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# Measuring EMF

You open a coke bottle and want the drink poured into your glass. Well, we are no Harry Potter to achieve that task by magic. We need to invest our energy to do some work of lifting and tilting the bottle so that the liquid falls into your glass. But, it doesn't have to happen that way. The liquid can stay in the bottle, choose not to flow into your glass. It still happens, why? There is pressure inside the bottle. The liquid is, thus, falling from the high-pressure region inside the bottle (and of course with gravity) to the low-pressure region down into your glass.

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Similarly, electrons move from a region of high potential to the region of low potential. If the difference in pressure is what drives water from over head water tanks to your taps, then the difference in potentials at the two electrodes drives the electrons from high potential to low potential. This flow of electrons is electricity/current.

Here, in this article, we are going to explore the emf, which is nothing but the maximum potential difference between electrodes.

• We will introduce you to the definition of emf through the perspective of chemistry, and the simplest form of expression used to calculate it, with an example.
• We will go over the units of emf.
• Then we will explain about the devices that measure emf.
• We will then explain you about another phenomena- back emf.
• We will conclude by the applications of measuring emf in chemistry.

## EMF Definition

EMF is the abbreviation for electromotive force. Although the name has force in it, it is actually not a force, but a form of energy. Let us look into the definition of EMF from the perspective of chemistry.

Electromotive force is defined as the maximum difference in electrode potentials[1] of two electrodes of a cell. EMF is denoted by E. EMF is sometimes referred to as voltage.

$$E_{cell} = E_{Cathode} - E_{Anode}$$

EMF under standard conditions-the standard emf is:

$$E^ \circ_{cell} = E^ \circ_{Cathode} - E^ \circ_{Anode}$$

Have you noticed the emf written on the AA batteries? 1.5 V is the emf of an AA battery.

Calculate the voltage of the following cell whose reduction potentials of half-cells are:

$$Ag^+ | Ag = +0.80 V$$ and $$Zn | Zn^{+2} = -076V$$

Solution:

The equation from the definition is:

$$E_{cell} = E_{Cathode} - E_{Anode}$$

As oxidation takes place at the anode, the reduction potential of zinc represents the anode half-reaction where zinc is being oxidised from $$Zn (0)$$ to $$Zn (+2)$$. Likewise, the reduction potential of Ag represents the reduction half-reaction.

Plugging in the values,

$$E_{cell} = 0.80 - (-0.76)$$

We get,

$$E_{cell} = 1.56 V$$

### What is electrode potential?

To understand what it is, let us first recapitulate the processes that happen at each electrode.

Fig. 1: Daniel cell.

The above picture represents a Daniel cell, an example of voltaic cell. You already know from the article- Electrochemical Cells, what happens and how electricity is generated. Let us cover the main points to understand the electrode potential.

Zinc, dipped in zinc sulfate is the anode half-cell. The zinc metal atoms lose electrons that pass through the wire and reach the cathode where the copper ion in the electrolyte accepts those electrons. This is the net ionic reaction.

Thus, Zinc, on losing electrons becomes oxidised changing into its cation- $$Zn^{+2}$$ . This is oxidation-half-reaction. (These zinc cations jump into the electrolyte.)

As the zinc oxidises to zinc cations, there a separation of charge develops between the electrode and electrolyte. This separation of charge leads to a potential difference of that electrode which is called single electrode potential. Thus, the tendency of an electrode to generate a potential difference between itself and the electrolyte is called the single electrode potential of the half-cell( $$Zn$$ in $$ZnSO_4$$ ).

Similarly, Copper ions (+2) get reduced to copper atoms(0) which is reduction half-reaction. (The reduced copper now gets deposited on the copper electrode.) This will result in a potential difference in this cathode half cell between the electrode and electrolyte.

Simply put,

The tendency of a metal electrode to get oxidised or reduced resulting in a potential difference between the electrode and electrolyte is called electrode potential/single electrode potential of that half-cell.

The tendency of metal at anode to get oxidised is called oxidation potential, while the tendency of metal at cathode to get reduced is called reduction potential. If the electrode potential is measured under standard conditions, it is called standard electrode potential.

