Introduction:
In this scenario, a platinum electrode is immersed in a solution containing 0.1 M Fe2+ and 0.1 M Fe3+. The electrode is coupled with the Standard Hydrogen Electrode (SHE). The concentration of Fe3+ is then increased to 1.0 M without any change in the concentration of Fe2+. We need to determine the change in electromotive force (EMF) in centivolts (cV) in this situation.

Explanation:

1. Half-Reactions:
To understand the change in EMF, we need to consider the half-reactions occurring at the platinum electrode and the SHE.

At the platinum electrode:
Fe3+ + e- → Fe2+ (1)

At the SHE:
2H+ + 2e- → H2 (2)

2. Nernst Equation:
The Nernst equation relates the EMF of a cell to the activities (or concentrations) of the species involved in the half-reactions. It is given by:

E = E° - (RT/nF) * ln(Q) (3)

Where:
E is the cell potential
E° is the standard cell potential
R is the gas constant
T is the temperature in Kelvin
n is the number of electrons transferred in the balanced equation
F is the Faraday constant
Q is the reaction quotient

3. Calculating the EMF:
To calculate the change in EMF, we can use the Nernst equation and substitute the concentrations of Fe2+ and Fe3+ in the reaction quotient (Q).

Initially, when [Fe3+] = 0.1 M and [Fe2+] = 0.1 M, the reaction quotient (Q1) is given by:
Q1 = [Fe2+] / [Fe3+] = 0.1 / 0.1 = 1

Let's assume the standard potential E° of the cell is E°cell.

Using the Nernst equation (3) for the initial condition, we have:
E1 = E°cell - (RT/nF) * ln(1) = E°cell

Now, when [Fe3+] is increased to 1.0 M while keeping [Fe2+] unchanged, the new reaction quotient (Q2) is:
Q2 = [Fe2+] / [Fe3+] = 0.1 / 1.0 = 0.1

Using the Nernst equation (3) for the new condition, we have:
E2 = E°cell - (RT/nF) * ln(0.1)

4. Calculating the Change in EMF:
The change in EMF (ΔE) can be calculated by subtracting E1 from E2:
ΔE = E2 - E1 = [E°cell - (RT/nF) * ln(0.1)] - E°cell
ΔE = -(RT/nF) * ln(0.1)

5. Converting to centivolts:
To convert the change in EMF to centivolts, we can use the conversion factor 1 V = 100 cV.

ΔE(cV) = ΔE(V) * 100