An engineer designing a boiler needs to know, in grams, how much oxygen is required to burn the fuel and how much carbon dioxide will come out of the chimney. The balanced equation on its own does not give grams: it gives a ratio of molecules. The bridge between what you weigh on the balance and what the equation counts is the mole.
The molar ratio: reading the coefficients directly
When measuring the volumes of gas in the formation of water, $2\ \text{L}$ of hydrogen react exactly with $1\ \text{L}$ of oxygen, but by mass they combine in a proportion of $2\ \text{g}$ of hydrogen for every $16\ \text{g}$ of oxygen. Why do chemical substances combine in simple ratios of particles and not of grams?
Balance this equation using the interactive and, once it is balanced, read its coefficients as moles: how many moles of hydrogen are needed for every mole of nitrogen?
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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 equation for the formation of water is $2\ \text{H}2 + \text{O}2 \rightarrow 2\ \text{H}2\text{O}$. If $4\ \text{mol}$ of hydrogen is completely burned: a) How many…
The equation for the formation of water is $2\ \text{H}_2 + \text{O}_2 \rightarrow 2\ \text{H}_2\text{O}$. If $4\ \text{mol}$ of hydrogen is completely burned:
A dozen large eggs weighs about $750\ \text{g}$, whereas a dozen lentils barely reaches $0{,}5\ \text{g}$, even though both groups contain exactly twelve items. If a mole always contains the same fixed number of particles, why does a mole of water weigh $18\ \text{g}$ and a mole of glucose weigh $180\ \text{g}$?
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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: $\text{C} = 12\ \text{u}$; $\text{O} = 16\ \text{u}$).
An amateur rocket burns $4\ \text{g}$ of hydrogen according to the equation $2\ \text{H}2 + \text{O}2 \rightarrow 2\ \text{H}2\text{O}$. Calculate, by converting through…
An amateur rocket burns $4\ \text{g}$ of hydrogen according to the equation $2\ \text{H}_2 + \text{O}_2 \rightarrow 2\ \text{H}_2\text{O}$. Calculate, by converting through moles, the mass of water vapour formed (molar masses: $\text{H}_2 = 2\ \text{g/mol}$; $\text{H}_2\text{O} = 18\ \text{g/mol}$).
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 even if the quantities are enormous: you just have to watch the units (kilograms, tonnes) before converting to moles.
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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 start: If the engineer burns $160\ \text{g}$ of methane ($\text{CH}_4$, $10\ \text{mol}$), they will need $20\ \text{mol}$ of $\text{O}_2$ ($640\ \text{g}$) and know that $10\ \text{mol}$ of $\text{CO}_2$, equivalent to $440\ \text{g}$, will be released through the chimney.
Summary
Let's practice! 8 medium exercises in this section