Question

Calculate \(\mathscr{E}^{\circ}\) values for the following cells. Which reactions are spontaneous as written (under standard conditions)? Balance the equations that are not already balanced. Standard reduction potentials are found in Table 18.1. a. \(\mathrm{H}_{2}(g) \longrightarrow \mathrm{H}^{+}(a q)+\mathrm{H}^{-}(a q)\) b. \(\mathrm{Au}^{3+}(a q)+\mathrm{Ag}(s) \longrightarrow \mathrm{Ag}^{+}(a q)+\mathrm{Au}(s)\)

Short answer

For the given cells: a. The standard cell potential, E°(Cell), is -2.414 V, which indicates a non-spontaneous reaction under standard conditions. b. The standard cell potential, E°(Cell), is 0.699 V, which indicates a spontaneous reaction under standard conditions.

Step-by-step solution

a. Reduction and Oxidation half-reactions for H2

To find E° for the given cell, we need to identify the two half-reactions: Oxidation half-reaction: \(\mathrm{H}_{2}(g) \longrightarrow 2\mathrm{H}^{+}(a q)+2e^{-}\) Reduction half-reaction: \(2e^{-}+\mathrm{H}^{-}(a q) \longrightarrow \mathrm{H}_{2}(g)\)

a. Standard reduction potentials

From Table 18.1, the standard reduction potential for each half-reaction is: E°(Oxidation) = 0 V E°(Reduction) = -2.414 V

a. Calculation of E° of the cell

Now, let's calculate the E° of the overall cell reaction: E°(Cell) = E°(Reduction) – E°(Oxidation) = (-2.414) - (0) = -2.414 V Since E°(Cell) < 0, the reaction is non-spontaneous under standard conditions.

b. Reduction and Oxidation half-reactions for Au3+ and Ag

To find E° for the given cell, we need to identify the two half-reactions: Oxidation half-reaction: \(\mathrm{Ag}(s) \longrightarrow \mathrm{Ag}^{+}(a q)+e^{-}\) Reduction half-reaction: \(\mathrm{Au}^{3+}(a q)+3e^{-} \longrightarrow \mathrm{Au}(s)\)

b. Standard reduction potentials

From Table 18.1, the standard reduction potential for each half-reaction is: E°(Oxidation) = 0.799 V E°(Reduction) = 1.498 V

b. Calculation of E° of the cell

Now, let's calculate the E° of the overall cell reaction: E°(Cell) = E°(Reduction) – E°(Oxidation) = (1.498) - (0.799) = 0.699 V Since E°(Cell) > 0, the reaction is spontaneous under standard conditions.

Key concepts

Standard Electrode Potentials

In electrochemistry, standard electrode potential is crucial for understanding how electrochemical cells work. The standard electrode potential, denoted as \( E^{\circ} \), is a measure of the tendency of a chemical species to be reduced, compared to the standard hydrogen electrode, which has an assigned potential of 0 volts.
Standard conditions assume all gases have a pressure of 1 atm, all solutions have a concentration of 1 M, and the temperature is 298 K.
Electrode potentials are typically given for reduction reactions. This means they measure how likely a species is to gain electrons. The higher the \( E^{\circ} \), the more likely the reaction is to occur as written.

• Standard conditions are important because they provide a common baseline for comparing different reactions.
• Reduction potentials can be positive or negative, affecting how they influence the overall cell potential.
• By looking at the table of standard electrode potentials, one can determine the feasibility of a reaction by evaluating the potential of each possible half-reaction.

Redox Reactions

Redox reactions involve the transfer of electrons between two species. The term 'redox' is a combination of reduction and oxidation.
In these reactions, one species gains electrons (reduction), while another loses electrons (oxidation). Each of these occurrences is represented by half-reactions, and combining these allows us to see the full redox reaction.
Understanding which species is oxidized and which is reduced is key.

• Oxidation involves the loss of electrons and an increase in oxidation state.
• Reduction involves the gain of electrons and a decrease in oxidation state.
• Balancing redox reactions requires ensuring that both mass and charge are balanced.

The electron flow in a redox reaction is what allows for the flow of electric current in electrochemical cells.
Knowing half-reactions helps in calculating the cell potential required to determine if a reaction is spontaneous.

Spontaneity of Reactions

To determine if a reaction is spontaneous, the cell potential \( E^{\circ}_{\text{cell}} \) is calculated. In general:

• If \( E^{\circ} > 0 \), the reaction is spontaneous under standard conditions.
• If \( E^{\circ} < 0 \), the reaction is non-spontaneous.

Spontaneity has implications for energy change. A spontaneous reaction releases energy when it occurs.
It's essential to note that a non-spontaneous reaction can still occur if energy is supplied.
For example, in the exercise given:

• For reaction a, \( E^{\circ}_{\text{cell}} = -2.414 \; V \), meaning it is non-spontaneous.
• For reaction b, \( E^{\circ}_{\text{cell}} = 0.699 \; V \), meaning it is spontaneous.

Understanding spontaneity is vital for predicting whether a reaction will proceed without external energy.