The change in the cell voltage when the ion concentrations in the cathode half-cell are increased by a factor of 10 is 0.05 v
The standard reduction potentials for iron and silver are as follows:
[tex]E^o_{(Fe^{2+}/Fe)} = -0.44 V\\E^o_{(Ag^{+}/Ag)} = 0.8 V\\[/tex]
In the given cell, the oxidation occurs at an anode which is a negative electrode whereas the reduction occurs at the cathode which is a positive electrode.
The given cell reactions are:
Oxidation half reaction (anode): [tex]Fe=>Fe^{2+}+2e^-[/tex]
Reduction half reaction (cathode): [tex]Ag^{+} +e^{-} =>Ag[/tex]
Then the anode and cathode will be [tex]E^o_{(Fe^{2+}/Fe)}[/tex]
and [tex]E^o_{(Ag^{+}/Ag)}[/tex] respectively.
The overall cell reaction will be,
[tex]2Ag^{+}+Fe=>Fe^{2+}+2Ag[/tex]
To calculate the [tex]E^o_{cell}[/tex] of the reaction, we use the equation:
Now we have to calculate the cell potential.
Using Nernst equation:
[tex]E_{cell}=E^0_{cell} - \frac{0.0592}{n} log \frac{[Fe^{2+}]}{[Ag^+]^2}[/tex]
where,
n = number of electrons in oxidation-reduction reaction = 2
[tex]E_{cell}[/tex] = emf of the cell = ?
Now put all the given values then we get:
[tex]E_{cell} = 1.24 - \frac{0.0592}{2} log \frac{1M}{(1M)^2} \\E_{cell} =1.24 V[/tex]
.
What is the change in the cell voltage when the ion concentrations in the cathode half-cell are increased by a factor of 10?
Hence, The ion concentrations in the cathode half-cell [tex](Ag^+/Ag)[/tex] are increased by a factor of 10 from 1 M to 10 M.
The emf of the cell potential [tex][Ag^+][/tex] will be 10 M.
Using Nernst equation:
[tex]E_{cell}=E^0_{cell} - \frac{0.0592}{n} log \frac{[Fe^{2+}]}{[Ag^+]^2}[/tex]
[tex]E_{cell} = 1.24 - \frac{0.0592}{2} log \frac{1M}{(10M)^2} \\E_{cell} =1.29 V[/tex]
Then the change in cell voltage will be:
[tex]E_{cell}=1.29v-1.24v=0.05v[/tex]
Thus, the change in the cell voltage when the ion concentrations in the cathode half-cell are increased by a factor of 10 is 0.05 v
Grade: 9
Subject: chemistry
Chapter: the change in the cell voltage
Keywords: the cathode, the cell voltage, half-cell, the change, the ion concentrations
