Question

how to solve nearnst equation

Answer 1

let me explain this to you through an example

Problem

Find the cell potential of a galvanic cellbased on the following reduction half-reactions at 25 °C
Cd2+ + 2 e- → Cd   E0 = -0.403 V
Pb2+ + 2 e- → Pb   E0 = -0.126 V
where [Cd2+] = 0.020 M and [Pb2+] = 0.200 M.

Solution

The first step is to determine the cell reaction and total cell potential.
In order for the cell to be galvanic, E0cell > 0.
, the cadmium reaction must be the oxidation reaction. Cd → Cd2+ + 2 e- E0 = +0.403 V
Pb2+ + 2 e- → Pb E0 = -0.126 V
The total cell reaction is:
Pb2+(aq) + Cd(s) → Cd2+(aq) + Pb(s)
and E0cell = 0.403 V + -0.126 V = 0.277 V
The Nernst equation is:
Ecell = E0cell - (RT/nF) x lnQ
where
Ecell is the cell potential
E0cell refers to standard cell potential
R is the gas constant (8.3145 J/mol·K)
T is the absolute temperature
n is the number of moles of electrons transferred by the cell's reaction
F is Faraday's constant 96485.337 C/mol )
Q is the reaction quotient, where
Q = [C]c·[D]d / [A]a·[B]b
where A, B, C, and D are chemical species; and a, b, c, and d are coefficients in the balanced equation:
a A + b B → c C + d D
In this example, the temperature is 25 °C or 300 K and 2 moles of electrons were transferred in the reaction.


RT/nF = (8.3145 J/mol·K)(300 K)/(2)(96485.337 C/mol)
RT/nF = 0.013 J/C = 0.013 V
The only thing remaining is to find the reaction quotient, Q.
Q = [products]/[reactants]
**For reaction quotient calculations, pure liquid and pure solid reactants or products are omitted.**
Q = [Cd2+]/[Pb2+]
Q = 0.020 M / 0.200 M
Q = 0.100
Combine into the Nernst equation:
Ecell = E0cell - (RT/nF) x lnQ
Ecell = 0.277 V - 0.013 V x ln(0.100)
Ecell = 0.277 V - 0.013 V x -2.303
Ecell = 0.277 V + 0.023 V
Ecell = 0.300 V

Answer

The cell potential for the two reactions at 25 °C and [Cd2+] = 0.020 M and [Pb2+] = 0.200 M is 0.300 volts.