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Chapter 20: Problem 84

What is a disproportionation reaction? Use the following reduction potentials \(\mathrm{ClO}_{3}^{-}+3 \mathrm{H}^{+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{HClO}_{2}+\mathrm{H}_{2} \mathrm{O} \quad \mathscr{E}^{\circ}=1.21 \mathrm{~V}\) \(\mathrm{HClO}_{2}+2 \mathrm{H}^{+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{HClO}+\mathrm{H}_{2} \mathrm{O} \quad \mathscr{E}^{\circ}=1.65 \mathrm{~V}\) to predict whether \(\mathrm{HClO}_{2}\) will disproportionate.

Short Answer

Expert verified
A disproportionation reaction is a redox reaction in which a single reactant is both oxidized and reduced, resulting in two different products. To predict whether \(\mathrm{HClO}_{2}\) will disproportionate, we combine the given half-reactions to form the potential disproportionation reaction: \(\mathrm{ClO}_{3}^{-}+\mathrm{HClO} \longrightarrow 2\mathrm{HClO}_{2}\) and calculate the standard cell potential: \(\mathscr{E}_{\text{disproportionation}}^{\circ} = 1.21\mathrm{~V} - 1.65\mathrm{~V} = -0.44\mathrm{~V}\) Since the standard cell potential is negative, the disproportionation of \(\mathrm{HClO}_{2}\) is not spontaneous, meaning it will not disproportionate.

Step by step solution

01

Write down the given half-reactions

The given half-reactions are: 1. \(\mathrm{ClO}_{3}^{-}+3 \mathrm{H}^{+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{HClO}_{2}+\mathrm{H}_{2} \mathrm{O}\quad \mathscr{E}^{\circ}=1.21 \mathrm{~V}\) 2. \(\mathrm{HClO}_{2}+2 \mathrm{H}^{+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{HClO}+\mathrm{H}_{2} \mathrm{O}\quad \mathscr{E}^{\circ}=1.65 \mathrm{~V}\)
02

Reverse the second half-reaction to make it an oxidation reaction

To make the second half-reaction an oxidation reaction, reverse it and change the sign of the standard cell potential: \(\mathrm{HClO}+\mathrm{H}_{2} \mathrm{O}\longrightarrow \mathrm{HClO}_{2}+2 \mathrm{H}^{+}+2 \mathrm{e}^{-} \quad \mathscr{E}^{\circ}=-1.65 \mathrm{~V}\)
03

Combine the half-reactions to form the potential disproportionation reaction

Now, we can combine the two half-reactions (oxidation and reduction) to form the potential disproportionation reaction: \(\mathrm{ClO}_{3}^{-}+3 \mathrm{H}^{+}+2 \mathrm{e}^{-} + \mathrm{HClO}+\mathrm{H}_{2}\mathrm{O} \longrightarrow\) \(\mathrm{HClO}_{2}+\mathrm{H}_{2}\mathrm{O} +\mathrm{HClO}_{2}+2 \mathrm{H}^{+}+2 \mathrm{e}^{-}\) Simplifying the reaction, we get: \(\mathrm{ClO}_{3}^{-}+\mathrm{HClO} \longrightarrow 2\mathrm{HClO}_{2}\)
04

Calculate the standard cell potential for the disproportionation reaction

To calculate the standard cell potential, add the standard cell potentials of the two half-reactions: \(\mathscr{E}_{\text{disproportionation}}^{\circ} = \mathscr{E}_{1}^{\circ} + \mathscr{E}_{2}^{\circ} = 1.21\mathrm{~V} - 1.65\mathrm{~V} = -0.44\mathrm{~V}\) Since the standard cell potential is negative, the disproportionation of \(\mathrm{HClO}_{2}\) is not spontaneous, meaning it will not disproportionate.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Reduction Potential
Reduction potential is a measure of the tendency of a chemical species to acquire electrons and be reduced. It is quantified in volts (V) and reflects the species' ability to be involved in redox reactions. Each specific half-reaction has its own standard reduction potential. By comparing these values, one can predict the spontaneity of a redox reaction.

Higher reduction potential means a greater tendency to gain electrons. In the exercise, the reduction potentials given are important in predicting disproportionation. For instance, if HClO extsubscript{2} had a high reduction potential, it could indicate a tendency towards reduction in a redox reaction, impacting the stability and behavior of the molecule.
Redox Reactions
Redox reactions, or oxidation-reduction reactions, are chemical reactions in which electrons are transferred between species. In these reactions, one species undergoes oxidation while another species undergoes reduction.
  • Oxidation involves the loss of electrons.
  • Reduction involves the gain of electrons.
In the provided reaction, we split the whole into two half-reactions indicating the separate oxidation and reduction processes, helping to predict the tendency of a particular species to undergo oxidation or reduction.

The concept of redox reactions is vital in determining the overall cell potential and spontaneity of the reaction, representing the sum of each individual half-reaction.
Cell Potential
Cell potential, or electromotive force (EMF), refers to the voltage difference between two half-cells in a redox reaction. It signifies the driving force behind the reaction, indicating whether the process is spontaneous or not.

In the context of the original exercise, we calculated the standard cell potential for the potential disproportionation reaction using the reduction potentials. The sum of the reduction potential for one half-reaction and the reversed potential for the other yields the cell potential.
The calculated cell potential was negative, indicating non-spontaneity. Only reactions with a positive cell potential are spontaneous, making this analysis crucial for predicting chemical behavior in electrochemical cells.
Oxidation and Reduction
Oxidation and reduction are two essential processes in chemistry, always occurring simultaneously in a redox reaction. They describe the transfer of electrons from one reactant to another.
  • In oxidation, a substance loses electrons, increasing its oxidation state.
  • In reduction, a substance gains electrons, decreasing its oxidation state.
In the exercise, HClO extsubscript{2} was analyzed to see if it could be oxidized and reduced simultaneously, a process known as disproportionation. However, the calculated negative cell potential reveals that the combination of oxidation and reduction isn't spontaneous, indicating that the molecule does not naturally disproportionate under the given conditions.

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