Calculate ℰ^∘ and ΔG^∘ for the reaction 2 H2 O(l) ⟶2 H2(g)+O2(g) at 298 K . Using thermodynamic

Calculate ℰ^∘ and ΔG^∘ for the reaction 2 H2 O(l) ⟶2...

Key Concepts

Standard Cell Potential

The standard cell potential is a measure of the voltage generated by an electrochemical cell under standard conditions. It is related to the tendency of a redox reaction to occur and is computed from tabulated standard reduction potentials of the half?reactions involved. In energy calculations, it serves as the electrical driving force to do work, and it is directly connected to the Gibbs free energy change of the reaction.

Standard Gibbs Free Energy Change

The standard Gibbs free energy change, ?G°, indicates the spontaneity of a reaction under standard conditions. It is determined by the equation ?G° = -nFE°, where n is the number of moles of electrons transferred and F is Faraday’s constant. A negative ?G° implies a spontaneous process, while a positive one suggests non-spontaneity.

Temperature Dependence of Thermodynamic Quantities

When assuming that the enthalpy change (?H°) and the entropy change (?S°) are constant with temperature, the temperature dependence of the Gibbs free energy can be described by the relation ?G = ?H - T?S. This relationship allows one to estimate ?G° at different temperatures from values determined at a reference temperature, linking thermodynamic predictions with experimental temperature variations.

Relationship Between ?G and Electrochemical Work

The connection between Gibbs free energy change and cell potential is fundamental in electrochemistry. The equation ?G° = -nFE° bridges the chemical thermodynamics and the electrical work aspects of a reaction. This relationship helps in converting between the free energy change associated with a reaction and the electromotive force generated when the reaction takes place in an electrochemical cell.

Transcript

00:01 We are given an overall cell reaction, and we first want to find the values of both the standard cell potential, as well as the standard change in gibbs free energy of the overall reaction.

00:13 Based on the overall reaction, we can break it down into these two half reactions from the standard reduction potentials table, along with the corresponding half reactions.

00:24 If we multiply the top equation by two, then we see that we can cancel out formal.

00:31 Of electrons on either side as well as 4h plus ions on each side.

00:38 And so now we can clearly see that we have 2h2o liquid going to o2 gas plus 2h2 gas.

00:54 And again, that is the overall reaction that we are given in the problem statement.

01:00 And now we can find the standard cell potential based on those two reduction potentials that we were given in the table and we flipped the sign of the second half reactions so that it undergoes oxidation to fulfill the form of the overall reaction that we were given.

01:21 And when we add those two potentials together, we see that it comes out to negative 1 .23 volts.

01:32 And now we want to find the change in gibbs free energy at standard conditions, which is equal to negative n -f -e.

01:43 N is equal to those four moles of electrons that we canceled out.

01:50 F is faraday's constant, which is 96 ,485 coolums per mole of electrons, and the standard cell potential we just found was negative 1 .23 jules per coulum.

02:11 And so when we calculate that all out, to find, to find, to find delta g, we can divide by 1 ,000 to get the final answer in units of kilojoules.

02:20 And when we do that, we see that it comes out to about 475 kilojoules.

02:32 And now we want to use data, thermodynamic data in the appendix in order to solve for these same two values at temperatures of zero degrees celsius as well as 90 degrees celsius.

02:46 And we are assuming that delta h and delta s are independent of temperature.

02:51 So we know that the overall equation that relates delta g to those other two variables is delta g equals delta h minus t delta s.

03:05 And we know how we can find the overall change in an enthalpy and entropy for a given reaction based on the data in the appendix.

03:18 And so once we have those values, we can plug in a temperature of both 0 and 90 degrees celsius to determine delta g.

03:26 And then we can backsolve using the delta g equals negative nfe equation to find the standard cell potential at each temperature.

03:36 So we first need to find delta h and delta s at standard conditions for that overall reaction because they're independent of temperature and will be equal to the same values at either one of those temperatures.

03:48 So starting with delta h, the change in enthalpy of the overall reaction, we know this is equal to the total change in enthalpy of the products minus a total change in enthalpy of the reactants.

04:04 When we look at the product side, we see that we have o2 and h2 gas.

04:10 Those are both naturally forming diatomic gas molecules, and so their enthalpy of formation is zero in either case.

04:18 So that means that the total enthalpy change of the products is equal to zero...

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