A possible reaction for a fuel cell is CH4( g)+2 O2( g) →CO2( g)+2 H2 O(ℓ) (a) Write the oxidati

A possible reaction for a fuel cell is CH4( g)+2 O2( g)...

A possible reaction for a fuel cell is $$ \mathrm{CH}_{4}(\mathrm{~g})+2 \mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{CO}_{2}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(\ell) $$ (a) Write the oxidation and reduction half-reactions that occur, assuming a basic electrolyte. (b) Use standard free energies of formation from Appendix $G$ to calculate $\Delta G^{\circ}$ for a methane-oxygen cell. From the standard free energy change, calculate the potential this cell could produce under standard conditions. (c) Calculate the number of kilojoules of electrical energy produced when 1 g methane, $\mathrm{CH}_{4}$, is consumed.

A possible reaction for a fuel cell is $$ \mathrm{CH}_{4}(\mathrm{~g})+2 \mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{CO}_{2}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(\ell) $$
(a) Write the oxidation and reduction half-reactions that occur, assuming a basic electrolyte.
(b) Use standard free energies of formation from Appendix $G$ to calculate $\Delta G^{\circ}$ for a methane-oxygen cell. From the standard free energy change, calculate the potential this cell could produce under standard conditions.
(c) Calculate the number of kilojoules of electrical energy produced when 1 g methane, $\mathrm{CH}_{4}$, is consumed.

Key Concepts

Oxidation and Reduction Half-Reactions

In an electrochemical cell, the overall reaction is separated into two half?reactions: one for oxidation (loss of electrons) and one for reduction (gain of electrons). In a fuel cell reaction, identifying these half?reactions is crucial to understand the electron flow and the roles of the fuel and oxidizing agent, regardless of the specific reactants involved.

Basic Electrolyte Conditions

When a reaction occurs in a basic electrolyte, the reaction environment is rich in hydroxide ions (OH–). This influences the half?reactions by requiring the balancing of oxygen and hydrogen atoms through the addition of water and OH–, reflecting the impact of pH on redox processes.

Standard Free Energy of Formation

The standard free energy of formation values allow us to calculate the overall free energy change (?G°) for a reaction from the free energy of each substance in its standard state. This concept is fundamental in thermodynamics and provides the means to assess the spontaneity and feasibility of a reaction under standard conditions.

Relationship Between Free Energy Change and Cell Potential

The link between the standard free energy change (?G°) and the cell potential (E°cell) is given by the equation ?G° = -nFE°cell, where n is the number of moles of electrons exchanged and F is Faraday’s constant. This relationship is central in electrochemistry, connecting thermodynamic properties with electrical work produced by the cell.

Stoichiometry and Energy Calculations

Stoichiometric calculations are used to relate the amount of reactant consumed to the energy produced. By converting the free energy change per mole of reaction to an energy per given mass of fuel, one can assess the efficiency and practical energy output of a fuel cell. This concept integrates chemical reaction stoichiometry with energy conversion metrics.

Transcript

00:01 In this question, we're going to be focusing on a reaction where we've got ch4 relating with 2o2 to produce co2 and 2 moles of h2o.

00:11 Now for the first part of this question, it is important to know that oxidation occurs at the anode while reduction okay's at the capital.

00:19 So the oxidation half equation is going to be ch4 plus 8oh negative producing co2 plus 6h2o plus eight electrons then the reduction half equation we have 2 o2 plus 4 h2 o plus 8 electrons producing c o2 plus this is actually producing o h negative 8 moles of the oh negative and here this is the is the two half -cell equations then moving on to the next part it is important to recall that the gives energy change under standard conditions is equal to negative nf the standard cell potential so the cell potential under standard conditions is going to be the gibbs energy change divided by nf multiplied by a negative right there so what we can do is determine the gibbs energy change of the overall reaction and for us to do that we need to appreciate that gibbs as a state function can be determined as the sum of the gibbs energy change of formation of the product minus the sum of the gibbs energy change of formation of the reactants.

01:37 Now that we have this we can make the substitution.

01:40 This is going to be equal to.

01:42 We are producing one more of co2 with a gibbs energy change of formation of negative 394 .36 and two moles of h2, each with a negative 237 .18 gives energy change of formation.

01:58 So from this we then subtract.

01:59 Some of the gibbs energy change of formation of the reactants where we have one more of methane with a negative 50 .75 plus two more of oxygen each with a zero gives energy change of formation.

02:13 This gives us a standard gibbs energy change that is equal to negative 817 .97 kilojoules which is negative 817 .97 by 10 to the power 3...

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