Consider the following half-reactions and E° values: (c) Write the cell reaction for part (b), and calculate the values of E°, ∆G° (in kilojoules), and K for this reaction at 25 °C

Video transcript

Hello. In this problem, we are asked to refer to the following half reactions and their standard reduction potential values for the combination of reactions that produces the largest voltage of 25°C were asked by the overall cell reaction to determine the standard cell potential. The change in Gibbs, free energy and the equilibrium constant. The reactions that will then provide the largest voltage are those that have the greatest difference in their standard reduction potentials. That will be the first and the third. So the one that has the largest most positive standard reduction potential is the one that has the greatest potential to be reduced. So that reaction will occur at the cathode, the one that has the smallest most negative standard reduction potential. Then this reaction in reverse will take place at the an ode. So writing our reactions then at the cathode, we have bismuth being reduced. The standard reduction potential is 0.240V. Yeah, node then have Valium being oxidized. The standard oxidation potential is equal to the negative of the standard reduction potential. This is equal to 0.549. So we'll combine these two half reactions to get an overall reaction. In order to do that. The moles of electrons being gained has to equal those being lost. So we'll take the reaction occurring at the cathode and multiply through by three. This will then give us an overall reaction of the modes of business ions reacting with thallium. The Form three moles of Bismuth plus Valium irons brand standard cell potential then will be equal to the standard reduction potential plus the standard oxidation potential. This is 0.240V plus 0.549V. This works out to then 0.789V. So we have our overall fast reaction and we have the standard cell potential for this overall reaction. The next thing we're asked to find then these are changing, gives free energy, so the change and gives energy then is related to the standard cell potential. This is equal to then we have three moles of electrons being exchanged. We have the charge on one mole of electrons equal to a fair day, which is 96,004 and 85 columns. And we have our standard cell potential which is 0.789V the call that and is equal to a jewel. And we can convert our jewels kill jules. So our moles of electrons cancels, cancels, bolts, cancels jewels cancels. And we're left with kill jules. So this works out to -288. Kill jules. So this is our changing gives you energy for the overall reaction? We can then make use of change and gives for energy for the overall reaction to find our equilibrium constant, rearranging equation. And solving for equilibrium constant. Are you equilibrium constant? Then have the exponent of the negative of changing good for energy. Goodbye to buy. R gas constant times are temperature. And so our units of joules will cancel Kelvin cancels. We find then that our equilibrium constant is equal to 8.83 times 10 to the 39. So overall reaction, the standard cell potential, the change in gibbs, free energy and our equilibrium constant. All correspondent to answer B. Thanks for watching. Hope. This helped.