# How Do You Calculate Molar Absorptivity?

• rwooduk
In summary: I don't know, it just made more sense to work in that range I guess. And no, I didn't use the entire volume of the solution, I just filled the cuvette up to the top. As for the spectrometer, it's a model I think is called an SBS.
rwooduk

## Homework Statement

I have calculated the molar absorptivity of phenol, I'm pretty sure it's correct but I can't for the life of me figure out what I've done. Any help would be really appreciated.

## Homework Equations

Beers Law:

A = εbc

Where A is absorbance, ε is the molar absorptivity, b is the path length the radiation traverses (1 cm) and c is the concentration of the compound in solution (mol L-1).

## The Attempt at a Solution

I have an absorbance of 0.0745. Then to get the number of moles I have done the following:

0.0283 and 10601 are constants as they appear throughout my calculations, but I have absolutely no idea where they have come from. Kicking myself for not keeping this in my lab book... lesson learned!

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There is something wrong with your units. Molar absorptivity is generally reported in units of M-1 cm-1 (or L mol-1 cm-1). It is possible to convert this figure to an absorption cross section, but this would have units of distance^2.

Ygggdrasil said:
There is something wrong with your units. Molar absorptivity is generally reported in units of M-1 cm-1 (or L mol-1 cm-1). It is possible to convert this figure to an absorption cross section, but this would have units of distance^2.

Sorry maybe I wasn't very clear, the equation has been rearranged for c(=9.7 x 10^-6 moles). It's the constants that are confusing me, would there be any reason to shift the absorbance value by 0.0283? I must have done it for a reason.

Blank?

Surprisingly large value and I would expect it to be negative, but that's the only thing I can think of.

Several points you need to cover:

1) Absorbance of 0.0745 is a little bit lower than the range you should be working in (0.1 to 0.9 is optimal). There must have been some reasons why you had to work in such absorbance range.

2) If you rearranged the equation so that the right side gives you moles of the molecule of whatever solution you used, then you must've multiplied both sides of the original equation by the volume of the solution. Do you remember if you used the entire volume of the original solution or the volume of how much you put in the cuvette? By the way, a typical cuvette can hold around 3 mL.

3) Most of the modern absorption spectrometers come with a software that automatically corrects for blank measurement you did prior to measuring the sample. If not, then I believe Borek is right, although as he said the value is indeed too big and should be negative. Do you remember the manufacturer/model of the spectrometer? A rough description would still help to some degree (does the machine look "modern" or "old"?).

4) Most π-π* transition of low-molecular weight molecules will have a molar absorptivity around minimum of 5000 to 10000 M-1 cm-1 at the peak. If it is a symmetry-forbidden transition, then lower (for example benzene). For phenol, I suspect the transition of the longest wavelength would have roughly around 2000 M-1 cm-1 due to slight reduction of symmetry compared to benzene. Which peak did you work with?

Borek said:
Blank?

Surprisingly large value and I would expect it to be negative, but that's the only thing I can think of.
HAYAO said:
Several points you need to cover:

1) Absorbance of 0.0745 is a little bit lower than the range you should be working in (0.1 to 0.9 is optimal). There must have been some reasons why you had to work in such absorbance range.

2) If you rearranged the equation so that the right side gives you moles of the molecule of whatever solution you used, then you must've multiplied both sides of the original equation by the volume of the solution. Do you remember if you used the entire volume of the original solution or the volume of how much you put in the cuvette? By the way, a typical cuvette can hold around 3 mL.

3) Most of the modern absorption spectrometers come with a software that automatically corrects for blank measurement you did prior to measuring the sample. If not, then I believe Borek is right, although as he said the value is indeed too big and should be negative. Do you remember the manufacturer/model of the spectrometer? A rough description would still help to some degree (does the machine look "modern" or "old"?).

4) Most π-π* transition of low-molecular weight molecules will have a molar absorptivity around minimum of 5000 to 10000 M-1 cm-1 at the peak. If it is a symmetry-forbidden transition, then lower (for example benzene). For phenol, I suspect the transition of the longest wavelength would have roughly around 2000 M-1 cm-1 due to slight reduction of symmetry compared to benzene. Which peak did you work with?

Thanks for the replies, it definitely wasn't a blank, just very low levels of phenol.

Yes, the low absorbance range was because at higher concentrations the phenol did not show any change during the process. Only used the cuvette volume. The machine is brand new, definitely not an issue.

I'm using the 4-AAP method, basically NH4Cl, NH4OH 30% as buffer solution, 4-AAP, and K3Fe(CN)6. In the presence of phenol it gives a peak at 510 nm.

I think I must have adjusted the absorbance to account for a shift in the peak, i.e. the peak wasn't at 510 nm it was slightly to the left or right.

The only thing I can think of is that a calculative method for phenol was given in a paper somewhere (with the value ε=10601 for phenol) and I used the same thing. I'll take a look through my endnote library today.

Many thanks for the suggestions and advice! Just had a little panic yesterday!

rwooduk said:
Thanks for the replies, it definitely wasn't a blank, just very low levels of phenol.

Yes, the low absorbance range was because at higher concentrations the phenol did not show any change during the process. Only used the cuvette volume. The machine is brand new, definitely not an issue.

I'm using the 4-AAP method, basically NH4Cl, NH4OH 30% as buffer solution, 4-AAP, and K3Fe(CN)6. In the presence of phenol it gives a peak at 510 nm.

I think I must have adjusted the absorbance to account for a shift in the peak, i.e. the peak wasn't at 510 nm it was slightly to the left or right.