To avoid confusion, IUPAC just gave us all these single electrode potential values in the form of their single standard reduction potentials.For example, zinc has a oxidation potential of +0.76 V. This is the measure of its capacity to oxidise. It wants to oxidise readily, thus acting as a reducing agent. It doesn't want to reduce as readily as it intends to oxidise. Therefore, its reduction potential should be very low. Ideally, it is opposite to that of its oxidation potential. It can be written in the following way:$$E_{oxd} = - E_{red}$$ $$E_ {Zn | Zn^{+2}} = - E_{Zn^{+2} | Zn}$$ $$+0.76 V = -0.76 V$$

This reduction potential is the standard reduction potential. Standard reduction potentials are calculated by placing the half cell with unknown reduction potential against the reference electrode whose reduction potential is considered as zero. The Standard Hydrogen Electrode (SHE) is the most commonly used reference electrode.

This standard electrode potential is the emf of that half-cell. The difference in the electrode potentials of the half-cells is the total emf of the cell, also called cell potential, E or $$\epsilon$$

### EMF, the driver of electron flow

For the electrons to flow, there must be some energy that propels them forward. The difference in electrode potentials - the Potential difference, or the total emf of the cell, makes the electrons flow.

#### How emf makes the electrons flow?

Electrons have potential energy in them. As there is an increase in the number of electrons, the overall potential energy increases, thus making the anode half-cell as a region with high potential energy (PE).[2] Also, accumulation of electrons leads to repulsions and electrons just want to get away from there. While on the other hand, the region of cathode is short of electrons, hence short of potential energy-thus, cathode is a region with low potential energy.[2]

Now, this potential difference (High vs low) causes the electrons to move from anode (high PE) to cathode (low PE) just like in a water fall where the water from high-pressure flows down to the region of low pressure. This flow of electrons generates electricity as discussed in the introduction.

This potential difference is the driving factor for the movement of electrons and generation of electricity. EMF is the difference in the individual potential differences (electrode potentials/reduction potentials) of the two electrodes. Just like the difference in masses is again a mass and measured in grams , the difference in individual potential differences is again a potential difference measured in Volts.

Hence, $$E_{Cathode}- E_{Anode\}$$ gives us the emf of that cell.

#### The journey of electrons in terms of reduction potential

This concept of potential energy is not to be confused with electrode potentials. Anode has low electrode potential-meaning low reduction potential-and this is the reason the metal at anode does not want to get reduced, but wants to oxidise. Hence, wants to kick the electrons. On the other hand, Cathode has high electrode potential-meaning high reduction potential, so it grabs the incoming electrons.

Fig. 2: Representation of an anode and a cathode.

To put the journey of electrons in terms of reduction potential, we can say that in a galvanic cell, electrons travel from a region of low potential (Anode) to high potential (Cathode)- [from a region where the tendency to get reduced is low to a region where the tendency to get reduced is high.]

A half-cell is a metal rod (called electrode) dipped in a solution of its metal ions (called electrolyte). It is important to note that it is impossible to measure the absolute single electrode potential/ reduction potential of an electrode. It is always measured relatively which means using a standard reference electrode like SHE.

## EMF units of measurement

EMF is measured in Volts (the SI unit). In physics, emf is also described as the work done-measured in Joules to move a unit charge- in Coulomb from one point to the other.

Thus, Volt, $$V = \frac{W} {Q}$$

Where:

• W = Work done = J
• Q = Unit charge = Coulomb

$$V=\frac{J}{C}$$

Volt is also the unit for standard reduction potential.

## EMF Measuring Devices

Two devices are used to measure the emf- the Potentiometer and the Voltmeter.

Usually, the potentiometer is preferred over the voltmeter because the potentiometer does not draw any current from the circuit to measure the emf, thus does not disturb the circuit. Voltmeter, on the other hand, will draw some current from the circuit to measure the emf. Therefore, the potentiometer is more reliable and accurate as compared to the voltmeter,but, at the same time, more expensive than the voltmeter which is a disadvantage.

