Calculate Ag When Al3 0.31 M and Ecell 2.417 V

This calculator determines the standard Gibbs free energy change (ΔG) when the concentration of Al³⁺ is 0.31 M and the cell potential (Ecell) is 2.417 V. The calculation uses the Nernst equation, which relates the cell potential to the Gibbs free energy change.

Introduction

The standard Gibbs free energy change (ΔG) is a fundamental thermodynamic property that describes the energy available to do work in a chemical reaction. When dealing with electrochemical cells, the Nernst equation provides a way to calculate ΔG based on the cell potential (Ecell) and the concentrations of the species involved.

In this calculation, we're given:

Concentration of Al³⁺ (c) = 0.31 M
Cell potential (Ecell) = 2.417 V

We'll use these values to determine ΔG using the Nernst equation.

Formula

The Nernst equation relates the cell potential to the Gibbs free energy change:

ΔG = -nFEcell

Where:

ΔG = Gibbs free energy change (J)
n = number of moles of electrons transferred
F = Faraday constant (96,485 C/mol)
Ecell = cell potential (V)

For the reaction Al³⁺ + 3e⁻ → Al, n = 3.

Calculation

Using the given values:

ΔG = -3 × 96,485 C/mol × 2.417 V ΔG = -3 × 96,485 × 2.417 ΔG = -709,308.9 J

The negative sign indicates that the reaction is spontaneous and releases energy.

For the given concentration of Al³⁺ (0.31 M), the calculation remains the same since the Nernst equation uses the standard cell potential (E°) which is independent of concentration. The given Ecell (2.417 V) is already the standard cell potential for this reaction.

Interpretation

The calculated ΔG of -709,308.9 J means:

The reaction releases 709,308.9 joules of energy per mole of Al formed
The reaction is highly spontaneous
The negative value confirms that the reaction will proceed in the forward direction

Note: The concentration of Al³⁺ (0.31 M) does not affect the ΔG calculation in this case because we're using the standard cell potential (E°). If we were calculating the actual cell potential (Ecell) for a non-standard concentration, we would use the Nernst equation with the standard potential and the concentration.

FAQ

What is the difference between ΔG and ΔG°?: ΔG is the Gibbs free energy change for a reaction at any concentration, while ΔG° is the standard Gibbs free energy change for a reaction at standard conditions (1 M concentration for solutes).
Why is the ΔG value negative?: A negative ΔG indicates that the reaction is spontaneous and releases energy. In this case, the formation of Al from Al³⁺ is highly favorable.
How does concentration affect ΔG?: For the standard Gibbs free energy change (ΔG°), concentration does not affect the value. However, for actual Gibbs free energy change (ΔG), concentration affects the cell potential through the Nernst equation.
What is the significance of the Faraday constant?: The Faraday constant (96,485 C/mol) represents the charge of one mole of electrons. It's used to convert between electrical energy and chemical energy in electrochemical reactions.
Can ΔG be calculated from Ecell alone?: Yes, using the relationship ΔG = -nFEcell. This is the basis of the Nernst equation, which connects electrochemical potential to thermodynamic potential.