IChO 1972 · Theory problem 3

Electrolysis of sodium chloride solution with copper electrodes

A volume of \(200\ \mathrm{cm^3}\) of a 2-normal sodium chloride solution (\(\rho = 1.10\ \mathrm{g\,cm^{-3}}\)) was electrolysed at permanent stirring in an electrolytic cell with copper electrodes. Electrolysis was stopped when \(22.4\ \mathrm{dm^3}\) (at STP) of a gas were liberated at the cathode.

Problem:

3.1 Calculate the mass percentage of \(\ce{NaCl}\) in the solution after electrolysis.

Relative atomic masses:

\(A_{\mathrm r}(\ce{H}) = 1;\quad A_{\mathrm r}(\ce{O}) = 16;\quad A_{\mathrm r}(\ce{Na}) = 23;\quad A_{\mathrm r}(\ce{Cl}) = 35.5;\quad A_{\mathrm r}(\ce{Cu}) = 64.\)

Official English text of the problem.

Answers

  • 3.1 \(\boxed{12.7\%\ \ce{NaCl}\text{ by mass}}\) in the remaining liquid solution, under the copper(II) hydroxide model described below.

Solution

3.1

Sodium chloride, \(\ce{NaCl}\) (ionic SMILES [Na+].[Cl-]), supplies one equivalent per mole, so its initial concentration is \(2\ \mathrm{mol\,dm^{-3}}\). Thus,

\[ n_0(\ce{NaCl}) =2\ \mathrm{mol\,dm^{-3}}\times0.200\ \mathrm{dm^3} =0.400\ \mathrm{mol}, \]

\[ m_0(\ce{NaCl}) =0.400(23+35.5) =23.4\ \mathrm g. \]

The initial solution mass is

\[ m_0(\text{solution}) =\rho V =1.10\ \mathrm{g\,cm^{-3}}\times200\ \mathrm{cm^3} =220\ \mathrm g. \]

The cathodic gas is hydrogen, \(\ce{H2}\), [H][H]. In aqueous solution, water, \(\ce{H2O}\), O, is reduced rather than sodium ions, \(\ce{Na+}\), [Na+]. This produces hydroxide ions, \(\ce{OH-}\), [OH-]:

\[ \ce{2H2O(l) + 2e- -> H2(g) + 2OH-(aq)}. \]

The copper electrode is an active anode. In the conventional copper(II) treatment, copper dissolves as copper(II) ions, \(\ce{Cu^{2+}}\), [Cu+2]:

\[ \ce{Cu(s) -> Cu^{2+}(aq) + 2e-}. \]

Stirring brings the copper(II) and hydroxide ions together, precipitating copper(II) hydroxide, \(\ce{Cu(OH)2}\), [Cu+2].[OH-].[OH-]:

\[ \ce{Cu^{2+}(aq) + 2OH-(aq) -> Cu(OH)2(s)}. \]

The disconnected ionic SMILES indicate composition and charges; they do not depict a crystal lattice.

Adding these reactions gives

\[ \boxed{\ce{Cu(s) + 2H2O(l) -> Cu(OH)2(s) + H2(g)}}. \]

Sodium ions and chloride ions, \(\ce{Cl-}\), [Cl-], are spectators, so the mass of dissolved sodium chloride remains \(23.4\ \mathrm g\).

Using the molar gas volume at STP,

\[ n(\ce{H2}) =\frac{22.4\ \mathrm{dm^3}} {22.4\ \mathrm{dm^3\,mol^{-1}}} =1.00\ \mathrm{mol}. \]

The net reaction therefore consumes \(2.00\ \mathrm{mol}\) of water:

\[ m(\text{water consumed}) =2.00\times18.0 =36.0\ \mathrm g. \]

Consequently, the final liquid solution mass, excluding the precipitate, is

\[ m_f(\text{solution})=220-36.0=184\ \mathrm g. \]

Equivalently, the mass balance includes \(64\ \mathrm g\) of copper entering from the anode, \(98\ \mathrm g\) of hydroxide precipitating, and \(2\ \mathrm g\) of hydrogen escaping:

\[ m_f(\text{solution})=220+64-98-2=184\ \mathrm g. \]

Hence,

\[ \boxed{ w(\ce{NaCl}) =\frac{23.4}{184}\times100\% =12.7\%. } \]

The solution was checked against the official solution.