4. (a) Use the standard reduction potentials at 25° C in Table 18.1 in Tro, Fridgen...

a) To calculate the standard EMF of an electrochemical cell, we need to figure out the reduction half and oxidation half , followed by their standard reduction potentials.

In the given reaction, Beryllium undergoes oxidation, while sodium cation undergoes reduction.

Be + 2 Na+ --> Be2+ + 2Na

The 2 reactions in this case are :

Oxidation half : Be --> Be2+ + 2e- Eoox = - Eored = - ( -1.847 ) V = 1.847 V

Reduction half : 2 Na+ + 2e- --> 2Na   = 2* Eored = 2( - 2.71) V = - 5.42 V

Eocell =  Eoox + 2* Eored = 1.847 - 5.42 = -3.573 V

Note: The negative value implies that for this electrochemical cell to work, the reverse reaction needs to happen (i.e) Sodium needs to get oxidised to sodium cation and the beryllium cation must undergo reduction to form beryllium.

Be2+ + 2Na --> Be + 2 Na+   EMF = + 3.573 V

b) n = number of electrons transferred during the reaction = 2

c) At 25oC, ΔG = -nFE, where n = number of electrons transferred during the reaction, F= faraday's constant, E = Eocell

we know that n=2 , F=96500 C/mol , Eocell = -3.573 V

ΔG = - 2 mol* 96500 C/mol * (-3.573) J/C = 689589 J = 690 kJ

As the value obtained is positive, the reaction is not spontaneous and hence the cell will not function.

For the reverse reaction, ΔG = - 2 mol* 96500 C/mol * (3.573) J/C = - 690 kJ .

The negative value suggests that this reaction is spontaneous.

d) To find the value of equilibrium constant, we use the nernst equation.

EMF = Eocell - 0.059/n(log Kc)

At equilibrium, EMF = 0

Hence, Eocell = 0.059/n(log Kc)

3.573 = 0.059/2 ( log Kc)

log Kc =  3.573*2/0.059 = 121

Equlibrium constant, Kc = 1.01 * 10121