# Difference Spectrum

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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 untill 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 begining 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:

GCT
Homework Helper

## 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 untill 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 begining 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.