## Introduction: What is Nernst Equation?

## What is Nernst Equation?

For analytical chemistry as well as in important life processes such as nerve conduction and membrane potential, the Nernst equation has great utility. Electrochemical cells and hence the Nernst equation is widely used in the calculation of solution pH, solubility product, constant equilibrium, and other thermodynamic properties, potentiometric titrations, and the calculation of cell membrane resting potentials. The Nernst equation lends the relationship between the potential of the electrode and the potential of the standard electrode. It is also used to calculate free energy from the Gibbs, and to predict the spontaneity of an electrochemical reaction.

### Terms and What They Stand for in the Nernst Equation

E

_{cell}stands for cell potential of the cellE

_{0 }stands for cell potential under standard conditionsR stands for the universal gas constant

T stands for temperature

n stands for the number of electrons transferred in the redox reaction

F stands for the Faraday constant

Q stands for the reaction quotient

### Nert Equation Demonstration

For the electrode reaction, Nernst demonstrated that:

Mn+ (aq) + ne– → M(s)

The electrode potential can be represented by any concentration measured in respect of the standard hydrogen electrode:

\[E_{\left ( M^{n+}/M \right )}=E^{0}_{M^{n+}/M}-\frac{RT}{nF}ln\frac{[M]}{[M^{n+}]}\]

However, solid M concentration is taken as unity, and the above equation may be represented as:

\[E_{\left ( M^{n+}/M \right )}=E^{0}_{M^{n+}/M}-\frac{RT}{nF}ln\frac{[1]}{[M^{n+}]}\]

In Daniel cell, the electrode potential for any given Cu^{2+} and Zn^{2+} ion concentration, the above equation can be written as:

For Cathode:

\[E_{\left(Cu^{2+}/Cu\right )}=E^{0}_{Cu^{2+}/Cu}-\frac{RT}{2F}ln\frac{[M]}{[Cu^{2+}+\left ( aq \right )]}\]

For Anode:

\[E_{\left(Zn^{2+}/Zn\right )}=E^{0}_{Zn^{2+}/Zn}-\frac{RT}{2F}ln\frac{[M]}{[Zn^{2+}+\left ( aq \right )]}\]

The cell potential,

\[E_{cell}=E^{0}_{cell}-ln\frac{[Zn^{2+}]}{[Cu^{2+}]}\]

It is clear from the above equation that E(cell) depends on the concentration of both Cu^{2 +} and Zn^{2 + }ions. It increases with an increase in Cu^{2 +} ion concentration and a decrease in the Zn^{2 +} ion concentration. By translating the natural logarithm into the above final E(cell) equation, it reduces to base 10 and substitutes the values of R, F, and T= 298 K.

### Nernst Equation Formula

\[E_{cell}=E^{0}_{cell}-\frac{0.059}{2}log\frac{[Zn^{+2}]}{[Cu^{+2}]}\]

The same number of electrons (n) is to be used for both the electrodes and therefore for the following cell:

Ni(s) | Ni^{2+} (aq) || Ag+ (aq) | Ag(s)

The equation Nernst can be described as:

\[E_{cell}=E^{0}_{cell}-\frac{RF}{2F}ln\frac{[Ni^{+2}]}{[Ag^{+2}]}\]

### Determination of the Equilibrium Constant Using Nernst Equation

When the reactants and the products are taken as part of the chemical reaction reach the point of equilibrium, the value of ΔG becomes 0. This means that there is no change in Gibb’s free energy anymore. Consequently, the reaction quotient and the equilibrium constant (Kc) become the same. As we all know that ΔG is equal to -nFE, the cell potential at equilibrium is thus 0.

By substituting the values of Q and E into the Nernst equation, we reach the equation given below:

0 = E^{0}cell – (RT/nF) ln K_{c}

After further substitution, we reach:

E^{0}cell = (0.0592V/n) log Kc

Ultimately, the equation can be presented in this form:

log Kc = (nE^{0}cell)/0.0592V

Via this method, the relationship between the standard cell potential and the equilibrium constant is established and demonstrated. When K_{c }is greater than 1, the value of E_{0}cell will be greater than 0. This suggests that the equilibrium will shift in the forward direction. In contrast to this, when K_{c} is less than 1, E0cell will turn out to be negative. This implies that the backward reaction will be favoured.

### Importance of Nernst Equation

The Nernst Equation allows for cell potential determination under non - standard conditions. It relates the measured cell potential to the quotient of the reaction and allows the exact determination of constants of equilibrium (including constants of solubility).

### Nernst Equation Applications

### To Determine Solubility Products

The Nernst equation can be used with the minimal error where sufficiently low concentrations of ions are in equilibrium with a sparingly soluble salt. Instead of directly measuring the concentration of the relevant ions, the more common and easier method would be to establish a cell in which one of the electrodes involves the insoluble salt that has a net cell reaction, just as the salt dissolves.

