**Electrochemical Cells Nernst Equation and Gibbs Energy**

__Syllabus:-__

- Electrolytic cells & Galvanic cells
- The function of Salt Bridge
- Redox reaction, EMF of the cell, standard electrode potential
- Standard hydrogen electrode (SHE)
- Nernst equation and its application to Chemical cell
- Equilibrium Constant from Nernst Equation
- Electrochemical Cell and Gibbs Energy

**Electrochemistry:** It is a branch of chemistry that deals with the relationship between chemical energy and electrical energy and their interconversions.

**Redox Reactions:** Oxidation is the process that involves the loss of electrons & reduction is a process in which it involves the gain of electrons. The reactions which involve both that reaction simultaneously are called a __redox reaction__.

**Electrochemical Cells****:** These are devices that __convert the chemical energy of some redox reactions to electrical energy__. They are also called Galvanic cells or Voltaic cells. An example for a __Galvanic cell is Daniel cell.__

It is constructed by dipping a Zn rod in ZnSO_{4} solution and a Cu rod in CuSO_{4} solution. The two solutions are connected externally by a metallic wire through a voltmeter and a switch and internally by a salt bridge.

A salt bridge is a U-tube containing an inert electrolyte like NaNO_{3} or KNO_{3} in a gelly like substance. __The functions of a__ __salt bridge are:__

- To complete the electrical circuit
- To maintain the electrical neutrality in the two half cells.

- Cu
^{2+}+ 2 e^{–}→ Cu(s) (reduction half reaction) - Zn(s) → Zn
^{2+}+ 2 e^{–}(oxidation half reaction)

These reactions occur in two different portions of the Daniel cell. The reduction half-reaction occurs on the copper electrode while the oxidation half-reaction occurs on the zinc electrode. These two portions of the cell are also called ** half-cells or redox couples**. The copper electrode may be called the reduction half-cell and the zinc electrode, the oxidation half-cell.

Electrochemical Cells Nernst Equation and Gibbs Energy

**Electrode Potential:** This tendency of a metal to lose or gain an electron when it is in contact with its own solution is called ** electrode potential**.

**Standard** **electrode** **potential** **(E0)**: The electrode potential measured at standard conditions.ie at 298K,1 atm pressure, and at 1 molar concentration.

**Standard ****hydrogen electrode ****(SHE)**: The reference electrode used to measure single electrode potential. Its potential is assumed to be zero. It consists of a platinum wire dipped in HCl of 1 molar concentration. Hydrogen gas at 1 atm. is passed through the solution. The electrode can be represented as Pt, H_{2} /H^{+}(1M).

**Nernst Equation For A Cell Reaction:-**

Let us consider a general equation

aA + bB → cC + dD

E = E^{0}_{cell} – 2.303 RT × log [C]^{c} [D]^{d}

nF [A]^{a} [B]^{b}

Where E^{0} is the standard electrode potential,

*R* is the gas constant (8.314 JK^{–1} mol^{–1})

*F* is Faraday constant (96500 C mol^{–1})

*T* is the temperature in Kelvin.

__Nernst equation can be written as__:

Putting the above values Nernst equations can be written as

**E****quilibrium Constant from Nernst Equation:**

** **Electrochemical Cells Nernst Equation and Gibbs Energy

**Electrochemical Cell and Gibbs Energy of the Reaction:**

Electrical work done in one second is equal to electrical potential multiplied by total charge passed. The reversible work done by a galvanic cell is equal to a decrease in its Gibbs energy and therefore if the emf of the cell is *E* and *nF* is the amount of charge passed and ∆*G* is the Gibbs energy of the reaction, then

∆G = – nFE_{cell}

If the concentration of all the reacting species is unity, then E_{cell} = E^{0}_{cell} and we have

∆G^{0} = – nFE^{0} _{cell}

Thus, from the measurement of E^{0}_{cell}, we can calculate the standard Gibbs energy of the reaction.