Exercises: Stoichiometric calculations

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.

1. a) How many moles of oxygen are needed to burn $3\ \text{mol}$ of methane?
2. b) How many moles of carbon dioxide and how many of water are formed then?

The glucose used by your muscles when playing sports 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 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.

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:

1. a) How many moles of oxygen are consumed?
2. b) How many moles of water are formed?

In the synthesis of ammonia, $\text{N}_2 + 3\ \text{H}_2 \rightarrow 2\ \text{NH}_3$, $6\ \text{mol}$ of hydrogen reacts with sufficient nitrogen.

1. a) How many moles of nitrogen are consumed?
2. b) How many moles of ammonia are obtained?

At 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 moles, the mass of water vapor formed (molar masses: $\text{H}_2 = 2\ \text{g/mol}$; $\text{H}_2\text{O} = 18\ \text{g/mol}$).

A home furnace 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:

1. a) The mass of oxygen it consumes.
2. b) The mass of carbon dioxide it emits.

(molar masses: $\text{CH}_4 = 16\ \text{g/mol}$; $\text{O}_2 = 32\ \text{g/mol}$; $\text{CO}_2 = 44\ \text{g/mol}$).

You want to obtain $90\ \text{g}$ of water by reacting hydrogen with oxygen according to the equation $2\ \text{H}_2 + \text{O}_2 \rightarrow 2\ \text{H}_2\text{O}$. Calculate, by converting through moles, what mass of oxygen is needed (molar masses: $\text{O}_2 = 32\ \text{g/mol}$; $\text{H}_2\text{O} = 18\ \text{g/mol}$).

A chemical plant reacts $28\ \text{g}$ of nitrogen with excess hydrogen according to the equation $\text{N}_2 + 3\ \text{H}_2 \rightarrow 2\ \text{NH}_3$. Calculate, by converting through moles, the mass of ammonia obtained (molar masses: $\text{N}_2 = 28\ \text{g/mol}$; $\text{NH}_3 = 17\ \text{g/mol}$).

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 sparkler burns $12\ \text{g}$ of magnesium according to the equation $2\ \text{Mg} + \text{O}_2 \rightarrow 2\ \text{MgO}$. Calculate, by converting through moles, the mass of magnesium oxide formed (molar masses: $\text{Mg} = 24\ \text{g/mol}$; $\text{MgO} = 40\ \text{g/mol}$).

A steel part containing $56\ \text{g}$ of iron oxidizes 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: $\text{Fe} = 56\ \text{g/mol}$; $\text{Fe}_2\text{O}_3 = 160\ \text{g/mol}$).

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: $\text{H}_2 = 2\ \text{g/mol}$; $\text{NH}_3 = 17\ \text{g/mol}$).

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:

1. a) The mass of hydrogen obtained.
2. b) The mass of oxygen released.

(molar masses: $\text{H}_2\text{O} = 18\ \text{g/mol}$; $\text{H}_2 = 2\ \text{g/mol}$; $\text{O}_2 = 32\ \text{g/mol}$).

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 summarizes the experiment data:

1. a) Calculate the moles of each reactant and deduce which one is in excess.
2. b) What mass of water is formed?
3. c) What mass of excess reactant remains unreacted?

(molar masses: $\text{H}_2 = 2\ \text{g/mol}$; $\text{O}_2 = 32\ \text{g/mol}$; $\text{H}_2\text{O} = 18\ \text{g/mol}$).

$14\ \text{g}$ of nitrogen and $6\ \text{g}$ of hydrogen are introduced into a reactor to produce ammonia: $\text{N}_2 + 3\ \text{H}_2 \rightarrow 2\ \text{NH}_3$.

1. a) Calculate the moles of each reactant and deduce which one is used up first.
2. b) What mass of ammonia is obtained?
3. c) What mass of the other reactant is left over?

