Relationship between Em and E0

The relationship between Em and E0 is important in electrochemistry as it helps to determine the standard electrode potential (E0) of a half-cell reaction from its measured electrode potential (Em).

The equation that relates Em to E0 is known as the Nernst equation, which is given as:

Em = E0 - (RT/nF) ln(Q)

Where:
Em = Measured electrode potential
E0 = Standard electrode potential
R = Gas constant (8.314 J/K mol)
T = Temperature in Kelvin
n = Number of electrons transferred in the half-reaction
F = Faraday constant (96,485 C/mol)
ln = Natural logarithm
Q = Reaction quotient

The value of E0 can be calculated using the Nernst equation when the values of Em, R, T, n, F, and Q are known.

Options provided in the question:

a) Em = -0.537 E0
b) Em = -0.737 E0
c) Em = -0.637 E0 (Correct answer)
d) Em = -0.707 E0

Among the given options, the correct relationship between Em and E0 is option 'c', where Em = -0.637 E0. This means that the measured electrode potential (Em) is approximately two-thirds of the standard electrode potential (E0) for the given half-cell reaction.

This relationship can be used to determine E0 from Em or vice versa. It is important to note that the Nernst equation assumes that the half-cell reaction is at equilibrium and that the concentrations of the reactants and products are known.