# Why Do Absorbance Values Change in the Difference Spectrum of 4-Nitrophenol?

• ~christina~
In summary, the difference spectrum of 4-nitrophenol obtained by considering shape and absorbance values over a chosen range of wavelengths shows changes in the y-axis corresponding to \Delta Absorbance. The difference spectrum is the result of subtracting the basic 4-nitrophenol spectrum from the acidic 4-nitrophenol spectrum. The values of \Delta Absorbance can be greater than 0, less than 0, or equal to 0 depending on the changes in molar absorptivity at each wavelength. This can be explained using Beer's Law, as the molar absorptivity (a) is one of the parameters that changes at each wavelength, along with concentration (c)
~christina~
Gold Member
Difference Spectrum of 4-nitrophenol

## Homework Statement

difference spectrum of 4-nitrophenol

Difference spectrum obtained has y-axis coresponding to $$\Delta$$ Absorbance.
Consider shape and absorbance values over chosen range of wavelengths.

Use beer lambert relationship, explain why some absorbance values are:
a) > 0
b) < 0
c) at one $$\lambda$$ $$\Delta Abs = 0$$

Hint:
1. What parameters in teh beer lambert equation besides Absorbance is changing at each wavelength?
2. How does this affect the difference spectrum?

## Homework Equations

A=abc

3. The Attempt at a Solution

graph descriptions of the y axis:
absolute basic graph 4-nitrophenol: the graph is above the x-axis and curves up from 0.07 - 0.48 and then curves downward from that point to -0.006.
absolute acidic graph: the graph is shaped like an exponential decay line. It starts at 0.265 and then goes downwards to 0.012 and then just goes along the x-axis until hitting 0
basic-acidic difference graph:
The graph looks exactly like the absolute basic graph except that the graph line has shifted downwards towards the (-) axis. The line of the curve going upwards (same as basic)
starts below the x-axis at -0.07 and then curves upwards and goes through the x-axis at 0. Then it hits 0.25 and then curves downwards from there all the way to 0.01 and then proceeds to go along the x-axis close to 0.

I know that the difference spectrum is basically the basic 4-nitrophenol spectrum (looks like exponential decay) - basic spectrum (looks like a curve going up).
But I'm not sure how to explain why some values are below 0, greater than 0, or are = 0.

I know that when Abs= 0 there is 100% transmittance of the light going through the solution.
Also know that at Isosbestic point (where the basic and acid graphs intersected at the beginning of the curves) was where the molar absorptivity (a) was the same for both the species. Is this the reason that the $$\Delta Abs= 0$$ was at about the same x value on the graph difference graph? (close to it about 350 vs 346) I do think it has something to do with it but I'm not sure. (Where the graphs of the absolute spectra intersected, that was the same place that the basic-acidic graph spectra's line went through the zero point of the graph)

I can't explain why using beer's law, how come some values on the difference graph are below 0 and some are above 0. All I can say is that the difference of the spectra caused this, but I don't know how to explain it using beer's law.

Last edited:

~christina~ said:

## Homework Statement

difference spectrum of 4-nitrophenol

Difference spectrum obtained has y-axis coresponding to $$\Delta$$ Absorbance.
Consider shape and absorbance values over chosen range of wavelengths.

Use beer lambert relationship, explain why some absorbance values are:
a) > 0
b) < 0
c) at one $$\lambda$$ $$\Delta Abs = 0$$

Hint:
1. What parameters in teh beer lambert equation besides Absorbance is changing at each wavelength?
2. How does this affect the difference spectrum?

## Homework Equations

A=abc

3. The Attempt at a Solution

graph descriptions of the y axis:
absolute basic graph 4-nitrophenol: the graph is above the x-axis and curves up from 0.07 - 0.48 and then curves downward from that point to -0.006.
absolute acidic graph: the graph is shaped like an exponential decay line. It starts at 0.265 and then goes downwards to 0.012 and then just goes along the x-axis until hitting 0
basic-acidic difference graph:
The graph looks exactly like the absolute basic graph except that the graph line has shifted downwards towards the (-) axis. The line of the curve going upwards (same as basic)
starts below the x-axis at -0.07 and then curves upwards and goes through the x-axis at 0. Then it hits 0.25 and then curves downwards from there all the way to 0.01 and then proceeds to go along the x-axis close to 0.

