Question

Given that \(\mathrm{E}_{\mathrm{N}^{1+} / \mathrm{Ni}}^{0}=-0.25 \mathrm{~V} ; \mathrm{E}_{\mathrm{Cu}^{2+} / \mathrm{Cu}}^{0}=+0.34 \mathrm{~V}\) \(E_{A \mathrm{~B}^{+} / \mathrm{Ag}}^{0}=+0.80 \mathrm{~V} ; \mathrm{E}_{\mathrm{Zn}^{2+} / Z \mathrm{n}}^{0}=-0.76 \mathrm{~V}\) Which of the following redox processes will not take place in specified direction? (a) \(\mathrm{Zn}(\mathrm{s})+2 \mathrm{H}^{+}(\mathrm{aq}) \rightarrow \mathrm{Zn}^{2+}(\mathrm{aq})+\mathrm{H}_{2}(\mathrm{~g})\) (b) \(\mathrm{Cu}(\mathrm{s})+2 \mathrm{H}^{+}(\mathrm{aq}) \rightarrow \mathrm{Cu}^{2+}(\mathrm{aq})+\mathrm{H}_{2}(\mathrm{~g})\) (c) \(\mathrm{Cu}(\mathrm{s})+2 \mathrm{Ag}^{+}(\mathrm{aq}) \rightarrow \mathrm{Cu}^{2+}(\mathrm{aq})+2 \mathrm{Ag}(\mathrm{s})\) (d) \(\mathrm{Ni}^{2+}(\mathrm{aq})+\mathrm{Cu}(\mathrm{s}) \rightarrow \mathrm{Ni}(\mathrm{s})+\mathrm{Cu}^{2+}(\mathrm{aq})\)

Short answer

All reactions are spontaneous in the specified directions.

Step-by-step solution

Understand Standard Reduction Potentials

We are given several standard reduction potentials: - \( \mathrm{E}_{\mathrm{N}^{1+} / \mathrm{Ni}}^{0} = -0.25 \, \mathrm{V} \) - \( \mathrm{E}_{\mathrm{Cu}^{2+} / \mathrm{Cu}}^{0} = +0.34 \, \mathrm{V} \) - \( \mathrm{E}_{\mathrm{Ag}^{+} / \mathrm{Ag}}^{0} = +0.80 \, \mathrm{V} \) - \( \mathrm{E}_{\mathrm{Zn}^{2+} / \mathrm{Zn}}^{0} = -0.76 \, \mathrm{V} \)Understanding these values will help us determine which reactions are spontaneous.

Calculate Standard Electrode Potentials for Reactions

For each reaction, we will need to calculate the standard electrode potential (\( E^0_{\text{cell}} \)) using the formula: \[ E^0_{\text{cell}} = E^0_{\text{cathode}} - E^0_{\text{anode}} \] where the cathode is where reduction takes place and the anode is where oxidation occurs.

Determine Electrode Potentials for Each Reaction

- **For Reaction (a):** - Reduction: \( 2 \mathrm{H}^+ + 2e^- \rightarrow \mathrm{H}_2 \), \( E^0 = 0 \) V - Oxidation: \( \mathrm{Zn} \rightarrow \mathrm{Zn}^{2+} + 2e^- \), \( E^0 = +0.76 \) V \( E^0_{\text{cell}} = 0 - (-0.76) = +0.76 \) V - **Reaction will take place.**- **For Reaction (b):** - Reduction: \( 2 \mathrm{H}^+ + 2e^- \rightarrow \mathrm{H}_2 \), \( E^0 = 0 \) V - Oxidation: \( \mathrm{Cu} \rightarrow \mathrm{Cu}^{2+} + 2e^- \), \( E^0 = -0.34 \) V \( E^0_{\text{cell}} = 0 - (-0.34) = +0.34 \) V - **Reaction will take place.**- **For Reaction (c):** - Reduction: \( 2 \mathrm{Ag}^+ + 2e^- \rightarrow 2 \mathrm{Ag} \), \( E^0 = +0.80 \) V - Oxidation: \( \mathrm{Cu} \rightarrow \mathrm{Cu}^{2+} + 2e^- \), \( E^0 = -0.34 \) V \( E^0_{\text{cell}} = 0.80 - 0.34 = +0.46 \) V - **Reaction will take place.**- **For Reaction (d):** - Reduction: \( \mathrm{Ni}^{2+} + 2e^- \rightarrow \mathrm{Ni} \), \( E^0 = -0.25 \) V - Oxidation: \( \mathrm{Cu} \rightarrow \mathrm{Cu}^{2+} + 2e^- \), \( E^0 = -0.34 \) V \( E^0_{\text{cell}} = -0.25 - (-0.34) = +0.09 \) V - **Reaction will take place.**

Conclusion

Since all calculated \( E^0_{\text{cell}} \) values are positive, all reactions are spontaneous. However, for practical decision making, we would typically choose the process with the greatest positive potential when making assumptions about which reactions are more favorable.

Key concepts

Standard Reduction Potentials

In electrochemistry, standard reduction potentials give us insight into how substances gain or lose electrons. These potentials, assigned in volts (V), are measured under standard conditions and help us predict the spontaneity of a redox reaction.
Standard reduction potentials refer to half-reactions, where the reduction part of a reaction is shown. For instance, the reduction potential for the conversion from copper ions, Cu^{2+}, to solid copper (Cu) is positive, at +0.34 V, indicating a strong tendency to gain electrons.

• A positive potential suggests a higher likelihood that a substance will gain electrons and therefore be reduced.
• A more negative potential implies a substance is more likely to lose electrons, thus acting as an oxidizing agent when flipped to oxidation.

The list of standard potentials allows us to compare different substances and predict the direction of electron flow in redox reactions.

Redox Reactions

Redox, or reduction-oxidation reactions, are chemical reactions involving the transfer of electrons between two substances. One substance gets oxidized (loses electrons), and the other gets reduced (gains electrons).
To always identify redox reactions:

• Identify the substance that gains electrons. This substance undergoes reduction.
• Find which substance loses electrons, signifying oxidation.
• Note that redox reactions always have both reduction and oxidation processes occurring simultaneously.

The given reactions in the exercise illustrate this. For example, when copper (Cu) reacts with silver ions (Ag^+), the copper oxidizes by losing electrons, while the silver ions reduce as they gain electrons.
Overall, by using standard reduction potentials, one can predict which direction a redox reaction is likely to favor based on the value of standard electrode potentials.

Electrode Potentials

Electrode potentials are crucial in understanding the cell's ability to drive an electric current. They're determined by the difference in potential between the cathode and the anode, essentially indicating the maximum possible voltage of the electrochemical cell.
For any reaction:

• The cathode is the site of reduction, and its potential is derived from the standard reduction potential table.
• The anode, where oxidation occurs, involves flipping the standard reduction potential to represent oxidation.
• The overall cell potential is calculated using:\[ E^0_{\text{cell}} = E^0_{\text{cathode}} - E^0_{\text{anode}} \] This value should be positive for the reaction to be spontaneous in the specified direction.

In the example reactions, this involves using given potentials such as -0.76 V for zinc and +0.80 V for silver, calculating the net potential to determine if the reactions will proceed spontaneously.