Problem 21 - General Chemistry: Principles and Modern Applications

Question

Use the data in Appendix D to calculate the standard cell potential for each of the following reactions. Which reactions will occur spontaneously? (a) \(\mathrm{H}_{2}(\mathrm{g})+\mathrm{F}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{H}^{+}(\mathrm{aq})+2 \mathrm{F}^{-}(\mathrm{aq})\) (b) \(\mathrm{Cu}(\mathrm{s})+\mathrm{Ba}^{2+}(\mathrm{aq}) \longrightarrow \mathrm{Cu}^{2+}(\mathrm{aq})+\mathrm{Ba}(\mathrm{s})\) (c) \(3 \mathrm{Fe}^{2+}(\mathrm{aq}) \longrightarrow \mathrm{Fe}(\mathrm{s})+2 \mathrm{Fe}^{3+}(\mathrm{aq})\) (d) \(\mathrm{Hg}(1)+\mathrm{HgCl}_{2}(\mathrm{aq}) \longrightarrow \mathrm{Hg}_{2} \mathrm{Cl}_{2}(\mathrm{s})\)

Step-by-Step Solution

Answer

The standard cell potentials for each reaction were calculated and the spontaneous reactions were determined to be those reactions with positive standard cell potentials.

Step 1: Identify Half-Reactions

Using Appendix D, the standard reduction potentials documented, the half-reactions for each chemical reaction are identified. For example, for reaction (a), the half-reactions involved are: \[2 H^{+}(aq) + 2e^{-} \rightarrow H_{2}(g)\] and \[-2 F^{-}(aq) \rightarrow F_{2}(g) + 2e^{-}\] Corresponding potentials are taken from Appendix D.

Step 2: Calculate Cell Potentials

Using the potentials obtained, the standard cell potential (\(E^{0}\)) of each reaction is calculated by subtracting the potential of the oxidation half-reaction from the reduction half-reaction. Each reaction will give: (a) \(E_{cell}^{a}\), (b) \(E_{cell}^{b}\), (c) \(E_{cell}^{c}\), and (d) \(E_{cell}^{d}\).

Step 3: Determine Spontaneity

The reactions that occur spontaneously are those with positive \(E^{0}\). Determine which of \(E_{cell}^{a}\), \(E_{cell}^{b}\), \(E_{cell}^{c}\), and \(E_{cell}^{d}\) are positive.

Key Concepts

Electrochemical Cell

An electrochemical cell is a device capable of either generating electrical energy from chemical reactions or using electrical energy to cause chemical changes. These cells consist of two half-cells connected by a salt bridge, with each half-cell containing an electrode and an electrolyte.

In our exercise, several electrochemical reactions are presented, and in order to understand how to calculate the standard cell potential, a student must first comprehend the basic components of these cells. Each reaction can be separated into two half-reactions: one representing oxidation (loss of electrons) and another representing reduction (gain of electrons).

Electrochemical cells are broadly classified into two types:

• Galvanic (voltaic) cells - These are cells in which spontaneous chemical reactions produce electrical energy.
• Electrolytic cells - Cells that consume electrical energy to drive non-spontaneous chemical reactions.

Understanding this distinction is pivotal for determining the spontaneity of reactions in electrochemical cells.

Reduction Potentials

The concept of reduction potentials is central to understanding electrochemistry. The reduction potential, often represented by the symbol \( E^{\circ} \), measures the tendency of a chemical species to gain electrons and thereby be reduced. Each half-reaction in an electrochemical cell has an associated standard reduction potential, which is typically measured under standard conditions (1 M concentration of all aqueous species, 1 atm pressure for gases, and 25°C temperature).

To calculate the cell's overall potential, we use the half-cell potentials listed in reference materials such as Appendix D from our exercise. The

Standard Cell Potential

\( E^{\circ}_{cell} \) of the entire electrochemical reaction can be found by taking the difference between the reduction potential of the cathode (where reduction occurs) and the anode (where oxidation occurs).

It's important to remember that the more positive the reduction potential, the greater the species' tendency to be reduced. During calculations, reversing the half-reaction for oxidation requires also changing the sign of the associated reduction potential. Students often forget this which can lead to incorrect results.

Spontaneous Reactions

A spontaneous reaction is one that occurs naturally without external intervention. In the context of electrochemical cells, the spontaneity of a reaction can be determined by the sign of the standard cell potential (\(E^{\circ}_{cell}\)). When the standard cell potential is positive, the reaction is spontaneous and can produce electrical energy, as is the case with galvanic cells.

The exercise we are looking at asks students to calculate the standard cell potential for several reactions to identify which ones are spontaneous. The calculation of standard cell potentials involves using values obtained from a standard reduction potential table and applying the Nernst equation if conditions are not standard.

Furthermore, it is worth noting that not only does a positive cell potential indicate spontaneity, but a negative cell potential suggests that energy must be supplied for the reaction to proceed, characteristic of electrolytic cells. Hence, understanding the standard cell potential and its relation to spontaneity is crucial for anyone studying electrochemistry. It is also essential for students to practice the calculation and conceptual understanding thoroughly to confidently apply these principles to solve problems.