(molar masses: $\text{N}_2 = 28\ \text{g/mol}$; $\text{H}_2 = 2\ \text{g/mol}$; $\text{NH}_3 = 17\ \text{g/mol}$).

A quarry supplies a lime factory with limestone containing $80\ \%$ calcium carbonate (the remainder is unreactive impurities). $250\ \text{g}$ of this rock is loaded into the kiln: $\text{CaCO}_3 \rightarrow \text{CaO} + \text{CO}_2$. The bar shows the composition of the rock:

1. a) What mass of calcium carbonate actually enters the kiln?
2. b) Calculate, by converting through moles, the mass of quicklime ($\text{CaO}$) obtained.

(molar masses: $\text{CaCO}_3 = 100\ \text{g/mol}$; $\text{CaO} = 56\ \text{g/mol}$).

When calcining $100\ \text{g}$ of pure calcium carbonate, $\text{CaCO}_3 \rightarrow \text{CaO} + \text{CO}_2$, theory states that $56\ \text{g}$ of quicklime should be obtained. However, a real kiln has only produced $42\ \text{g}$, as compared by the bars in the figure.

1. a) Calculate the percentage yield of the kiln.
2. b) Propose a reason explaining why the kiln does not reach $100\ \%$.

According to equation $\text{N}_2 + 3\ \text{H}_2 \rightarrow 2\ \text{NH}_3$, $28\ \text{g}$ of nitrogen should yield $34\ \text{g}$ of ammonia. In a real reactor, only $20.4\ \text{g}$ has been collected.

1. a) Calculate the percent yield of the reaction.
2. b) Explain two reasons why a factory might not achieve the theoretical yield of $100\ \%$.

In a furnace, $32\ \text{g}$ of methane is burned with $96\ \text{g}$ of oxygen: $\text{CH}_4 + 2\ \text{O}_2 \rightarrow \text{CO}_2 + 2\ \text{H}_2\text{O}$.

1. a) Calculate the moles of each reactant and deduce which one is the limiting reactant.
2. b) What mass of carbon dioxide is emitted?
3. c) What mass of oxygen is left over?

(molar masses: $\text{CH}_4 = 16\ \text{g/mol}$; $\text{O}_2 = 32\ \text{g/mol}$; $\text{CO}_2 = 44\ \text{g/mol}$).

A steel mill receives iron ore with $80\ \%$ iron(III) oxide (the remainder is inert gangue). In the blast furnace, the oxide reacts according to $\text{Fe}_2\text{O}_3 + 3\ \text{CO} \rightarrow 2\ \text{Fe} + 3\ \text{CO}_2$. $200\ \text{g}$ of ore is loaded:

1. a) What mass of $\text{Fe}_2\text{O}_3$ does that charge contain?
2. b) Calculate, by converting through moles, the mass of iron obtained.

(molar masses: $\text{Fe}_2\text{O}_3 = 160\ \text{g/mol}$; $\text{Fe} = 56\ \text{g/mol}$).

Compare the oxygen required by two gaseous fuels. On the one hand, the combustion of methane: $\text{CH}_4 + 2\ \text{O}_2 \rightarrow \text{CO}_2 + 2\ \text{H}_2\text{O}$; on the other, that of propane: $\text{C}_3\text{H}_8 + 5\ \text{O}_2 \rightarrow 3\ \text{CO}_2 + 4\ \text{H}_2\text{O}$.

1. a) Calculate the mass of oxygen required to burn $16\ \text{g}$ of methane.
2. b) Calculate the mass of oxygen required to burn $44\ \text{g}$ of propane.
3. c) Express both results in grams of oxygen per gram of fuel and reason, looking at the formulas of the two gases, why the one with a higher proportion of hydrogen in its molecule consumes more oxygen per gram.

(molar masses: $\text{CH}_4 = 16\ \text{g/mol}$; $\text{C}_3\text{H}_8 = 44\ \text{g/mol}$; $\text{O}_2 = 32\ \text{g/mol}$).