Question

Given that \(E_{\text {cell }}^{\circ}=3.20 \mathrm{V}\) for the reaction $$2 \mathrm{Na}(\mathrm{in} \mathrm{Hg})+\mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{Na}^{+}(\mathrm{aq})+2 \mathrm{Cl}^{-}(\mathrm{aq})$$ What is \(E^{\circ}\) for the reduction \(2 \mathrm{Na}^{+}(\mathrm{aq})+2 \mathrm{e}^{-} \longrightarrow\) \(2 \mathrm{Na}(\text { in } \mathrm{Hg}) ?\)

Short answer

The \(E^{\circ}\) for the reduction \(2 \mathrm{Na}^{+}(\mathrm{aq})+2 \mathrm{e}^{-} \longrightarrow 2 \mathrm{Na}(\text { in } \mathrm{Hg})\) will be \(-3.20 \mathrm{V}\).

Step-by-step solution

Recognize the Given Cell Reaction

The given cell reaction involving transformation of Na in mercury to \(Na^{+}\) in solution is: \[2\mathrm{Na}(\text {in} \mathrm{Hg})+\mathrm{Cl}_{2}(\text {g})\longrightarrow 2 \mathrm{Na}^{+}(\mathrm{aq})+2\mathrm{Cl}^{-}(\mathrm{aq})\] The provided \(E_{\text {cell }}^{\circ}\) for this reaction is \(3.20 \mathrm{V}\).

Determine the Correct Reaction

The reaction for which we want to find the standard cell potential (\(E^{\circ}\)) is the reduction of sodium ions to sodium metal: \[2 \mathrm{Na}^{+}(\mathrm{aq})+2 \mathrm{e}^{-} \longrightarrow 2 \mathrm{Na}(\text { in } \mathrm{Hg})\] It’s the reverse of one half of the given cell reaction.

Apply the Concept of Cell Reversal

In electrochemistry, when a cell reaction is reversed, the polarity of the cell's electromotive force (\(E_{\text {cell }}^{\circ}\)) also reverses. This is due to the fact the reverse cell reaction now involves reduction of Na+ ions to Na metal, whereas in the given cell reaction, Na metal is being oxidized to Na+ ions. Hence, \(E^{\circ} = -E_{\text {cell }}^{\circ}\) for the reduction of \(2 \mathrm{Na}^{+}(\mathrm{aq})+2 \mathrm{e}^{-} \longrightarrow 2 \mathrm{Na}(\text { in } \mathrm{Hg})\).

Key concepts

Cell Potential

Cell potential, commonly referred to as the standard cell potential when measured under standard conditions, is a key concept in understanding electrochemical reactions. It is a measure of the total potential difference between two electrodes in an electrochemical cell. This potential difference arises from the energy required to transfer electrons from one electrode to another, or effectively, how ready the electrons are to move.

In the context of the given exercise, the standard cell potential, denoted as \(E_{\text{cell}}^{\circ}\), for the reaction of sodium (\(\text{Na}\)) in mercury with chlorine gas is given as 3.20 V. This value indicates the voltage or electromotive force (EMF) that drives the electrons from the sodium metal to the sodium ions. The larger the cell potential, the more likely the reaction is to occur spontaneously.

Understanding cell potential helps in predicting the feasibility and direction of an electrochemical reaction. Higher cell potentials often correspond to more spontaneous reactions. This principle serves as a foundation for designing batteries and other electrochemical systems.

Reduction Reaction

A reduction reaction involves the gain of electrons by a chemical species. In electrochemistry, this is often seen at the cathode of an electrochemical cell where reduction occurs.

In the exercise, the focus is on reducing sodium ions \(\left(\text{Na}^+\right)\) back to sodium metal. This reaction is written as \[2 \ \text{Na}^{+}(\text{aq}) + 2 \ \text{e}^{-} \rightarrow 2 \ \text{Na}(\text{in Hg})\]. Simply put, the sodium ions are gaining electrons to become neutral sodium atoms again.

Key points about reduction reactions include:

• Reduction results in a decrease in oxidation state due to the gain of electrons.
• It always occurs in conjunction with oxidation (loss of electrons) of another species in a redox reaction.
• In electrochemical cells, reduction typically takes place at the cathode.

Grasping the concept of reduction is crucial for understanding how energy is transformed and utilized in electrochemical processes like batteries.

Electromotive Force (EMF)

Electromotive force, abbreviated as EMF, refers to the energy supplied by a cell or a battery. While the name suggests force, it is actually a measure of energy provided to drive the free movement of electrons in a circuit.

This force is measured in volts and represents the potential difference between the two electrodes when no current is flowing in the circuit. In other words, it is the maximum potential difference between the two electrodes of an electrochemical cell.

In the given problem, the EMF is represented by the cell potential \(E_{\text{cell}}^{\circ}\) which equals 3.20 V for the forward reaction. Understanding this value is crucial because when the reaction is reversed, the sign of this EMF changes, showing that the opposite reaction – the reduction of sodium ions – opposes the initial reaction energetically. This reversal implies the standard electrode potential for the reverse reaction is \(-3.20 \mathrm{V}\).

By understanding how EMF works, students can better assess the amount of electrical energy available to power electronic devices, or how electrochemical cells work, including batteries we use daily.