Calculate Equilibrium Constant for Spontaneous Cell Reaction | Electrochem Help

[geffman1]

Homework Statement

Refer to the cell below:
Pt / MnO4-(0.10 M), Mn2+(0.20 M).H+(0.010M) // Cr3+(0.40 M), Cr2O72-(0.30 M), H+(0.010M) / Pt
The standard reduction potentials are as follows:
MnO4- + 8H+ + 5e- --> Mn2+ + 4H2O; E° = 1.51 V
Cr2O72- + 14 H+ + 6e- --> 2 Cr3+ + 7H2O; E° = 1.33 V
What is the value of the equilibrium constant at 25°C for the net spontaneous cell reaction?



a. 7.3 x 10^-11

b. 6.1 x 10^-92

c. 91

d. 1.1 x 10^3

e. 2.1 x 10^91

any help would br greatful appreciated. thanks

 

[Borek]

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[Blueshift5]

The value of the equilibrium constant for the net spontaneous cell reaction can be calculated using the Nernst equation:

Ecell = E°cell - (0.0592/n)logQ

Where Ecell is the cell potential, E°cell is the standard cell potential, n is the number of electrons transferred in the reaction, and Q is the reaction quotient.

In this case, n = 5 and the reaction quotient can be calculated as follows:

Q = ([Mn2+][H+]^8)/([MnO4-][H+]^8) x ([Cr3+][H+]^14)/([Cr2O72-][H+]^14)

= ([Mn2+]/[MnO4-]) x ([Cr3+]/[Cr2O72-])

= [(0.20 M)/(0.10 M)] x [(0.40 M)/(0.30 M)]

= 2 x 1.33 = 2.66

Substituting the values into the Nernst equation:

Ecell = (1.51 V) - (0.0592/5)log(2.66)

= 1.51 - (0.01184)log(2.66)

= 1.51 - 0.0333

= 1.48 V

Now, using the equation:

∆G° = -nFE°cell

Where ∆G° is the standard free energy change, n is the number of electrons transferred, and F is the Faraday constant (96,485 C/mol)

We can calculate the standard free energy change for the reaction:

∆G° = -5 x (96,485 C/mol) x (1.48 V)

= -710,182 J/mol = -710.2 kJ/mol

Finally, using the equation:

K = e^(-∆G°/RT)

Where K is the equilibrium constant, R is the gas constant (8.314 J/mol·K), and T is the temperature in Kelvin (25°C = 298 K)

K = e^(-(-710,182 J/mol)/(8.314 J/mol·K x 298 K))

= e^2.84

= 17.1

Therefore, the value of the equilibrium constant for the net spontaneous cell reaction is approximately 17.1. The correct answer is not listed among the