Problem 35 - Chemistry The Molecular Science

Question

Choose the correct answers: In a product-favored chemical reaction, the standard cell potential, \(E_{\text {cell }}^{\circ}\), is (greater/less) than zero, and the Gibbs free energy change, \(\Delta_{\mathrm{r}} G^{\circ},\) is (greater/less) than zero.

Step-by-Step Solution

Answer

The standard cell potential \(E_{\text{cell}}^{\circ}\) is greater than zero, and \(\Delta_{\mathrm{r}} G^{\circ}\) is less than zero.

Step 1: Understanding Cell Potential

In a product-favored reaction, the standard cell potential \(E_{\text{cell}}^{\circ}\) is positive. This is because the reaction tends to proceed in the forward direction, producing more products, which indicates a spontaneous process.

Step 2: Relating Cell Potential to Gibbs Free Energy

The relationship between Gibbs free energy change \(\Delta_{\mathrm{r}} G^{\circ}\) and cell potential \(E_{\text{cell}}^{\circ}\) is given by the equation: \[ \Delta_{\mathrm{r}} G^{\circ} = -nFE_{\text{cell}}^{\circ} \] where \(n\) is the number of moles of electrons exchanged and \(F\) is Faraday's constant.

Step 3: Determining Sign of Gibbs Free Energy Change

Since \(E_{\text{cell}}^{\circ}\) is positive for a product-favored reaction, \(-nFE_{\text{cell}}^{\circ}\) will be negative, thus \(\Delta_{\mathrm{r}} G^{\circ}\) will be less than zero, indicating a spontaneous process.

Key Concepts

Chemical Reactions

Chemical reactions involve the transformation of one or more substances into new substances through the breaking and forming of chemical bonds. These reactions can be either product-favored or reactant-favored. A product-favored reaction, as the name suggests, results in more products being formed, indicating that the process is spontaneous. Such reactions can be influenced by a variety of factors including temperature, pressure, and concentration. Understanding whether a reaction is product-favored is crucial for predicting the direction in which it will proceed. In electrochemistry, as seen in standard cell potential calculations, the focus is often on the flow of electrons and how energy changes occur during the reaction.

Gibbs Free Energy

Gibbs Free Energy, represented as \Delta_{\mathrm{r}} G, is a vital concept in determining the spontaneity of a chemical reaction. It combines enthalpy (heat content) and entropy (disorder) into a single value that predicts whether a reaction will proceed without the input of additional energy. The formula \( \Delta_{\mathrm{r}} G = \Delta H - T \Delta S \) emphasizes that both heat and disorder contribute to a reaction’s feasibility. When \( \Delta_{\mathrm{r}} G \) is less than zero, the reaction is spontaneous, implying a natural tendency to move forward. This is often linked to a positive standard cell potential in electrochemical processes, aligning with reactions that release energy and favor product formation.

Standard Cell Potential

The standard cell potential, denoted as \(E_{\text{cell}}^{\circ}\), measures how much voltage (energy per charge) a redox reaction generates under standard conditions. It serves as an indicator of the reaction's ability to do work. A positive \(E_{\text{cell}}^{\circ}\) means the reaction is spontaneous. This is because a positive potential reflects a greater tendency for electron flow, which translates into energy being released. The connection between \(E_{\text{cell}}^{\circ}\) and Gibbs Free Energy is fundamentally found in the equation \( \Delta_{\mathrm{r}} G^{\circ} = -nFE_{\text{cell}}^{\circ} \), revealing that a positive \(E_{\text{cell}}^{\circ}\) results in a negative \( \Delta_{\mathrm{r}} G^{\circ} \), further confirming spontaneity and product favorability in the reaction.