IChO 1972 · Theory problem 2

Mixture of iron and iron oxides

A mixture of metallic iron with freshly prepared iron (II) and iron (III) oxides was heated in a closed vessel in the atmosphere of hydrogen. An amount of 4.72 g of the mixture when reacted, yields 3.92 g of iron and 0.90 g of water.

When the same amount of the mixture was allowed to react with an excess of a copper(II) sulphate solution, 4.96 g of a solid mixture were obtained.

Problems:

2.1 Calculate the amount of 7.3 % hydrochloric acid (\(\rho = 1.03\ \mathrm{g\,cm^{-3}}\)) which is needed for a total dissolution of 4.72 g of the starting mixture.

2.2 What volume of a gas at STP is released?

Relative atomic masses:

\(A_r(\ce{O}) = 16;\quad A_r(\ce{S}) = 32;\quad A_r(\ce{Cl}) = 35.5;\quad A_r(\ce{Fe}) = 56;\quad A_r(\ce{Cu}) = 64\)

Official English text of the problem.

Answers

  • 2.1: 70 g of 7.3 % hydrochloric acid solution, corresponding to approximately \(68\ \mathrm{cm^3}\).
  • 2.2: Hydrogen, \(\ce{H2}\), SMILES [H][H]: \(0.448\ \mathrm{dm^3}\) at STP, or approximately \(0.45\ \mathrm{L}\).

Solution

2.1. Composition of the mixture and acid requirement

Let the initial amounts of metallic iron, iron(II) oxide \(\ce{FeO}\), and iron(III) oxide \(\ce{Fe2O3}\) be \(x,y,z\) mol, respectively.

The oxides can be represented compositionally by the ionic SMILES [Fe+2].[O-2] and [Fe+3].[Fe+3].[O-2].[O-2].[O-2]. These represent formal ion proportions, not their crystal structures.

Hydrogen reduces both oxides to iron, producing water, \(\ce{H2O}\), SMILES O:

\[ \ce{FeO + H2 -> Fe + H2O} \]

\[ \ce{Fe2O3 + 3H2 -> 2Fe + 3H2O}. \]

The total amount of iron atoms is therefore

\[ x+y+2z=\frac{3.92}{56}=0.0700\ \mathrm{mol}. \]

The water yield gives the initial amount of oxygen atoms:

\[ y+3z=\frac{0.90}{18}=0.0500\ \mathrm{mol}. \]

This agrees with the mass lost by the solid:

\[ 4.72-3.92=0.80\ \mathrm{g} =0.0500\ \mathrm{mol}\times16\ \mathrm{g\,mol^{-1}}. \]

In the copper(II) sulphate experiment, metallic iron dissolves while an equimolar amount of copper is deposited. The net ionic equation is

\[ \ce{Fe + Cu^2+ -> Fe^2+ + Cu}. \]

Here copper(II) ion is \(\ce{Cu^2+}\), SMILES [Cu+2], and iron(II) ion is \(\ce{Fe^2+}\), SMILES [Fe+2].

With the oxides retained in the solid residue, each mole of metallic iron replaced by copper increases its mass by \(64-56=8\ \mathrm{g}\). Thus

\[ x=\frac{4.96-4.72}{64-56}=0.0300\ \mathrm{mol}. \]

Consequently,

\[ y+2z=0.0700-0.0300=0.0400, \qquad y+3z=0.0500, \]

giving

\[ \boxed{x=0.0300,\qquad y=0.0200,\qquad z=0.0100\ \mathrm{mol}}. \]

The corresponding masses are

\[ m(\ce{Fe})=1.68\ \mathrm{g},\quad m(\ce{FeO})=1.44\ \mathrm{g},\quad m(\ce{Fe2O3})=1.60\ \mathrm{g}, \]

which sum to \(4.72\ \mathrm{g}\).

Hydrochloric acid is aqueous hydrogen chloride, \(\ce{HCl}\), SMILES Cl. It supplies hydrogen ions, \(\ce{H+}\), SMILES [H+], and chloride ions, \(\ce{Cl-}\), SMILES [Cl-]. The hydrogen ions are hydrated in solution; the following equations use conventional net ionic notation.

The oxides dissolve according to

\[ \ce{FeO + 2H+ -> Fe^2+ + H2O}, \]

\[ \ce{Fe2O3 + 6H+ -> 2Fe^3+ + 3H2O}. \]

Iron(III) ion, \(\ce{Fe^3+}\), has SMILES [Fe+3]. Crucially, it reacts with metallic iron:

\[ \ce{Fe + 2Fe^3+ -> 3Fe^2+}. \]

Thus the \(0.0100\ \mathrm{mol}\) of \(\ce{Fe2O3}\) produces \(0.0200\ \mathrm{mol}\) of iron(III), consuming \(0.0100\ \mathrm{mol}\) of metallic iron without evolving hydrogen. The combined reaction is

\[ \ce{Fe + Fe2O3 + 6H+ -> 3Fe^2+ + 3H2O}. \]

The remaining metal,

\[ 0.0300-0.0100=0.0200\ \mathrm{mol}, \]

reacts with acid:

\[ \ce{Fe + 2H+ -> Fe^2+ + H2}. \]

Therefore, the total hydrochloric acid requirement is

\[ \begin{aligned} n(\ce{HCl}) &=2n(\ce{FeO})+6n(\ce{Fe2O3}) +2n(\text{remaining }\ce{Fe})\\ &=2(0.0200)+6(0.0100)+2(0.0200)\\ &=0.140\ \mathrm{mol}. \end{aligned} \]

Using \(M(\ce{HCl})=36.5\ \mathrm{g\,mol^{-1}}\),

\[ m(\ce{HCl})=0.140\times36.5=5.11\ \mathrm{g}. \]

For a 7.3 % solution by mass,

\[ m_{\text{solution}}=\frac{5.11}{0.073}=70.0\ \mathrm{g}, \]

and hence

\[ \boxed{ V_{\text{solution}} =\frac{70.0}{1.03} =67.96\ \mathrm{cm^3} \approx68\ \mathrm{cm^3}. } \]

2.2. Volume of gas released

The gas is hydrogen. Only the metal remaining after reduction of iron(III) contributes to its yield:

\[ n(\ce{H2})=0.0300-0.0100=0.0200\ \mathrm{mol}. \]

Using the conventional STP molar volume \(22.4\ \mathrm{dm^3\,mol^{-1}}\),

\[ \boxed{ V(\ce{H2})=0.0200\times22.4 =0.448\ \mathrm{dm^3} =448\ \mathrm{cm^3}. } \]

As a check, the overall dissolution reaction for the determined proportions is

\[ \ce{3Fe + 2FeO + Fe2O3 + 14H+ -> 7Fe^2+ + 5H2O + 2H2}. \]

The solution was checked against the official solution. Where this solution differs from the official solution, the official solution contains an error or a misprint.