A cell representation is given: Ag/AgCl $\parallel$ FeCl$_2$, FeCl$_3$ / Pt
Which of the following can increase the EMF of the cell?
(i) By increasing concentration of Fe$^{2+}$
(ii) By increasing concentration of Fe$^{3+}$
(iii) By decreasing concentration of Fe$^{2+}$
(iv) By decreasing concentration of Fe$^{3+}$
(v) By increasing concentration of Cl$^-$

Question

Consider following reaction :
$Fe(OH)_2 + 2e^- \rightarrow Fe(s) + 2OH^-$ , $E^{\circ} = -0.88 \text{ V}$
$AgBr(s) + e^- \rightarrow Ag(s) + Br^-(aq)$ , $E^{\circ} = 0.07 \text{ V}$
Select the correct statement.
(1) $E^{\circ}_{cell} = -0.95 \text{V}$
(2) $E^{\circ}_{cell}$ is an extensive property
(3) $Fe$ is getting reduced
(4) Net cell reaction: $Fe(s) + 2OH^-(aq) + 2AgBr(s) \rightarrow Fe(OH)_2 + 2Ag(s) + 2Br^-(aq)$

Answer 1

To determine which changes will increase the EMF (Electromotive Force) of the given cell, it is essential to understand the cell reaction and apply the Nernst equation. The given cell is represented as:

$Ag/AgCl \parallel FeCl_2, FeCl_3 / Pt$

The cell consists of a reference electrode, Ag/AgCl, and a redox couple of iron in different oxidation states, typically represented by the reaction:

$Fe^{3+} + e^- \rightarrow Fe^{2+}$

The Nernst Equation for this half-cell reaction is:

$E = E^\circ - \frac{RT}{nF} \ln \left( \frac{[Fe^{2+}]}{[Fe^{3+}]} \right)$

where:

$E$ is the electrode potential.
$E^\circ$ is the standard electrode potential.
$R$ is the universal gas constant.
$T$ is the temperature in Kelvin.
$n$ is the number of moles of electrons transferred (here, $n = 1$).
$F$ is the Faraday constant.
$[Fe^{2+}]$ and $[Fe^{3+}]$ are the molar concentrations of Fe²⁺ and Fe³⁺ ions, respectively.

To increase the EMF, we need to increase the value of $E$. From the Nernst equation, it is noted that $E$ increases when:

The concentration of $Fe^{2+}$ decreases because it appears in the denominator inside the logarithm. Lowering the concentration increases the negative term (since the log term becomes more negative), effectively increasing $E$.
The concentration of $Fe^{3+}$ increases, adding to the numerator inside the logarithm, thus decreasing the negative magnitude of the log term and increasing $E$.

Thus, examining the given options:

Option (i): By increasing the concentration of $Fe^{2+}$: This would decrease the EMF, as it increases the denominator.
Option (ii): By increasing the concentration of $Fe^{3+}$: This increases the EMF.
Option (iii): By decreasing the concentration of $Fe^{2+}$: This increases the EMF.
Option (iv): By decreasing the concentration of $Fe^{3+}$: This would decrease the EMF, as it decreases the numerator.
Option (v): The concentration of Cl^- ions affects the Ag/AgCl electrode potential, and typically increasing the concentration of Cl^- can stabilize the cell reaction, potentially increasing the EMF.

Therefore, the options contributing to an increase in EMF are: iii, iv, v.

Correct Answer: iii, iv, v

Show Hint

The Correct Option is B

Solution and Explanation

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