Question

The standard voltage, \(E^{\circ},\) for the reaction of \(\mathrm{Zn}(\mathrm{s})\) and \(\mathrm{Cl}_{2}(\mathrm{g})\) is \(+2.12 \mathrm{V}\). What is the standard free energy change, \(\overline{\Delta G}^{\circ},\) for the reaction?

Short answer

The standard free energy change, \( \overline{\Delta G}^{\circ} \), is \(-408.356 \, kJ/mol\).

Step-by-step solution

Understand the Relationship Between Voltage and Free Energy

We need to find the standard free energy change, \( \overline{\Delta G}^{\circ} \), using the standard voltage, \( E^{\circ} \). The relationship we will use is given by the formula: \[ \overline{\Delta G}^{\circ} = -nFE^{\circ} \] where \( n \) is the number of moles of electrons exchanged, \( F \) is the Faraday constant (approximately \( 96485 \, C/mol \)), and \( E^{\circ} \) is the standard cell potential.

Determine the Number of Electrons, n

The reaction of \( \mathrm{Zn}(\mathrm{s}) \) and \( \mathrm{Cl}_{2}(\mathrm{g}) \) can be represented as: \( \mathrm{Zn(s)} + \mathrm{Cl}_2(\mathrm{g)} \rightarrow \mathrm{Zn^{2+}}(\mathrm{aq)} + 2\mathrm{Cl}^{-}(\mathrm{aq)} \). In this reaction, two electrons are transferred when zinc is oxidized and chlorine is reduced. Therefore, \( n = 2 \).

Calculate \( \overline{\Delta G}^{\circ} \) Using the Formula

Substitute the values \( n = 2 \), \( F = 96485 \, C/mol \), and \( E^{\circ} = +2.12 \, V \) into the formula: \[\overline{\Delta G}^{\circ} = -(2)(96485)(2.12) \]Calculate this expression to find \( \overline{\Delta G}^{\circ} \).

Compute the Result

By performing the multiplication: \( 2 \times 96485 \times 2.12 = 408356.4 \). Thus, \( \overline{\Delta G}^{\circ} = -408356.4 \, J/mol \). You can also express this in kilojoules as \( -408.356 \, kJ/mol \).

Key concepts

Standard Cell Potential

The standard cell potential, denoted as \( E^{ullet} \), is a fundamental concept used in electrochemistry. It defines the voltage or electrical potential difference between two half-cells in a galvanic cell under standard conditions. These standard conditions typically include solutions at 1 M concentration, gases at 1 atm pressure, and a temperature of 25°C (298 K).
Understanding the standard cell potential is crucial because it helps to determine the direction in which electrons will flow through an electrochemical cell. If the cell potential is positive, the reaction is spontaneous, meaning it can occur without any external energy input. It also gives an indication of the cell's ability to produce electric current.

• A higher positive value of \( E^{ullet} \) signifies a greater tendency for the reduction reaction to occur.
• A negative \( E^{ullet} \) typically indicates a non-spontaneous reaction unless driven by an external source.

In essence, the standard cell potential is used to predict the feasibility and direction of electrochemical reactions and plays a vital role in applications like batteries and electrolysis.

Faraday Constant

The Faraday constant, represented by the symbol \( F \), is a key element in the field of electrochemistry. It is defined as the total charge of one mole of electrons and has a value of approximately 96,485 coulombs per mole (C/mol). This constant is vital for calculations involving the transfer of charges in reactions or systems involving electrodes.
When dealing with electrochemical equations and reactions, the Faraday constant allows us to convert moles of electrons transferred in a reaction to the total charge transferred, thus linking chemical changes to electrical energy.

• In equations, \( F \) is often used to calculate the change in free energy from the cell potential, as seen in \( \overline{\Delta G}^{\circ} = -nFE^{\circ} \).
• It also connects the Avogadro's number and electron charge, defining the total charge carried by Avogadro's number of electrons.

Using this constant is crucial in electrochemistry for analyzing reactions and can help in calculating important parameters such as energy changes.

Electrochemistry

Electrochemistry is a branch of chemistry that studies the interaction between electrical energy and chemical reactions. This includes the processes where chemical energy is converted into electrical energy and vice versa.
Electrochemistry encompasses a variety of significant processes, including:

• Galvanic or Voltaic Cells: Producing electrical energy from spontaneous redox reactions.
• Electrolytic Cells: Driving non-spontaneous reactions with electrical energy.
  
• Understanding redox (reduction-oxidation) reactions where electron transfer occurs.

One of the core concepts in electrochemistry is the study of how chemical reactions can create a flow of electrons or current, which is utilized in devices such as batteries and fuel cells. Understanding electrochemistry enables the development of new technologies that harness these processes for various applications.

Electron Transfer

Electron transfer is at the heart of many processes in electrochemistry, involving the movement of electrons from one species to another. This fundamental concept explains how oxidation and reduction reactions occur.
In a typical redox reaction:

• The substance that loses electrons is oxidized.
• The substance that gains electrons is reduced.

The ability of substances to either donate or accept electrons is crucial in understanding how reactions occur and is the basis for predicting the direction of redox processes.

Electron transfer is pivotal in many applications:

• In biological systems, it drives processes like cellular respiration and photosynthesis.
• In everyday technology, it powers batteries and other electric storage devices.

By understanding electron transfer, chemists can manipulate chemical reactions for various applications, making it a cornerstone of both theoretical and applied chemistry.