Zn | Zn²⁺ (α = 0.1 M) || Fe²⁺ (α = 0.01 M) | Fe. The emf of the above cell is 0.2905 V. What is the equilibrium constant for the cell reaction?

Solution

For cell
$Zn | {Zn}^{2 +} (α = 0.1 M) | | {Fe}^{2 +} (α = 0.01 M) | Fe$
The cell reaction
$(i) Zn (s) \to {Zn}^{2 +} (aq) + 2 e (ii) {Fe}^{2 +} (aq) + 2 e \to Fe (s)$

$The overall reaction is Zn (s) + {Fe}^{2 +} (aq) \to {Zn}^{2 +} (aq) + Fe (s)$

On applying Nernst equation
   $E_{cell} = E °_{cell} - \frac{0.0591}{n} \log 10 \frac{[{Zn}^{2 +}]}{[{Fe}^{2 +}]} 0.2905 = E °_{cell} - \frac{0.0591}{2} \log_{10} \frac{0.1}{0.01}$

or $0.2905 = E °_{cell} - 0.0295 \times \log_{10} 10$

or $0.2905 = E °_{cell} - 0.0295 \times 1$

or $E °_{cell} = 0.2905 + 0.0295 = 0.32 V$

At equilibrium $(E_{cell} = 0)$

   $E_{cell} = E °_{cell} - \frac{0.0591}{n} \log_{10} K_{c}$

∴    $0 = E °_{cell} - \frac{0.0591}{n} \log_{10} K_{c}$

or $E °_{cell} = \frac{0.0591}{n} \log_{10} K_{c}$

or $0.32 = \frac{0.0591}{n} \log_{10} K_{c}$

or    $K_{c} = 10^{0.32 / 0.0295} .$

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Electrochemistry

Zn | Zn²⁺ (α = 0.1 M) || Fe²⁺ (α = 0.01 M) | Fe. The emf of the above cell is 0.2905 V. What is the equilibrium constant for the cell reaction?

Some More Questions From Electrochemistry Chapter

Why does the conductivity of a solution decrease with dilution?

Suggest a way to determine the Λ°_m value of water.

The molar conductivity of 0.025 mol L^–1methanoic acid is 46.1 S cm² mol^–1. Calculate its degree of dissociation and dissociation constant. Give λ°(H⁺) = 349.6 S cm²mol^–1 and λ° (HCOO^– ) = 54.6 s cm² mol^–1.

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Electrochemistry

Zn | Zn2+ (α = 0.1 M) || Fe2+ (α = 0.01 M) | Fe. The emf of the above cell is 0.2905 V. What is the equilibrium constant for the cell reaction?

Some More Questions From Electrochemistry Chapter

Why does the conductivity of a solution decrease with dilution?

Suggest a way to determine the Λ°m value of water.

The molar conductivity of 0.025 mol L–1 methanoic acid is 46.1 S cm2 mol–1. Calculate its degree of dissociation and dissociation constant. Give λ°(H+) = 349.6 S cm2 mol–1 and λ° (HCOO– ) = 54.6 s cm2 mol–1.

If the current of 0.5 ampere flows through a metallic wire for 2 hours, then how many electrons flow through the wire?

Suggest a list of metals that are extracted electrolytically.

Consider the reaction: Cr2O72– + 14H+ + 6e- → 2Cr3+ + 8H2OWhat is the quantity of electricity in coulombs needed to reduce 1 mol of Cr2O72-?

Write the chemistry of recharging the lead storage battery, highlighting all the materials that are involved during recharging.

Suggest two materials other than hydrogen that can be used as fuels in fuel cells.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Zn | Zn²⁺ (α = 0.1 M) || Fe²⁺ (α = 0.01 M) | Fe. The emf of the above cell is 0.2905 V. What is the equilibrium constant for the cell reaction?

Suggest a way to determine the Λ°_m value of water.

The molar conductivity of 0.025 mol L^–1methanoic acid is 46.1 S cm² mol^–1. Calculate its degree of dissociation and dissociation constant. Give λ°(H⁺) = 349.6 S cm²mol^–1 and λ° (HCOO^– ) = 54.6 s cm² mol^–1.

Consider the reaction: Cr₂O₇^2– + 14H⁺ + 6e- → 2Cr³⁺ + 8H₂O
What is the quantity of electricity in coulombs needed to reduce 1 mol of Cr₂O₇^2-?