Fig. 3: Photo of Voltmeter | Wikimedia Commons

## Back EMF measurement

The name itself gives us some information regarding this type of EMF. Back EMF or rear EMF is that potential difference that works against the applied voltage/actual emf, which can be defined as:

"The opposing emf that is generated in an electrolyte as the products of electrolysis (gases or gaseous ions) get adsorbed on to the surface of the electrodes is known as back emf or rear emf or counter emf."[3]

The best example to explain back emf is an electrolytic cell containing platinum electrodes dipped in sulfuric acid solution. We know what happens in electrolysis of acidified water. Hydrogen gas evolves at cathode, while oxygen gas evolves at anode. Some external voltage(EMF through battery) is applied to drive this reaction as this is non-spontaneous.

After a while, the electrolysis comes to a halt because of the adsorption of gases on the surface of the electrodes. This causes back emf ,which when surpasses the applied external voltage, causes the electrolysis to stop. To overcome this counter attack, we must slowly increase the external voltage. When this external emf again exceeds the back emf, the electrolysis proceeds smoothly.

## Applications of EMF Measurement

There are several applications of measuring emf. Here, we give you a list of a few significant applications:

• The Equilibrium constant for a half-cell reaction can be determined by measuring the emf.
• The gibb's free enegy.
• The solubility product of a sparingly soluble salt can be determined.
• The valency of the number of electrons transferred in a half cell reaction can be determined.
• Free energy.
• $$p^H$$ of a solution can be evaluated.
• Spontaneity of a electrochemical reaction can be determined. If the cell potential is positive, it is a spontaneous reaction (of the galvanic cell). If the cell potential is negative, it is a non-spontaneous reaction (of the electrolytic cell).

That concludes the topic of measuring emf. Through this article, we have explained what emf is and how it is responsible for the flow of electrons and in turn for the generation of electricity. Now you might have understood the concept behind the batteries you are using in your day-to-day life.

## Measuring EMF - Key takeaways

• Electromotive force is defined as the maximum difference in electrode potentials[1]of two electrodes of a cell. EMF is denoted by E. EMF is sometimes referred to as voltage.

$$E_{cell} = E_{Cathode} - E_{Anode}$$

• Electrons flow from Anode with (low reduction potential) to cathode (with high reduction potential).

• EMF is the potential difference that arises due to charge separation. This difference in potentials is the driving factor for the movement of electrons.

• The potential difference that is generated at the electrode/electrolyte interface gives the emf of that half-cell which is also called electrode potential or reduction potential of that half-cell. The cell potential is the difference in the electrode potentials of the two half-cells.

• EMF can be measured by two devices called- Potentiometer and Voltmeter.

• The units of emf are Volts or Joule/Coulomb.

• "The opposing emf that is generated in an electrolyte as the products of electrolysis (gases or gaseous ions) get adsorbed on to the surface of the electrodes is known as back emf or rear emf or counter emf."[3]

## References

1. https://goldbook.iupac.org/terms/view/E01974
2. https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Supplemental_Modules_(Analytical_Chemistry)/Electrochemistry/Basics_of_Electrochemistry
3. http://engineeringslab.com/tutorial_electrical/back-emf-or-polarisation-potential-1589.htm

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How do you measure EMF?

To measure the emf of a cell, we use the following equation:

ECell = ECathode - EAnode

What is the instrument used to measure EMF?

Voltmeter and potentiometer are the two instruments that can measure emf.

What unit is used to measure EMF?

The unit of the EMF is the volt, as you are measuring the voltage.

How do you directly measure the EMF of a cell?

We can measure the emf of a cell directly by connecting a voltmeter to the cell. A voltmeter gives the reading in Volts.

## Test your knowledge with multiple choice flashcards

State whether the following statement is true or false.If a reaction is spontaneous, the emf will be negative.

If a reaction produces a flow of electrons, is it electrolytic or voltaic?

What is the cell potential of a cell whose reduction potentials are given below:$$Zn | Zn^{+2} = -0.76 V$$$$Cu^{+2} | Cu = +0.34 V$$

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