Reversible cell voltage

If the total chemical energy content of the fuel, that is, the enthalpy of formation or the heating value, can be converted into electrical energy, then the maximum possible voltage is given as 

For a hydrogen fuel cell at the standard conditions, this is estimated as 

This is the voltage that would be achievable in a 100% efficient fuel cell. However, as we have mentioned, it is the Gibbs free energy that is available for conversion into electrical work in a fuel cell. 

The maximum electrical work in a fuel cell is obtained when all reactions are reversible with no losses and is equal to the change in the Gibbs free energy of formation at the reference standard temperature and pressure (STP), and it is given as 

In reality, the cell operating voltage would be lower than the value given by Equation 4.21 because of voltage losses caused by a number cell irreversibilities associated with the electrochemical reactions and transport processes that will be discussed in later chapters. 

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Figure 2-7 The Variation in the Reversible Cell Voltage as a Function of Reactant Utilization... 

This equation has a standard electrode potential of -0.447 V. Thus, the solution containing mercuric and chloride ions in contact with iron forms a battery. The reduction of the complex ions to metallic mercury is the cathodic reaction. The dissolution of iron is the anodic reaction. The overall reaction in the battery is given by the addition of Equation (13.42) and Equation (13.43). Due to the high value of its reversible cell voltage under standard conditions (0.85 V), it is expected that a very low equilibrium concentration of the complex ion can be achieved. 

Furthermore, the idealised pressure dependence of the entropy yields no change in the cell voltage caused by the system pressure. The reversible cell voltage resulting from the oxidation of hydrogen and carbon monoxide decreases with a higher system temperature and increases with a higher system pressure. 

Fig. 2.3 The reversible cell voltage of different fuels at different states (p, T) of the environment (linearised model and assumption of ideal gas).

From Eq. (151) it follows that a pressure increase from l to P2, causes an increase in the reversible cell voltage ... 

To develop any electrochemical process, a voltage should be applied between anodes and cathodes of the cell. This voltage is the addition of several contributions, such as the reversible cell voltage, the overvoltages, and the ohmic drops, that are related to the current in different ways. One of these contributions, the overvoltage, controls the rate of the transfer of electrons to the electrochemically active species through the electrode-electrolyte interface when there is no limitation in the availability of these active species on the interface (no mass-transfer control and no control by a preceding reaction). In this case, the relationship between the current that flows between the anodes and the cathodes of a cell and the overpotential is... 

If n mol of electrons (or n 3 coulombs of charge) passes through the external circuit of the galvanic cell when it is operated reversibly, and if is the reversible cell voltage, then... 

Reaction (18) represents the oxygen reduction process in acidic solution, the reversible potential then being +1.23 V. This leads to a reversible cell voltage of 0.2 V. The theoretical energy usage per tonne of chlorine in this way is unbeatable 160 kWh. 

The reversible cell voltage at any temperature of operation is designated V , whereas V° is specific to operation under standard conditions. 

Figure 1-17. The reversible cell voltage plotted at dififerent temperatures and pressures for three types of fuels...

Change of Free Enthalpy in Chemical Reactions. Reversible Cell Voltage... 

Sometimes we are interested in knowing the reversible cell voltage of various electrode combinations. However, the number of such combinations is extremely large, and tables of cell voltages would make up a huge amount of data. 

In order to simplify, the quantified concept half-cell potential or electrode potential has been introduced. This has been done by choosing a certain electrode reaction as reference, and defining the equilibrium potential of this electrode to be equal to zero. The numerical value of the equihbrium potential of any other electrode reaction X is given by the reversible cell voltage of the combination X-reference electrode, see Figure 3.7. 

AE is often called the electromotive force (EMF). But we will avoid using this term because it is potentially misleading An electric potential difference is not a force Instead, we will use the term reversible cell voltage ( zero-current cell voltage , open circuit voltage ). We will consider AE to be positive in the case discussed here. At standard conditions, the resulting value for the Daniell cell is... 

We know (compare Sect. 4.7) that there is a close relation between the reversible cell voltage A and the chemical drive Ji of the underlying total reaction. We will use our example to see how this works. We will rearrange Eq. (23.10) ... 

The reversible cell voltage is concentration dependent, just as the redox potential is. We will consider the general cell reaction... 

We mentioned in Sect. 23.2 that galvanic cells can make the energy released by a chemical reaction usable, but they can also be utilized as a measuring instrument for the differences of redox potentials and therefore the electron potentials of various redox pairs. Moreover, because the electron potential itself is determined by the chemical potentials of the substances making up the redox pair, it is also possible to find the fi values as well as the drive A of the underlying total reaction with the help of galvanic cells. Reversible cell voltages measured with zero current can be used to determine these quantities and derived ones such as equilibrium constants. 

Reversible cell voltage ( zero-current cell voltage ) (568) Elementary charge, charge quantum (16)... 

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