Nernst Equation

 

Nernst Equation – Easy Notes 📘

What is Nernst Equation?

The Nernst Equation is used to calculate the electrode potential 

or cell potential when concentration is not standard (not 1 M).

👉 Standard electrode potential is measured at:

• Concentration = 1 M
• Temperature = 298 K

But in real cells, concentration changes.
So, Nernst Equation helps us find the actual potential.

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General Nernst Equation

For reaction:

$$aA + bB + ne^- \rightarrow cC + dD$$

Nernst equation is:

$E_{cell}=E^\circ_{cell}-\frac{RT}{nF}\ln Q$

Where,

• $E_{cell}$ = cell potential
• $E^\circ_{cell}$ = standard cell potential
• $R$ = gas constant
• $T$ = temperature in Kelvin
• $n$ = number of electrons transferred
• $F$ = Faraday constant
• $Q$ = reaction quotient

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At 298 K (Important Formula)

The formula becomes simpler:

$E_{cell}=E^\circ_{cell}-\frac{0.0591}{n}\log Q$

This is the most used formula in numericals.

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Meaning of Q (Reaction Quotient)

$$Q = \frac{[Products]}{[Reactants]}$$

👉 Solids and pure liquids are NOT included.

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Example: Daniell Cell

Cell reaction:

$$Zn(s) + Cu^{2+}(aq) \rightarrow Zn^{2+}(aq) + Cu(s)$$

For this cell:

$$Q = \frac{[Zn^{2+}]}{[Cu^{2+}]}$$

So,

$E_{cell}=E^\circ_{cell}-\frac{0.0591}{2}\log\frac{[Zn^{2+}]}{[Cu^{2+}]}$

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Important Points ✨

1. Cell potential increases when:

• Concentration of product decreases
• Concentration of reactant increases

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2. If concentration becomes standard:

• $Q = 1$
  
• $\log 1 = 0$
  

Then,

$$E_{cell} = E^\circ_{cell}$$

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3. Value of n

$n$= total electrons exchanged in balanced equation.

Example:

• Zn → Zn²⁺ + 2e⁻
• Therefore $n = 2$
  

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Short Trick 🧠

Formula Remembering Trick:

$$\textbf{E = E° − correction factor}$$

As concentration changes, potential gets corrected.

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Why is Nernst Equation Important? ⭐

It helps to:

• Calculate actual cell potential
• Study concentration effect
• Calculate equilibrium constant
• Calculate pH
• Understand electrochemical cells

1. Represent the cell in which the following reaction takes place Example 

 Mg(s) + 2Ag+ (0.0001M) ® Mg2+(0.130M) + 2Ag(s) 

Calculate its E(cell) if ( ) o E cell = 3.17 V

2. The e.m.f and the standard e.m.f of a cell in the following reaction is 5V and 5.06V at room temperature, Ni(s) + 2Ag+(n) → Ni2+(0.02M) + 2Ag(s). What is the concentration of Ag+ ions?

a) 0.0125 M

b) 0.0174 M

c) 0.0625 M

d) 0.0314 M