# 5.3.9 Nernst Equation

### The Nernst Equation

• Under non-standard conditions, the cell potential of the half-cells is shown by the symbol Ecell
• The effect of changes in temperature and ion concentration on the Ecell can be deduced using the Nernst equation E = electrode potential under nonstandard conditions

E = standard electrode potential

R = gas constant (8.31 J K-1 mol-1)

T = temperature (kelvin, K)

z = number of electrons transferred in the reaction

F = Faraday constant (96 500 C mol-1)

ln = natural logarithm

• This equation can be simplified to • At standard temperature, R, T and F are constant
• ln x = 2.303 log10 x
• The Nernst equation only depends on aqueous ions and not solids or gases
• The concentrations of solids and gases are therefore set to 1.0 mol dm-3

#### Applying Nernst equation

• The concentrations of ions for the Fe3+/Fe2+ half-cell are as follows:

Fe3+ (aq) + e⇌ Fe2+ (aq)

[Fe3+] = 0.034 mol dm-3

[Fe2+] = 0.64 mol dm-3

• The Nernst equation for this half-reaction is, therefore: • The oxidised species is Fe3+ as it has a higher oxidation number (+3)
• The reduced species is Fe2+ as it has a lower oxidation number (+2)
• z is 1 as only one electron is transferred in this reaction
• An example of a half-cell in which two electrons are transferred is the Cu2+/Cu half-cell

Cu2+ (aq) + 2e⇌ Cu (s)

[Cu2+] = 0.0010 mol dm-3

• The Nernst equation for this half-reaction is: • The oxidised species is Cu2+ as it has a higher oxidation number (+2)
• The reduced species is Cu as it has a lower oxidation number (0)
• Cu is a solid and is not included in the Nernst equation (its concentration doesn’t change)
• z is 2 as 2 electrons are transferred in this reaction

#### Worked example: Calculating the electrode potential of a Cl2/Cl– half-cell Answer  = (+1.36) + (-0.0121)

= +1.35 V

#### Exam Tip

Make sure you always check what the temperature is. If the temperature is not 298 K (or 25oC) the full Nernst equation should be used.

You don’t need to know how to simplify the Nernst equation to You are only expected to use the equation when the temperature is 298 K (or 25 oC). ### Author: Francesca

Fran has taught A level Chemistry in the UK for over 10 years. As head of science, she used her passion for education to drive improvement for staff and students, supporting them to achieve their full potential. Fran has also co-written science textbooks and worked as an examiner for UK exam boards.
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