{H}_2 + \text{Cl}_2 \rightarrow \text{HCl}$.
Metallic calcium reacts with oxygen in the air to form calcium oxide, quicklime. Balance the equation: $\text{Ca} + \text{O}2 \rightarrow \text{CaO}$.
Metallic calcium reacts with oxygen in the air to form calcium oxide, quicklime. Balance the equation: $\text{Ca} + \text{O}_2 \rightarrow \text{CaO}$.
In the laboratory, oxygen can be obtained by heating potassium chlorate, which decomposes into potassium chloride and oxygen. Balance the equation:…
In the laboratory, oxygen can be obtained by heating potassium chlorate, which decomposes into potassium chloride and oxygen. Balance the equation: $\text{KClO}_3 \rightarrow \text{KCl} + \text{O}_2$.
Several substances: order avoids backtracking
The more substances there are, the easier it is to unbalance something you've already balanced. Following the order (metals, other nonmetals, H, O) reduces backtracking.
Algebraic method (supplement)
When trial and error gets tangled, assign a letter to each coefficient and set up one equation per element. For $a\ \text{Al} + b\ \text{HCl} \rightarrow c\ \text{AlCl}_3 + d\ \text{H}_2$: Al: $a = c$; Cl: $b = 3c$; H: $b = 2d$. If $c = 2$, then $a = 2$, $b = 6$, $d = 3$, the same result as before.
When a piece of aluminum is dropped into a test tube with hydrochloric acid, dissolved aluminum chloride and hydrogen bubbles are formed. Balance the equation:…
When a piece of aluminum is dropped into a test tube with hydrochloric acid, dissolved aluminum chloride and hydrogen bubbles are formed. Balance the equation: $\text{Al} + \text{HCl} \rightarrow \text{AlCl}_3 + \text{H}_2$.
When baking a cake, the sodium hydrogen carbonate in the baking powder decomposes with heat into sodium carbonate, water and the carbon dioxide that makes the dough…
When baking a cake, the sodium hydrogen carbonate in the baking powder decomposes with heat into sodium carbonate, water and the carbon dioxide that makes the dough rise. Balance the equation: $\text{NaHCO}_3 \rightarrow \text{Na}_2\text{CO}_3 + \text{H}_2\text{O} + \text{CO}_2$.
To weld railway tracks, the thermite reaction is used: aluminum powder mixed with iron(III) oxide reacts, giving off so much heat that the iron formed remains molten. a)…
To weld railway tracks, the thermite reaction is used: aluminum powder mixed with iron(III) oxide reacts, giving off so much heat that the iron formed remains molten.
- a) Balance the equation: $\text{Al} + \text{Fe}_2\text{O}_3 \rightarrow \text{Al}_2\text{O}_3 + \text{Fe}$.
- b) Explain why it is convenient to balance iron and aluminum first and leave oxygen until the end.
Fractional coefficients and the smallest whole numbers
Ethane, $\text{C}2\text{H}6$, accompanies methane in natural gas. a) Balance its combustion, $\text{C}2\text{H}6 + \text{O}2 \rightarrow \text{CO}2 + \text{H}2\text{O}$,…
Ethane, $\text{C}_2\text{H}_6$, accompanies methane in natural gas.
- a) Balance its combustion, $\text{C}_2\text{H}_6 + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O}$, keeping the coefficient of ethane equal to $1$ for now: you will find that the coefficient for oxygen turns out to be a fraction.
- b) Then multiply all the coefficients by the appropriate number to write the equation with the lowest possible integer coefficients.
Oxy-acetylene torches in workshops burn acetylene, $\text{C}2\text{H}2$, with oxygen and reach about $3\,000\ \celsius$. a) Balance the combustion equation:…
Oxy-acetylene torches in workshops burn acetylene, $\text{C}_2\text{H}_2$, with oxygen and reach about $3\,000\ \celsius$.
- a) Balance the combustion equation: $\text{C}_2\text{H}_2 + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O}$.
- b) If a fraction appeared while balancing it, explain how to convert the balanced equation into lowest integer coefficients and write the final equation.
When balancing the combustion of propane, a student wrote: $2\ \text{C}3\text{H}8 + 10\ \text{O}2 \rightarrow 6\ \text{CO}2 + 8\ \text{H}2\text{O}$. a) Check, by…
When balancing the combustion of propane, a student wrote: $2\ \text{C}_3\text{H}_8 + 10\ \text{O}_2 \rightarrow 6\ \text{CO}_2 + 8\ \text{H}_2\text{O}$.
- a) Check, by counting atoms, that their equation respects the conservation of atoms.
- b) Even so, the teacher marks it as "could be improved". Explain what it means that the coefficients must be the lowest possible integers and rewrite the equation correctly.
The equation in moles and hydrocarbons
Let's generalize the balancing of a complete combustion to any hydrocarbon $\text{C}_x\text{H}_y$.
Read backward, the equation lets you deduce an unknown formula: if you know the products of a balanced combustion, you count back the C and H atoms of the fuel.
Back to the beginning: in the stove, LP gas (propane and butane) burns with $\text{O}_2$ and produces $\text{CO}_2$ and $\text{H}_2\text{O}$. The balanced equation shows how many moles of oxygen each mole of gas uses up, and the atoms that go in are the same ones that come out.
The industrial synthesis of ammonia is written as $\text{N}2 + 3\ \text{H}2 \rightarrow 2\ \text{NH}3$, as shown in the figure using the particle model: Interpret it in…
The industrial synthesis of ammonia is written as $\text{N}_2 + 3\ \text{H}_2 \rightarrow 2\ \text{NH}_3$, as shown in the figure using the particle model:
Interpret it in two ways:
- a) Using molecules: how many molecules of nitrogen and hydrogen react and how many molecules of ammonia are formed.
- b) Using moles: how many moles of each gas are consumed when $2\ \text{mol}$ of ammonia are formed.
In the complete combustion of an unknown hydrocarbon $\text{X}$, the balanced equation is: $2\ \text{X} + 9\ \text{O}2 \rightarrow 6\ \text{CO}2 + 6\ \text{H}2\text{O}$.…
In the complete combustion of an unknown hydrocarbon $\text{X}$, the balanced equation is: $2\ \text{X} + 9\ \text{O}_2 \rightarrow 6\ \text{CO}_2 + 6\ \text{H}_2\text{O}$. The figure represents it using the particle model (one molecule of each type):
- a) Deduce, by counting the carbon and hydrogen atoms that must appear in the products, the molecular formula of $\text{X}$.
- b) Write the complete equation using the formula found.
The complete combustion of any hydrocarbon $\text{C}x\text{H}y$ follows the same pattern. a) Write the balanced general equation in terms of $x$ and $y$:…
The complete combustion of any hydrocarbon $\text{C}_x\text{H}_y$ follows the same pattern.
- a) Write the balanced general equation in terms of $x$ and $y$: $\text{C}_x\text{H}_y + \left(x + \frac{y}{4}\right)\ \text{O}_2 \rightarrow x\ \text{CO}_2 + \frac{y}{2}\ \text{H}_2\text{O}$, and justify it by counting atoms.
- b) Apply it to predict how many $\text{O}_2$ molecules are needed to burn one molecule of heptane, $\text{C}_7\text{H}_{16}$, a component of gasoline, and verify the result by balancing its combustion equation.