In: Chemistry
51. For a cell based on each of the following reactions run at standard conditions, calculate the emf of the cell, the standard free energy change of the reaction, and the equilibrium constant of the reaction: Get the Potentials from the table of standard reduction potentials available on Blackboard)
a) Mn(s) + Cd +2 (aq) ------> Mn+2 (aq) + Cd(s)
c) 2 Br - (aq) + I2 (s) --------> Br2 (l) + 2 I - (aq)
Equations:
EMF
Eºcell = ERED + ECAT
Gibbs free energy:
deltaGº = -nFEºcell
n, number of transferred electrons.
F, Faraday constant. (96485.3329 s.A/mol)
Eºcell, standard cell potential.
Nernst equation:
Ecell = Eºcell – (RT/nF)Ln(Q)
Ecell, cell potential.
Eºcell, standard cell potential.
R, gas constant (8.314 J/K.mol)
T, temperature (K).
n, number of transferred electrons.
F, Faraday constant. (96485.3329 s.A/mol)
At equilibrium:
Ecell = 0
Q = K (equilibrium constant)
Clear K:
K = e(Eºcell.n.F/R.T)
_______________
a)
Mn --> Mn2+ + 2e-
EºMn = 1.18 V
Cd2+ + 2e- --> Cd
EºCd = -0.403 V
Standard EMF:
Eºcell = 1.18 V - 0.403 V
Eºcell = 0.777 V
Standard Gibbs free energy:
n = 2
Use Gibbs free energy equation.
deltaGº = -149938.2 J/mol
Equilibrium constant:
n = 2
T = 298 K (standard temperature)
Use Nernst equation at equilibrium.
K = 1.9174x1026
_______________
b)
2Br- --> 2Br + 2e-
EºBr = -1.066 V
I2 + 2e- --> 2I-
EºI = 0.535 V
Standard EMF:
Eºcell = 0.535 V - 1.066 V
Eºcell = -0.531 V
Standard Gibbs free energy:
n = 2
Use Gibbs free energy equation.
deltaGº = 102467.4 J/mol
Equilibrium constant:
n = 2
T = 298 K (standard temperature)
Use Nernst equation at equilibrium.
K = 1.0926x10-18