how do i calculate a ratio of oxidised to reduced cytochrome c Fe2+ to Fe3+

given
E(mV) at 25 C and pH7 as 100
and absorbance at 550nm as 1.5

E is relative to standard hydrogen electrode

i don't know how im supposed to calculate it from this data

To calculate the ratio of oxidized (Fe3+) to reduced (Fe2+) cytochrome c, you need to understand the concept of the Nernst equation and how it relates to electron transfer reactions.

The Nernst equation is given by:
E = E˚ + (RT/nF) * ln([ox]/[red])

Where:
E is the measured potential in volts
E˚ is the standard electrode potential in volts
R is the ideal gas constant (8.314 J/(mol·K))
T is the temperature in Kelvin
n is the number of electrons transferred in the reaction
F is the Faraday constant (96485 C/mol)
[ox] and [red] are the concentrations of the oxidized and reduced species, respectively

In this case, cytochrome c can be oxidized from Fe2+ to Fe3+, so the number of electrons transferred is 1 (n = 1).

Given that the E value at 25°C and pH 7 for the Cytochrome c redox couple is 100 mV relative to the standard hydrogen electrode, we can substitute the values into the Nernst equation.

E = 0.10 V + (8.314 J/(mol·K)) * (298 K) / (1 * 96485 C/mol) * ln([Fe3+]/[Fe2+])

Now, you need to use the absorbance at 550 nm (1.5) to determine the concentration ratio of [Fe3+]/[Fe2+].

The absorbance of a substance is directly proportional to the concentration following Beer-Lambert's law, which states:
A = εcl

Where:
A is the absorbance
ε is the molar absorptivity (a constant depending on the substance and the wavelength)
c is the concentration
l is the path length of the cuvette (usually 1 cm)

We can rearrange the equation to determine the concentration:
c = A / (εl)

Since the molar absorptivity (ε) and the path length (l) are not given, we cannot calculate the exact concentrations of Fe3+ and Fe2+ directly.

However, you can still use the Nernst equation to determine the ratio of [Fe3+]/[Fe2+] using the absorbance value:

E = 0.10 V + (8.314 J/(mol·K)) * (298 K) / (1 * 96485 C/mol) * ln([Fe3+]/[Fe2+])

We can assume that the standard electrode potential (E˚) for the cytochrome c redox couple is zero, as it is not provided. This simplifies the equation:

E = (8.314 J/(mol·K)) * (298 K) / (1 * 96485 C/mol) * ln([Fe3+]/[Fe2+])

Now, substitute the absorbance value (A = 1.5) to the equation to get the ratio:

(8.314 J/(mol·K)) * (298 K) / (1 * 96485 C/mol) * ln([Fe3+]/[Fe2+]) = 1.5

You can rearrange the equation to solve for the ratio [Fe3+]/[Fe2+].