You are measuring the concentration of Fe2 in a sample by measuring the absorbance of its complex with ferroxine. Your sample, measured in a 1.00-cm pathlength cuvette, has an absorbance of 0.347 while the reagent blank in the same cuvette has an absorbance of 0.040. What would be the absorbance reading of these two solutions if measured in a cuvette with 4.00 cm pathlength?

0.347 x 4 = ?

0.040 x 4 = ?

To determine the absorbance reading of the two solutions in a cuvette with a 4.00 cm pathlength, we can use the Beer-Lambert Law. The Beer-Lambert Law states that the absorbance (A) of a sample is directly proportional to the concentration (C) of the absorbing species, the molar absorptivity (ε) of the species, and the pathlength (l) of the sample. Mathematically, it is represented as:

A = ε * C * l

In this case, we know the absorbance (A) of the sample in a 1.00 cm pathlength cuvette is 0.347, and the absorbance of the reagent blank is 0.040. We are trying to find the absorbance readings in a 4.00 cm pathlength cuvette.

To calculate the concentration (C) of Fe2 in the sample, we can use the equation:

A_sample = ε * C_sample * l_sample

A_reagent blank = ε * C_reagent blank * l_reagent blank

Since the two measurements share the same cuvette:

A_sample - A_reagent blank = ε * (C_sample - C_reagent blank) * l_sample

We can rearrange this equation to solve for C_sample:

C_sample = (A_sample - A_reagent blank) / (ε * l_sample) + C_reagent blank

Now, let's calculate the concentration of Fe2 in the sample using the provided data and equation:

C_sample = (0.347 - 0.040) / (ε * 1.00 cm) + 0.040

Next, we need to use the calculated concentration (C_sample) and the new pathlength (4.00 cm) to determine the absorbance readings in the cuvette with a 4.00 cm pathlength. We'll use the Beer-Lambert Law as follows:

A_new = ε * C_sample * l_new

where A_new is the absorbance in the cuvette with a 4.00 cm pathlength, ε is the molar absorptivity of the species, C_sample is the concentration of Fe2 in the sample, and l_new is the new pathlength.

Calculate A_new with the given values:

A_new = ε * C_sample * 4.00 cm

Finally, this will give you the absorbance readings of the two solutions if measured in a cuvette with a 4.00 cm pathlength.

To calculate the absorbance reading of the two solutions in a cuvette with a 4.00 cm pathlength, we can use the Beer-Lambert Law, which states that absorbance is directly proportional to the concentration of the absorbing species and the pathlength:

A = εcl

Where:
A = Absorbance
ε = Molar absorptivity (constant for a given substance)
c = Concentration
l = Pathlength

We can rearrange the equation to solve for the new absorbance (A_new):

A_new = (ε_new * c) * l_new

First, let's calculate the concentration (c) of the sample:

Absorbance (A_sample) = ε * c * l_sample

0.347 = ε * c * 1.00 cm

Next, let's calculate the concentration (c_blank) of the reagent blank:

Absorbance (A_blank) = ε * c_blank * l_blank

0.040 = ε * c_blank * 1.00 cm

We can divide the two equations to eliminate ε:

0.347 / 0.040 = (ε * c * 1.00 cm) / (ε * c_blank * 1.00 cm)

8.675 = c / c_blank

Now, we can substitute the value of c_blank with 1 because the concentration of the reagent blank is usually taken as 1:

8.675 = c / 1

Therefore, the concentration of the sample (c) is equal to 8.675.

Now, let's calculate the new absorbance (A_new) using a 4.00 cm pathlength:

A_new = (ε_new * c) * l_new

A_new = (ε_new * 8.675) * 4.00 cm

The absorbance reading of the sample in the cuvette with a 4.00 cm pathlength would be (ε_new * 8.675) * 4.00 cm.