Calculating EMF of Galvanic Cell

[ahmetbaba]

Homework Statement

What is the emf of the galvanic cell

Al(s)[Al+3(aq .18mol/liter) [] Fe+2(aq .85mol/liter)[Fe(s)

Homework Equations

The Attempt at a Solution

Al(s) ---> Al+3 + 3e E=-1.676 V

Fe+2 + 2e ---> Fe(s) E=-.440V


How do we proceed after this, and usually in the textbook questions, the number of electrons that are in each reaction are the same, so in this how do we correct that? Do we multiply everything on the top reaction with 2, including the "E", and the bottom reaction with 3, again including the E?

And do we switch the signs for these, or do we just take them as it is?

 

[nate808]

I would like to clarify and provide some additional information to help you solve this problem.

First, let's define what EMF stands for - it stands for "electromotive force" and is a measure of the electrical potential difference between two points in a circuit or cell. In simpler terms, it is the driving force that pushes electrons through a circuit.

In this case, we have a galvanic cell, which is a type of electrochemical cell that uses a spontaneous redox reaction to generate electricity. In this cell, the oxidation reaction of aluminum (Al) and the reduction reaction of iron (Fe) are taking place.

To calculate the EMF of this cell, we need to use the Nernst equation, which takes into account the concentrations of the reactants and products as well as the standard reduction potentials (E°) of the reactions. The Nernst equation is as follows:

EMF = E° - (RT/nF)ln(Q)

Where:
EMF = electromotive force (in volts)
E° = standard reduction potential (in volts)
R = gas constant (8.314 J/mol*K)
T = temperature (in Kelvin)
n = number of electrons transferred in the reaction
F = Faraday's constant (96,485 C/mol)
Q = reaction quotient

To solve this problem, we need to determine the standard reduction potentials for the reactions given and then use the Nernst equation to calculate the EMF of the cell.

To answer your question about the number of electrons in each reaction, we do not need to multiply anything by 2 or 3. The number of electrons transferred in a redox reaction is determined by the balanced chemical equation. In this case, the number of electrons transferred in the oxidation reaction of aluminum is 3, and the number of electrons transferred in the reduction reaction of iron is 2.

As for the signs of the standard reduction potentials, they are already taken into account in the Nernst equation. The standard reduction potentials are given as reduction half-reactions, so they already have the correct sign (positive or negative) for the Nernst equation.

I hope this helps clarify the process for calculating the EMF of a galvanic cell. Remember to always double check your units and make sure they cancel out to give you the correct unit for EMF (volts). Good luck!