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The standard emf of a cell, involving one electron change is found to be 0.591 V at 25° C. The equilibrium constant of the reaction is (F= 96500 C mol-1)
(AIEEE2004)
- a)1.0 x 101
- b)1.0 x 105
- c)1.0 x 1010
- d)1.0 x 1030
Correct answer is option 'C'. Can you explain this answer?
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Given data:
Standard EMF of the cell, E° = 0.591 V
Temperature, T = 25°C = 298 K
Faraday constant, F = 96500 C mol⁻¹
We know that the relationship between EMF and equilibrium constant is given by the Nernst equation:
E = E° - (RT/nF)lnQ
where,
E = cell EMF
E° = standard cell EMF
R = gas constant = 8.314 J K⁻¹ mol⁻¹
T = temperature in Kelvin
n = number of electrons involved in the reaction
F = Faraday constant
Q = reaction quotient = [products]/[reactants]
At equilibrium, Q = Kc (equilibrium constant in terms of concentration)
Therefore, the Nernst equation can be written as:
E = E° - (RT/nF)lnKc
Comparing with the given data, we get:
E° = 0.591 V
T = 298 K
F = 96500 C mol⁻¹
Hence, we can calculate the equilibrium constant as:
lnKc = (nF/E°)(E° - E)/(RT)
Kc = e^(nF(E° - E)/(RT))
Substituting the values, we get:
lnKc = (1*96500/0.591)(0.591 - 0)/(8.314*298)
lnKc = 45.44
Kc = e^45.44
Kc = 1.0 x 10¹⁰
Thus, the equilibrium constant of the given reaction is 1.0 x 10¹⁰. Therefore, the correct option is (C).
Standard EMF of the cell, E° = 0.591 V
Temperature, T = 25°C = 298 K
Faraday constant, F = 96500 C mol⁻¹
We know that the relationship between EMF and equilibrium constant is given by the Nernst equation:
E = E° - (RT/nF)lnQ
where,
E = cell EMF
E° = standard cell EMF
R = gas constant = 8.314 J K⁻¹ mol⁻¹
T = temperature in Kelvin
n = number of electrons involved in the reaction
F = Faraday constant
Q = reaction quotient = [products]/[reactants]
At equilibrium, Q = Kc (equilibrium constant in terms of concentration)
Therefore, the Nernst equation can be written as:
E = E° - (RT/nF)lnKc
Comparing with the given data, we get:
E° = 0.591 V
T = 298 K
F = 96500 C mol⁻¹
Hence, we can calculate the equilibrium constant as:
lnKc = (nF/E°)(E° - E)/(RT)
Kc = e^(nF(E° - E)/(RT))
Substituting the values, we get:
lnKc = (1*96500/0.591)(0.591 - 0)/(8.314*298)
lnKc = 45.44
Kc = e^45.44
Kc = 1.0 x 10¹⁰
Thus, the equilibrium constant of the given reaction is 1.0 x 10¹⁰. Therefore, the correct option is (C).
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The standard emf of a cell, involving one electron change is found to be 0.591 V at 25 C. The equilibrium constant of the reaction is (F= 96500 C mol-1)(AIEEE2004)a)1.0 x 101b)1.0 x 105c)1.0 x 1010d)1.0 x 1030Correct answer is option 'C'. Can you explain this answer?
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