Question

Discuss the spontaneity of an electrochemical reaction in terms of its standard emf \(\left(E_{\mathrm{cell}}^{\circ}\right)\).

Short answer

An electrochemical reaction is spontaneous if its standard emf \(E_{\mathrm{cell}}^{\circ}\) is positive.

Step-by-step solution

Understand the Concept of Spontaneity in Electrochemical Reactions

In electrochemistry, an electrochemical reaction is considered spontaneous if it occurs without the need for external energy. The spontaneity of a reaction can be determined by the standard electromotive force (emf), denoted as \(E_{\mathrm{cell}}^{\circ}\).

Recall the Relationship between Gibbs Free Energy and Standard Cell Potential

The spontaneity of a reaction can also be understood using Gibbs free energy (\(\Delta G^{\circ}\)). The relationship between \(\Delta G^{\circ}\) and \(E_{\mathrm{cell}}^{\circ}\) is given by the equation: \(\Delta G^{\circ} = -nFE_{\mathrm{cell}}^{\circ}\), where \(n\) is the number of moles of electrons exchanged and \(F\) is the Faraday constant (approximately 96485 C/mol).

Determine the Sign of the Standard Cell Potential

The sign of \(E_{\mathrm{cell}}^{\circ}\) determines the spontaneity. If \(E_{\mathrm{cell}}^{\circ}\) is positive, \(\Delta G^{\circ}\) is negative, suggesting that the reaction is spontaneous. Conversely, if \(E_{\mathrm{cell}}^{\circ}\) is negative, \(\Delta G^{\circ}\) becomes positive, indicating that the reaction is non-spontaneous.

Conclusion on Spontaneity

To conclude, the reaction is spontaneous if \(E_{\mathrm{cell}}^{\circ}\) is greater than zero and non-spontaneous if \(E_{\mathrm{cell}}^{\circ}\) is less than zero. This concludes the analysis of spontaneity in terms of standard emf.

Key concepts

Spontaneity of Reactions

In electrochemistry, spontaneity is a key concept that describes whether a reaction will proceed on its own without any additional energy input. A spontaneous reaction occurs when substances convert into more stable products, releasing energy in the process. This concept is vital for understanding how electrochemical reactions, such as those in batteries or cells, function effectively.
For an electrochemical reaction to be deemed spontaneous, the standard electromotive force (emf) or standard cell potential, represented by \(E_{\mathrm{cell}}^{\circ}\), must be positive. This indicates that the reaction can perform work as it progresses from reactants to products. Essentially, a positive \(E_{\mathrm{cell}}^{\circ}\) confirms that the reaction favors the formation of products under standard conditions, highlighting its spontaneous nature.

Gibbs Free Energy

Gibbs free energy, often denoted as \(\Delta G^{\circ}\), is a crucial thermodynamic function that helps determine reaction spontaneity beyond just electrochemistry. It is an energy measure that helps predict the direction of chemical processes. In simple terms, \(\Delta G^{\circ}\) tells us if a reaction can occur on its own:

• A negative \(\Delta G^{\circ}\) implies that the reaction is spontaneous.
• A positive \(\Delta G^{\circ}\) suggests that the reaction is non-spontaneous.

The relationship between Gibbs free energy and standard cell potential is given by the equation \(\Delta G^{\circ} = -nFE_{\mathrm{cell}}^{\circ}\). This equation shows that \(\Delta G^{\circ}\) is directly influenced by \(E_{\mathrm{cell}}^{\circ}\), where \(n\) is the number of moles of electrons transferred, and \(F\) is the Faraday constant (approximately 96485 C/mol). Thus, the greater the positive \(E_{\mathrm{cell}}^{\circ}\), the more negative \(\Delta G^{\circ}\) becomes, confirming the spontaneity of the reaction.

Electrochemistry Concepts

Electrochemistry involves the fascinating interplay between electrical and chemical processes, especially focusing on electron transfer reactions. These reactions either store or release energy in the form of electricity, which is central to applications such as batteries, fuel cells, and electrolysis.
Two main types of cells are involved:

• Galvanic (or voltaic) cells: These utilize spontaneous chemical reactions to generate electricity.
• Electrolytic cells: These use electrical energy to drive non-spontaneous reactions.

Within these cells, electrochemistry concepts such as electrode potential, cell voltage, and half-cell reactions play essential roles. Understanding these concepts helps in determining the efficiency and feasibility of electrochemical systems, and aids in the comprehensive interpretation of standard emf calculations for reactions.

Standard Cell Potential

The standard cell potential, \(E_{\mathrm{cell}}^{\circ}\), is a pivotal measure in electrochemistry. It quantifies the voltage produced by an electrochemical cell under standard conditions, which are typically set at 1 M concentration for solutions, 1 atm pressure for gases, and a temperature of 25°C (298 K). This uniformity allows for easy comparison between different reactions.
The standard cell potential is determined by calculating the difference between the electrode potentials of the cathode and the anode: \(E_{\mathrm{cell}}^{\circ} = E_{\mathrm{cathode}}^{\circ} - E_{\mathrm{anode}}^{\circ}\). A higher \(E_{\mathrm{cell}}^{\circ}\) indicates a stronger drive for the reaction to proceed spontaneously, while a negative value indicates that the reaction would require energy to proceed.
In practical terms, the standard cell potential assesses the capability of an electrochemical cell to do work, making it an indispensable tool for engineers and scientists designing batteries, electroplating processes, and more.