An engineer designing a reactor does not work with individual molecules; they work with tonnes. A balanced equation, on its own, only gives a ratio of particles: $1$ molecule of methane for every $2$ of oxygen. Turning that abstract ratio into the kilograms that have to be bought or that will come out of the chimney requires an essential intermediate step: the mole.
Molar mass: the bridge between the balance and the particle counter
If you put $12\text{ g}$ of carbon on one balance and $12\text{ g}$ of magnesium on another, both show the same mass, but since a magnesium atom weighs twice as much as a carbon atom, the second pan contains exactly half as many atoms: how can we count the particles of a substance simply by weighing it?
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The balanced equation for the combustion of methane, $\text{CH}4 + 2\ \text{O}2 \rightarrow \text{CO}2 + 2\ \text{H}2\text{O}$, can also be read in moles. a) How many…
The balanced equation for the combustion of methane, $\text{CH}_4 + 2\ \text{O}_2 \rightarrow \text{CO}_2 + 2\ \text{H}_2\text{O}$, can also be read in moles.
a) How many moles of oxygen are needed to burn $3\ \text{mol}$ of methane?
b) How many moles of carbon dioxide and how many of water are formed then?
The glucose used by your muscles when playing sport has the formula $\text{C}6\text{H}{12}\text{O}6$. Calculate its molar mass and explain in a sentence what this value…
The glucose used by your muscles when playing sport has the formula $\text{C}_6\text{H}_{12}\text{O}_6$. Calculate its molar mass and explain in a sentence what this value means (atomic masses: $\text{H} = 1\ \text{u}$; $\text{C} = 12\ \text{u}$; $\text{O} = 16\ \text{u}$).
A glass contains $36\ \text{g}$ of water. Knowing that the molar mass of water is $18\ \text{g/mol}$, calculate how many moles of water are in the glass.
A glass contains $36\ \text{g}$ of water. Knowing that the molar mass of water is $18\ \text{g/mol}$, calculate how many moles of water are in the glass.
A flask contains $0,5\ \text{mol}$ of carbon dioxide. Knowing that the molar mass of $\text{CO}2$ is $44\ \text{g/mol}$, calculate the mass of gas contained in the flask.
A flask contains $0,5\ \text{mol}$ of carbon dioxide. Knowing that the molar mass of $\text{CO}_2$ is $44\ \text{g/mol}$, calculate the mass of gas contained in the flask.
In a barbecue, $12\ \text{g}$ of carbon burns according to the equation $\text{C} + \text{O}2 \rightarrow \text{CO}2$. Calculate, by converting through moles, what mass…
In a barbecue, $12\ \text{g}$ of carbon burns according to the equation $\text{C} + \text{O}_2 \rightarrow \text{CO}_2$. Calculate, by converting through moles, what mass of carbon dioxide is formed (atomic masses: $\text{C} = 12\ \text{u}$; $\text{O} = 16\ \text{u}$).
A home boiler burns $16\ \text{g}$ of methane according to the equation $\text{CH}4 + 2\ \text{O}2 \rightarrow \text{CO}2 + 2\ \text{H}2\text{O}$. Calculate, by…
A home boiler burns $16\ \text{g}$ of methane according to the equation $\text{CH}_4 + 2\ \text{O}_2 \rightarrow \text{CO}_2 + 2\ \text{H}_2\text{O}$. Calculate, by converting through moles:
The method does not change with enormous quantities: you just have to watch the units. But real raw material is almost never pure: a piece of limestone may contain impurities that do not react, and only the pure fraction counts in the stoichiometric calculation.
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In a lime kiln, $100\ \text{g}$ of calcium carbonate decomposes according to the equation $\text{CaCO}3 \rightarrow \text{CaO} + \text{CO}2$. Calculate, by converting…
In a lime kiln, $100\ \text{g}$ of calcium carbonate decomposes according to the equation $\text{CaCO}_3 \rightarrow \text{CaO} + \text{CO}_2$. Calculate, by converting through moles, the mass of quicklime ($\text{CaO}$) obtained (molar masses: $\text{CaCO}_3 = 100\ \text{g/mol}$; $\text{CaO} = 56\ \text{g/mol}$).
A steel part containing $56\ \text{g}$ of iron oxidises completely according to the equation $4\ \text{Fe} + 3\ \text{O}2 \rightarrow 2\ \text{Fe}2\text{O}3$. Calculate,…
A steel part containing $56\ \text{g}$ of iron oxidises completely according to the equation $4\ \text{Fe} + 3\ \text{O}_2 \rightarrow 2\ \text{Fe}_2\text{O}_3$. Calculate, by converting through moles, the mass of iron(III) oxide formed (molar masses: $\text{Fe} = 56\ \text{g/mol}$; $\text{Fe}_2\text{O}_3 = 160\ \text{g/mol}$).
An electrolysis apparatus decomposes $90\ \text{g}$ of water according to the equation $2\ \text{H}2\text{O} \rightarrow 2\ \text{H}2 + \text{O}2$. Calculate, by…
An electrolysis apparatus decomposes $90\ \text{g}$ of water according to the equation $2\ \text{H}_2\text{O} \rightarrow 2\ \text{H}_2 + \text{O}_2$. Calculate, by converting through moles:
In a container, $10\ \text{g}$ of hydrogen is mixed with $64\ \text{g}$ of oxygen and a spark is ignited: $2\ \text{H}2 + \text{O}2 \rightarrow 2\ \text{H}2\text{O}$.…
In a container, $10\ \text{g}$ of hydrogen is mixed with $64\ \text{g}$ of oxygen and a spark is ignited: $2\ \text{H}_2 + \text{O}_2 \rightarrow 2\ \text{H}_2\text{O}$. The diagram summarises the experiment data:
a) Calculate the moles of each reactant and deduce which one is in excess.
b) What mass of water is formed?
c) What mass of excess reactant remains unreacted?
A reactor aims to produce $34\ \text{g}$ of ammonia according to the equation $\text{N}2 + 3\ \text{H}2 \rightarrow 2\ \text{NH}3$. Calculate, by converting through…
A reactor aims to produce $34\ \text{g}$ of ammonia according to the equation $\text{N}_2 + 3\ \text{H}_2 \rightarrow 2\ \text{NH}_3$. Calculate, by converting through moles, the minimum mass of hydrogen that must be fed in (molar masses: $\text{H}_2 = 2\ \text{g/mol}$; $\text{NH}_3 = 17\ \text{g/mol}$).
Back to the beginning: To burn $1\text{ kg}$ of methane ($16\text{ g/mol}$, $62{,}5\text{ mol}$), the $1:2$ ratio requires $125\text{ mol}$ of $\text{O}_2$ ($32\text{ g/mol}$): the engineer must supply exactly $4\text{ kg}$ of oxygen for every kilogram of gas.
Summary
Let's practice! 8 medium exercises in this section