Can someone explain the relationship between EMF and Gibbs free energy?

[Astra]

It was stated in my book that gibbs free energy will always have the opposite sign of EMF.

I was wondering why.

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[NextStepTutor_2]

It was stated in my book that gibbs free energy will always have the opposite sign of EMF.

I was wondering why.

The connection between cell potential, Gibbs energy and constant equilibrium are directly related in the following equations:

∆G is the change of Gibbs (free) energy for a system and ∆G° is the Gibbs energy change for a system under standard conditions (1 atm, 298K). Emf cell is the electromotive force (aka voltage or potential) between two half-cells. The greater the Emf of a reaction the greater the driving force of electrons through the system, the more likely the reaction will proceed (more spontaneous). Emf is measured in volts (V).

Think about the connection. If a reaction has an equilibrium that favors its products, then it is energetically favorable for the reaction to proceed forward on its own (spontaneous). If the reaction is an electrochemical reaction, that means the energy being given off by this spontaneous reaction will be electrical potential energy which is carried by the charges given off (aka voltage aka J/C)

Hope this helps, good luck!

 

[aldol16]

It has to do with which direction electrons want to go. The key equation here is W = q*V. This is from the equation from electric potential energy and the work-energy theorem. If you want electrons to move spontaneously from one point to another to do work, W must be negative. Since q is equal to -e (e = elementary charge), then V must be positive. In other words, electrons want to move from areas of low potential to areas of high potential. This V is also known as the electromotive force (electromotive = moving electrons). So V must be positive. Since we know that delta G gives the spontaneity of an equation and is negative when a reaction is spontaneous, then we can conclude that G and V must have opposite signs because spontaneity implies V positive and delta G negative.