The only thing I can think of is that a calculative method for phenol was given in a paper somewhere (with the value ε=10601 for phenol) and I used the same thing. I'll take a look through my endnote library today.

Many thanks for the suggestions and advice! Just had a little panic yesterday!
Those are some crucial experimental conditions that you should've provided in your OP...why did you decide to leave that out?

The peak around 510 nm is not due to phenol itself. It is due to the product of the reaction between antipyrine with phenol. So whatever value you used for molar absorptivity of phenol is irrelevant here. (You should know that the absorption of phenol in the longest wavelength is around 280 nm.)EDIT: there are some other experimental errors mentioned in your post, but I am going to leave that out for now.

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rwooduk
HAYAO said:
Those are some crucial experimental conditions that you should've provided in your OP...why did you decide to leave that out?

The peak around 510 nm is not due to phenol itself. It is due to the product of the reaction between antipyrine with phenol. So whatever value you used for molar absorptivity of phenol is irrelevant here. (You should know that the absorption of phenol in the longest wavelength is around 280 nm.)

Fair point. I just thought someone may be able to explain the why I inserted a plus sign into the equation i.e. they had done something similar. But from your reply, it is clear that this is not a standard calculation and I am now 100 % certain it was given in a paper somewhere. You are right I'm not sure why I was looking for the absorptivity of phenol! I'll take this as a slap across the wrist and a lesson learned... always keep a complete lab book! Thanks again.

rwooduk said:
Fair point. I just thought someone may be able to explain the why I inserted a plus sign into the equation i.e. they had done something similar. But from your reply, it is clear that this is not a standard calculation and I am now 100 % certain it was given in a paper somewhere. You are right I'm not sure why I was looking for the absorptivity of phenol! I'll take this as a slap across the wrist and a lesson learned... always keep a complete lab book! Thanks again.
Cool.

Then I would speculate that the extra 0.0283 might be some correction factor, e.g. the absorptivity not ideally linear with the concentration because of absorption wavelength shift, interference from other substance that lowers the absorptivity than the idealistic one, or some other issue. These kind of considerations may start you off (to understand what you should be looking for).

rwooduk
HAYAO said:
Cool.

Then I would speculate that the extra 0.0283 might be some correction factor, e.g. the absorptivity not ideally linear with the concentration because of absorption wavelength shift, interference from other substance that lowers the absorptivity than the idealistic one, or some other issue. These kind of considerations may start you off (to understand what you should be looking for).

That's it ! I remember now, I plotted the absorption vs. concentration (at the very start of my experiments) and used the gradient as some sort of correction. I just need to find the graph ! Awesome, thanks again !

HAYAO said:
EDIT: there are some other experimental errors mentioned in your post, but I am going to leave that out for now.

Hmm, missed this, please could you elaborate a little? I am not a chemist so it is definitely the weaker area of my PhD, unfortunately my examiner will likely be a chemist, so any mistakes I have made in this area could be a problem further down the line. Below is the phenol methodology FYI.

The basis for phenol concentration analysis was via the 4-aminoantipyrine (4-AAP) method in which phenol couples with 4-AAP in an alkaline solution (potassium hexacyanoferrate (III) at PH 7.9 to form a coloured antipyrine complex (AMPH) [19, 50]. This was detectable by UV spectrometry at 510 nm and gave a measurement for the amount of phenol in solution. A blank for UV analysis was made using 2 ml buffer solution containing NH4Cl and NH4OH in 100 ml distilled water, 2 ml 4-AAP reactant in 100 ml distilled water and 2 ml K3Fe(CN)6 catalyst in 100 ml distilled water. For gassed solutions the ‘before’ solution was the phenol solution (0.04 mM) prior to sonication, the ‘after’ solution was the phenol solution after sonication. The following were added to 100 ml of sonicated phenol solution; 2 ml of buffer solution (NH4Cl, NH4OH 30%), 2 ml 4-AAP and 2 ml K3Fe(CN)6 the mixture was then left for 15 minutes to ensure the reaction is complete, followed by spectral analysis.

Final update. I didn't even use Beers Law, I plotted absorbance vs. concentration. I now have the graph which I made. Thanks again for the help.

## 1. What is molar absorptivity?

Molar absorptivity, also known as molar extinction coefficient, is a measure of how strongly a particular substance absorbs light at a specific wavelength. It is used to quantify the amount of light absorbed by a substance in a solution and is dependent on the concentration of the solution.

## 2. How is molar absorptivity calculated?

Molar absorptivity is calculated by dividing the absorbance of a substance at a specific wavelength by its concentration and the path length of the light through the solution. This can be expressed in the formula: ε = A / (c x l), where ε is the molar absorptivity, A is the absorbance, c is the concentration, and l is the path length.

## 3. What is the unit of molar absorptivity?

The unit of molar absorptivity is typically reported as M^-1cm^-1, which stands for moles per liter per centimeter. This unit represents the amount of light absorbed by a substance at a specific wavelength, per unit concentration and path length.

## 4. How does molar absorptivity vary between substances?

Molar absorptivity varies between substances due to their unique chemical structures and functional groups. Some substances may have higher molar absorptivity values, indicating that they strongly absorb light, while others may have lower values, indicating weaker absorption.

## 5. How is molar absorptivity used in analytical chemistry?

Molar absorptivity is commonly used in analytical chemistry to determine the concentration of a substance in a solution. By measuring the absorbance of a solution at a specific wavelength and using the molar absorptivity value, the concentration of the substance can be calculated. This technique is widely used in fields such as environmental testing, pharmaceutical analysis, and biochemical research.

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