The overall reaction and equilibrium constant value for a...

The overall reaction and equilibrium constant value for a hydrogen-oxygen fuel cell at 298 $\mathrm{K}$ is $$2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l) \quad K=1.28 \times 10^{83}$$ a. Calculate $8^{\circ}$ and $\Delta G^{\circ}$ at 298 $\mathrm{K}$ for the fuel cell reaction. b. Predict the signs of $\Delta H^{\circ}$ and $\Delta S^{\circ}$ for the fuel cell reaction. c. As temperature increases, does the maximum amount of work obtained from the fuel cell reaction increase, decrease, or remain the same? Explain.

The overall reaction and equilibrium constant value for a hydrogen-oxygen fuel cell at 298 $\mathrm{K}$ is
$$2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l) \quad K=1.28 \times 10^{83}$$
a. Calculate $8^{\circ}$ and $\Delta G^{\circ}$ at 298 $\mathrm{K}$ for the fuel cell reaction.
b. Predict the signs of $\Delta H^{\circ}$ and $\Delta S^{\circ}$ for the fuel cell reaction.
c. As temperature increases, does the maximum amount of work obtained from the fuel cell reaction increase, decrease, or remain the same? Explain.

Key Concepts

Equilibrium Constant (K)

The equilibrium constant is a measure of the relative concentrations of reactants and products at equilibrium for a given reaction. In thermodynamics, it relates to the favorability of a reaction, and a very high value, as seen here, indicates that the reaction strongly favors the products under standard conditions.

Standard Free Energy Change (?G°)

The standard free energy change is a key thermodynamic quantity that indicates the amount of energy available to do work during a reaction at standard conditions. It can be calculated using the equilibrium constant via the relation ?G° = -RT ln K, and it determines the spontaneity of the reaction; a negative ?G° implies that the reaction is spontaneous under standard conditions.

Standard Enthalpy Change (?H°)

The standard enthalpy change represents the total heat exchange at constant pressure during a reaction under standard conditions. It gives insight into whether a reaction is exothermic (releasing heat) or endothermic (absorbing heat). In many reactions involving combustion or fuel cells, ?H° is typically negative, indicating an exothermic process.

Standard Entropy Change (?S°)

The standard entropy change measures the change in disorder or randomness in the system during a reaction. It helps determine the temperature dependence of the free energy change. A negative entropy change might occur when a reaction leads to fewer gas molecules or a more ordered system, whereas a positive change indicates an increase in disorder.

Temperature Dependence of Maximum Work

The maximum work obtainable from a reaction is connected to the free energy change and can be influenced by temperature. As temperature changes, the contributions of both enthalpy and entropy to the free energy change adjust accordingly, which in turn affects the maximum useful work that can be extracted from the reaction. In practical fuel cells, higher temperatures do not necessarily equate to more work since the balance between ?H° and T?S° determines the overall ?G°.

Transcript

00:01 We are given the overall cell reaction for a hydrogen -oxygen fuel cell, and in part a, we want to determine what the standard cell potential is, as well as the change and gives free energy at standard conditions.

00:14 We can look and see that these are the two half -reactions from the standard reduction potentials table that are combined together in order to produce the overall given reaction in the problem statement.

00:26 We see that if we multiply the pop equation by two, then we cancel out four electrons on each side, as well as four h plus ions on each side.

00:38 Now we can clearly see that we are left with the overall reaction that we are given of h2 gas plus o2 gas going to 2h2o liquid.

00:57 And we see that the standard cell potential comes out to 1 .5.

01:04 1 .23 volts.

01:08 And that's one of the quantities that we wanted to determine in part a.

01:11 And we can see and verify that we get that same value if we use the equilibrium constant k that we are given in the problem statement in case we can come up with these two half reactions.

01:23 So we know that from the nerns equation, when we were at equilibrium, cell potential is zero.

01:30 And if we are solving for the standard cell potential, then we do 0 .059.

01:36 And 1 divided by those 4 moles of electrons times the log of k, where k is equal to the given value of 1 .28 times 10 to the power of 83.

01:56 And now if we isolate this equation to solve for that standard cell potential, we see that it does indeed come out to that same value that we just found of 1 .23 volts.

02:08 So that is the answer for the standard cell potential of this fuel cell.

02:13 And now we can solve for the change in gibbs free energy at standard conditions, which we know is just negative n -f -e at standard conditions.

02:24 N is, again, equal to four moles of electrons.

02:30 F is faraday's constant, which is 96 ,485 quillums per mole of e.

02:41 Electrons and the standard cell potential is again 1 .23 volts or joules per coulum and we calculate that out we are left with energy units of joules and if we divide by a thousand we can get it in units of kilojoules and we find that delta g at standard conditions for this hydrogen oxygen fuel cell comes out to about negative four hundred seventy five kilojoules and now in part b, we want to predict what the signs are for delta h and delta s at standard conditions.

03:20 But we just found a value for delta g at standard conditions, and we know that the equation that relates those three variables is delta g at standard conditions is equal to delta h at standard conditions minus t delta s at standard conditions.

03:40 Well, we know from part a that we calculated a value of delta g at standard conditions to be negative.

03:47 So we know that this has to be negative...

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