Quantitative calculations in everyday life

Calculate the percentage composition of water, $\text{H}_2\text{O}$ (atomic masses: $\text{H} = 1\ \text{u}$; $\text{O} = 16\ \text{u}$). Check that the two percentages add up to $100\ \%$.

Ammonia, $\text{NH}_3$, is the raw material for the nitrogenous fertiliser industry. Calculate its mass percentage of nitrogen (atomic masses: $\text{N} = 14\ \text{u}$; $\text{H} = 1\ \text{u}$).

The marble used in worktops is calcium carbonate, $\text{CaCO}_3$. Calculate its percentage composition (atomic masses: $\text{Ca} = 40\ \text{u}$; $\text{C} = 12\ \text{u}$; $\text{O} = 16\ \text{u}$).

A bag of fertiliser from an agricultural warehouse has the label "NPK $15$-$15$-$15$" printed on it, indicating $15\ \%$ by mass of nitrogen, $15\ \%$ of phosphorus(V) oxide, and $15\ \%$ of potassium oxide.

1. a) Explain what the three numbers on the label mean.
2. b) If the bag contains $20\ \text{kg}$ of fertiliser, how many kilograms of each nutrient does it provide?

An iron ore arrives at the steelworks with a purity of $80\ \%$ in iron(III) oxide.

1. a) How many kilograms of iron(III) oxide are in $50\ \text{kg}$ of ore?
2. b) What does the remaining $20\ \%$ refer to?

A mine supplies an iron ore with a purity of $80\ \%$ iron(III) oxide, $\text{Fe}_2\text{O}_3$ (atomic masses: $\text{Fe} = 56\ \text{u}$; $\text{O} = 16\ \text{u}$).

1. a) Calculate the percentage by mass of iron in the pure oxide.
2. b) How many kilograms of iron can be obtained, at most, from one tonne ($1\,000\ \text{kg}$) of this ore?

Glucose has the molecular formula $\text{C}_6\text{H}_{12}\text{O}_6$.

1. a) What is its empirical formula? Explain what information each of the two formulas gives.
2. b) Give an example of a compound whose empirical and molecular formulas coincide and explain why this occurs.

The analysis of a laboratory moisturiser shows a percentage composition of $40,0\ \%$ of carbon, $6,7\ \%$ of hydrogen, and $53,3\ \%$ of oxygen (atomic masses: $\text{C} = 12\ \text{u}$; $\text{H} = 1\ \text{u}$; $\text{O} = 16\ \text{u}$).

1. a) Calculate the moles of each element present in $100\ \text{g}$ of the compound.
2. b) Deduce its empirical formula.

Vitamin C (ascorbic acid) in food supplements has a percentage composition of $40,9\ \%$ carbon, $4,5\ \%$ hydrogen and $54,5\ \%$ oxygen, and its molar mass is $176\ \text{g/mol}$ (atomic masses: $\text{C} = 12\ \text{u}$; $\text{H} = 1\ \text{u}$; $\text{O} = 16\ \text{u}$).

1. a) Determine its empirical formula. Hint: if the molar ratios are not integers, multiply them all by the same number until you get simple integers.
2. b) Determine its molecular formula.
3. c) A tablet contains $500\ \text{mg}$ of vitamin C: how many moles of vitamin C is this? Express the result to three significant figures.

A gaseous hydrocarbon has a percentage composition of $85,7\ \%$ carbon and $14,3\ \%$ hydrogen, and its molar mass is $42\ \text{g/mol}$ (atomic masses: $\text{C} = 12\ \text{u}$; $\text{H} = 1\ \text{u}$).

1. a) Determine its empirical formula.
2. b) Determine its molecular formula. What additional piece of data was needed compared to the previous part?

A liquid hydrocarbon found in petrol has a percentage composition of $85,7\ \%$ carbon and $14,3\ \%$ hydrogen, and its molar mass is $70\ \text{g/mol}$ (atomic masses: $\text{C} = 12\ \text{u}$; $\text{H} = 1\ \text{u}$).

1. a) Determine its empirical formula and the molar mass of that empirical formula.
2. b) Determine its molecular formula and check that it is consistent with the given molar mass.
3. c) Explain why percentage analysis alone can never distinguish between two compounds with the same empirical formula.

A gas sold in cylinders for cooking has a density of $1,96\ \text{g/L}$ at standard temperature and pressure (molar volume under these conditions: $22,4\ \text{L/mol}$) and a percentage composition of $81,8\ \%$ carbon and $18,2\ \%$ hydrogen (atomic masses: $\text{C} = 12\ \text{u}$; $\text{H} = 1\ \text{u}$).

1. a) Calculate its molar mass from the density and the molar volume.
2. b) Determine its empirical formula.
3. c) Determine its molecular formula and identify which gas it is.