Amount of substance: Practice Questions

Which of the following compounds has the highest percentage by mass of nitrogen?
(Relative atomic masses: \(\text{H} = 1.0\), \(\text{C} = 12.0\), \(\text{N} = 14.0\), \(\text{O} = 16.0\))

In an industrial reaction, \(10.0\text{ g}\) of calcium carbonate (\(M_r = 100.1\)) was thermally decomposed to produce calcium oxide (\(M_r = 56.1\)) and carbon dioxide:
\[\text{CaCO}_3\text{(s)} \rightarrow \text{CaO(s)} + \text{CO}_2\text{(g)}\]
The actual mass of calcium oxide obtained was \(4.20\text{ g}\). What is the percentage yield of calcium oxide?

A \(0.685\text{ g}\) sample of an unknown hydrated metal chloride, \(\text{MCl}_2 \cdot 2\text{H}_2\text{O}\), was dissolved in water. Excess acidified silver nitrate solution was added, precipitating all the chloride ions as silver chloride, \(\text{AgCl}\) (\(M_r = 143.4\)).
The precipitate was filtered, dried, and weighed \(0.803\text{ g}\).
What is the relative atomic mass (\(A_r\)) of the metal \(\text{M}\)?
(Relative atomic masses: \(\text{H} = 1.0\), \(\text{O} = 16.0\), \(\text{Cl} = 35.5\))

A compound contains carbon, hydrogen, and oxygen only. It has a percentage composition by mass of \(54.5\%\) carbon and \(9.1\%\) hydrogen, with the remainder being oxygen.
What is the empirical formula of this compound?
(Relative atomic masses: \(\text{H} = 1.0\), \(\text{C} = 12.0\), \(\text{O} = 16.0\))

A \(25.0\text{ cm}^3\) sample of sulfuric acid (\(\text{H}_2\text{SO}_4\)) requires \(30.0\text{ cm}^3\) of \(0.150\text{ mol dm}^{-3}\) sodium hydroxide (\(\text{NaOH}\)) for complete neutralisation.
What is the concentration of the sulfuric acid?

Calculate the mass, in grams, of potassium hydroxide ( ext{KOH}) needed to prepare exactly \(250.0\text{ cm}^3\) of a \(0.0800\text{ mol dm}^{-3}\) solution.
(\(A_r\) values: \(\text{K} = 39.1\), \(\text{O} = 16.0\), \(\text{H} = 1.0\))

A \(50.0\text{ cm}^3\) sample of a \(0.200\text{ mol dm}^{-3}\) barium chloride solution is mixed with excess sodium sulfate solution to precipitate barium sulfate according to the equation:
\[\text{Ba}^{2+}(\text{aq}) + \text{SO}_4^{2-}(\text{aq}) \rightarrow \text{BaSO}_4(\text{s})\]
Calculate the mass, in grams, of dry \(\text{BaSO}_4\) formed.
(Relative formula mass of \(\text{BaSO}_4 = 233.4\))

A \(0.500 \text{ g}\) sample of a group 2 metal carbonate, \(MCO_3\), reacts with excess hydrochloric acid to produce \(140 \text{ cm}^3\) of carbon dioxide gas at \(298 \text{ K}\) and \(100 \text{ kPa}\). Calculate the relative atomic mass of the metal \(M\). (\(R = 8.31 \text{ J K}^{-1} \text{ mol}^{-1}\))

A student carries out a neutralisation reaction between hydrochloric acid and calcium hydroxide.

The balanced equation for the reaction is:
\(2\text{HCl(aq)} + \text{Ca(OH)}_2\text{(aq)} \rightarrow \text{CaCl}_2\text{(aq)} + 2\text{H}_2\text{O(l)}\)

(a) Define the term relative formula mass (\(M_r\)).

(b) Calculate the relative formula mass (\(M_r\)) of calcium hydroxide, \(\text{Ca(OH)}_2\).
(Relative atomic masses: \(\text{H} = 1.0\), \(\text{O} = 16.0\), \(\text{Ca} = 40.1\))

(c) Calculate the amount, in moles, of \(\text{HCl}\) required to react completely with \(0.0250\text{ mol}\) of \(\text{Ca(OH)}_2\).

(d) Calculate the volume, in \(\text{cm}^3\), of a \(0.500\text{ mol dm}^{-3}\) solution of \(\text{HCl}\) containing this amount of \(\text{HCl}\).

A student synthesised hydrated iron(II) ammonium sulfate crystals, \((\text{NH}_4)_2\text{Fe}(\text{SO}_4)_2 \cdot 6\text{H}_2\text{O}\).

A sample of \(1.176\text{ g}\) of these crystals was dissolved in dilute sulfuric acid and made up to exactly \(100.0\text{ cm}^3\) in a volumetric flask.
A \(25.00\text{ cm}^3\) sample of this solution was titrated against a \(0.0150\text{ mol dm}^{-3}\) potassium dichromate(VI) solution, \(\text{K}_2\text{Cr}_2\text{O}_7\).
The titration required \(8.33\text{ cm}^3\) of the \(\text{K}_2\text{Cr}_2\text{O}_7\) solution to reach the end point.

The overall ionic equation for the titration is:
\[6\text{Fe}^{2+}(\text{aq}) + \text{Cr}_2\text{O}_7^{2-}(\text{aq}) + 14\text{H}^+(\text{aq}) \rightarrow 6\text{Fe}^{3+}(\text{aq}) + 2\text{Cr}^{3+}(\text{aq}) + 7\text{H}_2\text{O}(\text{l})\]

(a) Calculate the amount, in moles, of \(\text{Cr}_2\text{O}_7^{2-}\) used in the titration.
(b) Calculate the amount, in moles, of \(\text{Fe}^{2+}\) present in the \(25.00\text{ cm}^3\) sample.
(c) Calculate the total mass of \((\text{NH}_4)_2\text{Fe}(\text{SO}_4)_2 \cdot 6\text{H}_2\text{O}\) present in the original sample.
(\(\text{Relative formula mass of } (\text{NH}_4)_2\text{Fe}(\text{SO}_4)_2 \cdot 6\text{H}_2\text{O} = 392.0\))
(d) Calculate the percentage purity of the synthesised sample.