For example, we could use the silver-silver chloride electrode in the cell to calculate the Ksp for silver chloride: The question mark reflects the molarity concentration of the silver ions.

Potentiometric Titrations

In many situations, due to the presence of other ions and a lack of information on the activity coefficients of these ions, precise estimation of an ion concentration through direct measurement of the cell's potential is not feasible. In such situations, therefore, the concentration of the ions may be determined indirectly by titration with some other ion. For example, the initial concentration of an ion such as the Fe^{2+} ion may be found through titration with a strong oxidizing agent such as the solution containing the Ce^{4+} ion. The titration takes place in the left half cell that has a reference electrode in the right half cell

Pt(s) | Fe^{2+} , Fe^{3+} || Reference Electrode

The left cell originally only contains Fe^{2+}. As the titrant Ce^{4+} is added, the ferrous ion is oxidized to Fe^{3+} ions as the reaction comes to an end: Fe^{2+} Ce^{4+} ((Fe^{3+ }Ce^{3+}) The cell potential is measured as the Ce^{4+} is added in small amounts/drops. The left half-cell potential is controlled by the Nernst equation ratio of oxidized and reduced iron ion concentrations.:

E = 0.68 - 0.059log ([Fe^{2+}]/[Fe^{3+} ])

### Measurement of pH

Indeed, the pH of a solution is defined in terms of the activity of the hydrogen ion and not its concentration. A hydrogen electrode provides a direct indicator of hydrogen ion activity (aH^{+}), thus pH= -log aH^{+}. The H^{+} ion molarity is expressed by a question mark which is also a measure of the hydrogen ion concentration.

H2 (g, 1atm) | Pt | H+ (? M) || reference electrode.

### Limitations of the Nernst Equation

We are aware that the activity of an ion in a very dilute solution is nearly infinity. This activity can thus be expressed in terms of ion concentration. However, it is important to note that for solutions having very high concentrations, the ion concentration is not equal to the ion activity. To be able to use the Nernst equation in such cases, the true activity of the ion has to be determined using various experiments.

Although the Nernst equation is quite useful, it has another limitation. The equation cannot be used to measure cell potential when there is electricity flowing between the 2 electrodes given. The flow of current affects the activity of the ions that have accumulated on top of the electrode.

## FAQs on Nernst Equation

**1. What does the Nernst Equation Calculate?**

The Nernst equation calculates the equilibrium potential (also known as the Nernst potential) for an ion based on the ion charge (i.e., its valence) and its membrane-wide concentration gradient. The equation has a plethora of applications in electrochemistry and is quite helpful. Chemists make extensive use of this equation in their daily experiments. Further research is being carried out to modify the Nernst equation so that its limitations can be overcome. We have demonstrated how the equation can be derived too for students’ conceptual understanding.

**2. What is Nernst Equation and its application?**

The Nernst equation establishes a relationship between an electrochemical cell's cell potential, the normal cell potential, temperature, and the quotient for the reaction. Often, the Nernst equation is used to calculate an electrochemical cell's cell potential at any given temperature, pressure, and concentration of reactants. As we have highlighted above, the Nernst equation is used in a variety of applications. It is used to calculate the solubility product of a precipitation reaction, as part of potentiometric titrations, and to measure the pH of a solution.

**3. What is the value of F in the Nernst Equation?**

Nernst equation is a general equation in electrochemistry that relates free energy and cell potential to the Gibbs. It is very useful in determining cell potential, constant equilibrium, etc. The term equals 0.0592 V at standard temperature T = 298K, 2.303 RTF. if they wish to fare well in their Class 12 board exams and the other competitive exams they wish to appear for. You can check out Vedantu's website to know more.

**4. How is the nernst application important from the examination point of view?**

We all know that high-school science students looking to get admission into engineering and medical courses have to sit for many varied entrance exams held nationally. The Nernst equation is an essential part of electrochemistry, which is a unit taught as part of Physical Chemistry in Class 12. Thus, students must be well-versed with the Nernst equation and its numerous applicationsover all the topics to score well in their upcoming examinations. No topic in any subject should be left unread.

**5. What are the other important topics in electrochemistry?**

Electrochemistry in Class 12 starts with a basic introduction to the difference between an electrolytic and an electrochemical cell. The meaning of cell potential and electrode potential is then explained to students. Electrochemical reactions are demonstrated and students are taught how they can represent an equation on paper. Electroplating is another important topic that is part of Class 12 Electrochemistry. Students must try to c F stands for Faraday’s quotient. The value of F equals 96,485 coulombs per mole. For quick calculations, this value is frequently rounded up to 96,500 coulombs per mole. The total charge can be determined by multiplying the number of moles of electrons (n) with the Faraday constant.