Two electrochemical cells \(\mathrm{Zn}\left|\mathrm{Zn}^{2+} \| \mathrm{Cu}^{2+}\right| \mathrm{Cu}\) and \(\mathrm{Fe}\left|\mathrm{Fe}^{2+} \| \mathrm{Cu}^{2+}\right| \mathrm{Cu}\) are connected in series. What will be the net emf of the cell at \(25^{\circ} \mathrm{C} ?\)Given: \(\mathrm{Zn}^{2+} \mid \mathrm{Zn}=-0.73 \mathrm{~V}\) \(\mathrm{Cu}^{2+} \mid \mathrm{Cu}=+0.34 \mathrm{~V}\) \(\mathrm{Fe}^{2+} \mid \mathrm{Fe}=-0.41 \mathrm{~V}\) (a) \(+1.85\) (b) \(-1.85 \mathrm{~V}\) (c) \(+0.83 \mathrm{~V}\) (d) \(-0.83 \mathrm{~V}\)

Electromotive force, commonly abbreviated as EMF, is the energy provided by a cell or a battery per coulomb of charge. It is the measure of the cell's ability to move electrons from the negative electrode to the positive electrode to create an electric current. EMF is expressed in volts (V) and is often considered as the 'pressure' that pushes the charge through the circuit.

Understanding EMF is crucial when studying electrochemical cells, as it allows us to determine how much electrical energy a particular cell can produce. It's the difference in potential between the two electrodes when no current is flowing. The EMF of a cell can be calculated using the standard electrode potentials, where the EMF is the difference between the reduction potentials of the cathode and the anode.

Galvanic cells, also known as voltaic cells, are devices that convert chemical energy into electrical energy through spontaneous redox reactions. To calculate the voltage or EMF of a galvanic cell, we apply the following principle: subtract the standard electrode potential of the anode from that of the cathode. Mathematically, the cell voltage (E) can be expressed as:
\[ E = E_{cathode} - E_{anode} \]

For instance, using the given electrode potentials, a galvanic cell composed of zinc and copper would have its cell voltage calculated as follows:\[ E_{Zn-Cu} = (+0.34V) - (-0.73V) = +1.07V \]
Similarly, for a cell made of iron and copper:\[ E_{Fe-Cu} = (+0.34V) - (-0.41V) = +0.75V \]
These individual voltages of cells in series are added to determine the net EMF of the system. Understanding this process helps students solve related textbook problems and lays a foundation for grasping electrical circuits.

The electrochemical series is a list of elements arranged in order of their standard electrode potentials. Essentially, it is a ranking of metals (and some nonmetals) based on their reactivity when involved in redox reactions. The series is highly useful for predicting the direction of electron flow in electrochemical cells: elements with a higher positive electrode potential will undergo reduction (gain electrons), while those with a lower negative electrode potential will undergo oxidation (lose electrons).

During calculations, the electrochemical series helps us identify the anode and cathode in the galvanic cells. For example, given the potentials:\[ E_{Zn^{2+}/Zn} = -0.73V \]\[ E_{Cu^{2+}/Cu} = +0.34V \]\[ E_{Fe^{2+}/Fe} = -0.41V \]
Zinc, with its more negative potential, acts as the anode when paired with copper. Iron, which is less negative than zinc but more negative than copper, acts as an anode when paired with copper but would act as a cathode if paired with zinc. This hierarchy is essential for predicting reaction spontaneity and for constructing voltaic cells in a laboratory or educational setting.