Question

Show by calculation whether the disproportionation of chlorine gas to chlorate and chloride ions will occur under standard-state conditions in an acidic solution.

Short answer

The disproportionation of chlorine gas to chlorate and chloride ions will not occur under standard-state conditions in an acidic solution since the value of E˚Cell is negative (-0.11 V).

Step-by-step solution

Write Half-Reactions

Separate the overall redox reaction into two half-reactions. Chlorine is both oxidized and reduced in this process, forming chloride and chlorate ions. The half reactions are: \n 1. \(Cl2(g) + 2e^- ⟶ 2Cl^-(aq)\) (Reduction)\n 2. \(Cl2(g) + 6H2O (l) ⟶ 2ClO3^-(aq) + 12H^+ (aq) + 10e^-\) (Oxidation)

Determine the Reduction Potential

The standard reduction potential, E˚, can be obtained from standard reduction tables for each of the half-reactions. These are: \n 1. E˚(Cl2/Cl-) = +1.36 V \n 2. E˚(Cl2/ClO3-) = +1.47 V

Apply the Nernst Equation

According to the Nernst equation, the overall cell potential, E˚cell, is calculated as follows: \( E˚cell = E˚(Reduction) - E˚(Oxidation) \). Since chlorine is being reduced to chloride and oxidized to chlorate, we substitute the corresponding E˚s. \( E˚Cell = E˚(Cl2/Cl-) - E˚(Cl2/ClO3-) = +1.36 V - (+1.47 V)\

Determine Spontaneity of Reaction

The sign of E˚Cell tells us whether the reaction is spontaneous or not. A positive E˚Cell indicates a spontaneous redox reaction, while a negative E˚Cell indicates a non-spontaneous redox reaction. Hence, calculate E˚Cell. If our calculated E˚Cell is less than 0; the reaction is not spontaneous under standard conditions.

Key concepts

Redox Reactions

Redox reactions, short for reduction and oxidation reactions, involve the transfer of electrons between two species. In a redox reaction, one substance is oxidized (loses electrons) while another is reduced (gains electrons). This transfer of electrons allows for the conversion of chemical energy into electrical energy or vice versa.
In the disproportionation of chlorine gas in an acidic solution, chlorine acts as both the reducing and oxidizing agent.

• The reduction half-reaction: Chlorine gains electrons to form chloride ions: \(Cl_2(g) + 2e^- \rightarrow 2Cl^-(aq)\).
• The oxidation half-reaction: Chlorine loses electrons while reacting with water to form chlorate ions: \(Cl_2(g) + 6H_2O(l) \rightarrow 2ClO_3^-(aq) + 12H^+(aq) + 10e^-\).

Together, these reactions illustrate how a single element can undergo both oxidation and reduction, leading to different products.

Standard Reduction Potentials

The standard reduction potential, denoted as \(E^\circ\), is a measure of the tendency of a chemical species to gain electrons and thereby be reduced. Standard conditions mean that the concentration of ions involved is 1 mol/L, the pressure of gases is 1 atm, and the temperature is usually at 25°C.
Every half-reaction has an associated standard reduction potential, which can be found in tables of standard potentials. In our example:

• The reduction potential for \(Cl_2/Cl^-\) is \(+1.36\, V\), indicating it is a strong oxidizing agent.
• The reduction potential for \(Cl_2/ClO_3^-\) is \(+1.47\, V\). Here, \(Cl_2\) is oxidized, which reverses the potential, reflecting its strength as a reducing agent when reversed.

When analyzing redox reactions, these potentials allow for the prediction of which way the electrons will flow, helping determine the spontaneous or non-spontaneous nature of the overall reaction.

Spontaneity of Chemical Reactions

The spontaneity of a chemical reaction is a critical factor in understanding how reactions occur naturally. A reaction is considered spontaneous if it can proceed on its own without external energy input.
The measured cell potential \(E^\circ_{cell}\) is a direct indicator of this, calculated by subtracting the oxidation potential from the reduction potential. For the chlorine disproportionation reaction:

• \(E^\circ_{cell} = E^\circ_{(Cl_2/Cl^-)} - E^\circ_{(Cl_2/ClO_3^-)}\)
• Substituting values: \(E^\circ_{cell} = +1.36\, V - (+1.47\, V) = -0.11\, V\)

A negative \(E^\circ_{cell}\) indicates a non-spontaneous reaction under standard conditions.
This means the mixture of chlorine gas in acidic solution will not spontaneously disproportionate into chloride and chlorate ions without external energy assistance. Studying this behavior is important for predicting reactions in various chemical and industrial processes.