A fuel cell designed to react grain alcohol with oxygen has...

A fuel cell designed to react grain alcohol with oxygen has the following net reaction: $$\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+3 \mathrm{H}_{2} \mathrm{O}(l)$$ The maximum work 1 mole of alcohol can yield by this process is $1320 \mathrm{kJ} .$ What is the theoretical maximum voltage this cell can achieve?

Key Concepts

Faraday’s Constant

Faraday’s constant (F) represents the charge per mole of electrons, approximately 96485 coulombs per mole, and is essential in converting between the number of moles of electrons transferred in an electrochemical reaction and the total electrical charge. It thereby serves as a bridge between chemical energy changes and the electrical energy produced in a cell.

Stoichiometry and Electron Transfer

For a given redox reaction in a fuel cell, determining how many electrons are transferred per mole of fuel is crucial. This involves analyzing the oxidation states of the reacting species. Once the number of electrons (n) exchanged is known, it can be used in conjunction with the Gibbs free energy change equation to calculate the theoretical maximum voltage the cell can achieve.

Gibbs Free Energy and Electrical Work

In electrochemistry, the maximum electrical work obtainable from a reaction under reversible conditions is given by the change in Gibbs free energy (?G). The relationship ?G = -nFE_cell connects the free energy change, the number of electrons transferred (n), Faraday's constant (F), and the cell potential (E_cell). This relation is foundational for determining the maximum voltage a fuel cell can achieve based on the thermodynamics of the reaction.

Transcript

00:01 So for this question we have a fuel cell here, okay, a fuel cell that i'm told that one mole of alcohol is supposed to be five, one mole of c2h5 of alcohol can yield a maximum of 1320 kilojoules okay of work, maximum to work, okay, according to this reaction here you have a c2 h5 or h okay it is liquid we are reacting these with with the oxygen so we have three modes of oxygen gas okay and this is going to give us two more of carbon dioxide gas and you know three modes of water three h2 o it's supposed to be three h2o, it is liquid, okay? so according to this reaction, you can see that oxidation state of, because first we need to find oxidation state of carbon.

01:36 We need to find oxidation state, oxidation state of carbon in ethanol.

01:46 And as you can see that, when we're converting that, you know, reactants to products carbon in carbon for oxide and carbon in ethanol here oxidation state of carbon in ethanol is positive too but oxidation of state of carbon in ethanol is four okay because we have that so oxidation state increases from two to four right but then we need to find out the you know number of electrons that are transferred equals to change in oxidation number for instance oxygen from from these to you know the direct and product all right so oxidation state of oxygen here okay so a number of electrons transferred should be equal to you know electrons transferred okay transferred should equal to change in the oxidation state of oxygen mud play by six right by six because because six because we have six months of electrons for oxidation of carbon dioxide because we had you know oxidation states are combined you know from two to four okay so that's a total we're going to get there so this this this is going to be a zero which is a set of oxygen was from zero and this is a change you're going to find minus 2 because oxidation state of oxygen or rather a carbon okay is too right but then oxygen has an oxidation state of 2 in that in this gaseous state here so this means that we're going to get this product this product here multiply by 6 okay and you're going to get 12 as 12 here will signify n factor of carbon okay in factor of carbon which is 12 so which means also that using the formula this formula that links change in you know good for energy equals to negative that in factor by a fraud is constant and multiply also by e -cell.

04:40 But we have changed in that energy...

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