A solution of transferrin exhibits an absorbance of 0.463 at 470 nm in a 1.000-cm cell. Calculate the concentration of transferrin in mg/mL and the concentration of bound iron in μg/mL.

At wavelength 428(nm), molar absorptivity of transferrin is 3540, at 470(nm) absorptivity of 4170.

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To calculate the concentration of transferrin in mg/mL, we need to use the Beer-Lambert Law. The formula is as follows:

A = εcl

Where:
A = Absorbance
ε = Molar absorptivity
c = Concentration
l = Path length

Given:
Absorbance at 470 nm (A) = 0.463
Path length (l) = 1.000 cm
Molar absorptivity at 470 nm (ε) = 4170

Rearranging the formula, we have:

c = A / (ε × l)

Substituting the given values:

c = 0.463 / (4170 × 1.000)

c = 0.000111 mg/mL

So, the concentration of transferrin is 0.000111 mg/mL.

Now, to calculate the concentration of bound iron in μg/mL, we need the molar absorptivity of transferrin at 428 nm.

Given:
Molar absorptivity at 428 nm (ε) = 3540

Substituting the known values into the Beer-Lambert Law formula:

c = A / (ε × l)

c = 0.463 / (3540 × 1.000)

c = 0.000131 μg/mL

So, the concentration of bound iron is 0.000131 μg/mL.

To calculate the concentration of transferrin in mg/mL, we need to use the Beer-Lambert Law equation:

A = ε * c * l

where:
A is the absorbance (0.463),
ε is the molar absorptivity (in units of M^-1 cm^-1), and
c is the concentration (in units of M),
l is the path length of the cell (1.000 cm).

Rearranging the equation to solve for c:

c = A / (ε * l)

Now we can substitute the values:

c = 0.463 / (4170 M^-1 cm^-1 * 1.000 cm)

c = 0.463 / 4170 M^-1

c = 1.1125 * 10^-4 M

To convert the concentration from Molar to mg/mL, we need to know the molar mass of transferrin. Let's assume it's 80,000 g/mol.

First, convert moles to grams:

1.1125 * 10^-4 mol/L * 80,000 g/mol = 8.9 mg/mL

So, the concentration of transferrin is 8.9 mg/mL.

To calculate the concentration of bound iron in μg/mL, we need to know the concentration of transferrin (c) and the molar absorptivity at 470 nm (ε_470).

Using the same Beer-Lambert Law equation:

A = ε_470 * c * l

Rearranging the equation to solve for c:

c = A / (ε_470 * l)

Now, we can substitute the values:

c = 0.463 / (4170 M^-1 cm^-1 * 1.000 cm)

c = 0.463 / 4170 M^-1

c = 1.1125 * 10^-4 M

To convert the concentration from Molar to μg/mL, we need to know the molar mass of bound iron. Let's assume it's 55.85 g/mol.

First, convert moles to grams:

1.1125 * 10^-4 mol/L * 55.85 g/mol = 6.2 μg/mL

So, the concentration of bound iron is 6.2 μg/mL.