If I have a graph of concentration in Absorbance at 400nm vs [micromolar]of para-nitrophenol

The slope would be the extinction coefficient. (y=mx) if forced through 0
The problem is what is y?
I know y is the absorbance but it's given on a paper i have as, y= Absorbance at lmax

Can someone explain what lmax means?
I need to find the concentration of an unknown from this standard curve and I think I find it by first finding the epsilon from the graph, by using..

1. y=mx then:
m= # microM^-1 cm^-1
(not sure if it needs to be in M^-1 or how to convert it to that if I need it to be)
The m is the epsilon.
The problem is that the graph's slope is 0.003653 is molar absorption coefficient supposed to be that small?

2. then I take that and use it to find the concentration of the unknown solution, from beer's law, since I have the absorption of it.
Another issue is that the sample I did measure, was of a solution that I diluted in a ration of 1ml sample to 3ml pH10 buffer. The standard curve sample of 0.1M Paranitrophenol was also diluted with buffer prior to being analyzed, with same ratio of dilution.
First, finding the concentration of the diluted unknown is okay, as long as the absorption coefficient is right...by using A= ebc
A= known
e= calculated from graph above
c= concentration (can be found)
b= 1cm

But how am I to find the original concentration of the unknown stock paranitrophenol if I did not analyze it and was not told to....instruction ssay to, "calculate the concentration of the diluted unknown Paranitrophenol and the original unknown stock paranitrophenol using the standard curve generated"

To start with, "lmax" refers to the wavelength at which the substance absorbs light most strongly. In this case, it is mentioned as "Absorbance at lmax," which means the absorbance of the substance at the specific wavelength where it absorbs light the most.

Now, moving on to your questions:

1. The slope of the graph represents the molar absorption coefficient (also known as the molar absorptivity or the extinction coefficient) if the y-intercept or "forced through 0." The molar absorption coefficient represents how strongly a substance absorbs light at a specific wavelength. In this case, you need to determine the value of y, which represents the absorbance at lmax.

2. The molar absorption coefficient is usually reported in terms of M^-1 cm^-1 (molar per centimeter). If your slope is given as 0.003653, it might not be in the correct units. To convert it to the correct units, you can multiply it by 1000, which will give you the value in M^-1 cm^-1. So, in this case, the molar absorption coefficient would be 3.653 M^-1 cm^-1.

3. The dilution factor of the unknown solution and the standard curve sample should not affect the calculation of the molar absorption coefficient. The molar absorption coefficient remains constant regardless of the dilution factor. However, when you calculate the concentration of the unknown solution using the Beer-Lambert Law (A = ebc), it is important to consider the dilution factor and adjust the concentration accordingly. You would need to multiply the concentration you calculate by the dilution factor to obtain the concentration of the original unknown stock paranitrophenol.

To summarize the steps for finding the concentration of the unknown solution and the original unknown stock paranitrophenol:

1. Determine the molar absorption coefficient (e) by calculating the slope of the graph. Convert the slope to the correct units if needed.
2. Measure the absorbance (A) of the unknown solution.
3. Use the Beer-Lambert Law (A = ebc) to calculate the concentration (c) of the unknown solution, considering the dilution factor.
4. Adjust the concentration of the unknown solution by multiplying it by the dilution factor to obtain the concentration of the original unknown stock paranitrophenol.