The Gibbs Free Energy and Cell Voltage

Chapters 12 and 13 discussed the pressure-volume work associated with expanding and compressing gases. In electrochemistry a different kind of work, electrical work, is fundamental. If an amount of charge, Q, moves through a potential difference A, the electrical work is 

The minus sign appears in this equation because the same thermodynamic convention is followed as in Chapters 12 and 13—that work done by the system (here, an electrochemical cell) has a negative sign. Because work is measured in joules and charge in coulombs, has units of joules per coulomb. One volt (abbreviated V) is 1 joule per coulomb. Because the total charge Q is the current / multiplied by the time t in seconds during which the current is flowing, this equation for the electrical work can also be written 

The potential difference A% is positive for a galvanic cell, so meiec is negative in this case and net electrical work is performed by the galvanic cell. In an electrolytic cell, in contrast, A% is negative and rngiec is positive, corresponding to net electrical work done on the system by an external source such as an electric generator. 

00-V battery delivers a steady current of 1.25 A for a period of 1.50 hours. Calculate the total charge Q, in coulombs, that passes through the circuit and the electrical work done by the battery. 

This is the work done on the battery, so the work done by the battery is the negative of this, or -1-40.5 kj. 

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