I know that the difference spectrum is basically the basic 4-nitrophenol spectrum (looks like exponential decay) - basic spectrum (looks like a curve going up).
But I'm not sure how to explain why some values are below 0, greater than 0, or are = 0.

I know that when Abs= 0 there is 100% transmittance of the light going through the solution.
Also know that at Isosbestic point (where the basic and acid graphs intersected at the beginning of the curves) was where the molar absorptivity (a) was the same for both the species. Is this the reason that the $$\Delta Abs= 0$$ was at about the same x value on the graph difference graph? (close to it about 350 vs 346) I do think it has something to do with it but I'm not sure. (Where the graphs of the absolute spectra intersected, that was the same place that the basic-acidic graph spectra's line went through the zero point of the graph)

I can't explain why using beer's law, how come some values on the difference graph are below 0 and some are above 0. All I can say is that the difference of the spectra caused this, but I don't know how to explain it using beer's law.

I haven't actually done any experiments with this concept , from the hint , I'm guessing it is directing you to investigate the fact that the molar absorptivity is distinct at each wavelength ... the particular atom involved in the functional group has varying degrees of molar absorptivity corresponding to various wavelengths and this attribute can be altered by either deprotonating it or protonating it or groups that are nearby.

What is the x axis? Is this a titration of some sort - I'm guessing not - what is meant by basic and acidic graphs?

!

I would first like to clarify that the difference spectrum is a graph that shows the difference in absorbance between two spectra, in this case, the basic and acidic spectra of 4-nitrophenol. This can be calculated by subtracting the absorbance values of the basic spectrum from the acidic spectrum at each wavelength.

Now, to answer the question of why some values on the difference spectrum are above or below 0, we need to consider the Beer-Lambert law. This law states that the absorbance of a substance is directly proportional to the concentration of the substance and the path length of the light through the sample. Hence, when the concentration or path length changes, the absorbance value will also change.

In the case of the basic and acidic spectra of 4-nitrophenol, the concentration of the substance is changing due to the difference in pH. As the pH of the solution changes, the equilibrium between the basic and acidic forms of 4-nitrophenol also changes, resulting in different concentrations of each form. This change in concentration leads to a change in absorbance, which is reflected in the difference spectrum.

When the difference spectrum has a positive value, it means that the absorbance of the acidic spectrum is higher than the basic spectrum at that particular wavelength. This indicates that the acidic form of 4-nitrophenol has a higher concentration compared to the basic form at that pH. Similarly, when the difference spectrum has a negative value, it means that the absorbance of the basic spectrum is higher, indicating a higher concentration of the basic form.

At the isosbestic point, where the difference spectrum has a value of 0, it means that the absorbance of both the basic and acidic spectra is the same. This occurs because at this point, the concentrations of both forms are equal, resulting in equal absorbance values.

In summary, the difference spectrum of 4-nitrophenol reflects the changes in concentration of the basic and acidic forms of the molecule at different pH values, and this is in accordance with the Beer-Lambert law.

## What is a Difference Spectrum?

A Difference Spectrum is a graphical representation of the difference between two spectra, typically used in spectroscopy. It shows the changes in intensity or absorption of a sample at different wavelengths.

## How is a Difference Spectrum calculated?

A Difference Spectrum is calculated by subtracting the intensity or absorbance values of one spectrum from another. This can be done manually or using software programs.

## What information can be obtained from a Difference Spectrum?

A Difference Spectrum can provide information about the changes in chemical composition, concentration, or environment of a sample. It can also be used to identify specific molecules or compounds.

## How is a Difference Spectrum used in research?

A Difference Spectrum is commonly used in research to compare the spectral data of different samples, track changes over time, or identify differences between normal and abnormal samples.

## Can a Difference Spectrum be used for quantitative analysis?

Yes, a Difference Spectrum can be used for quantitative analysis by measuring the changes in intensity or absorbance at a specific wavelength and relating it to the concentration of a sample. However, it is more commonly used for qualitative analysis.

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