## beers law concentration calculation

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protchem12
Garter Posts: 7
Joined: Thu Jan 12, 2012 5:16 pm

### beers law concentration calculation

Hello,
I need help understanding the units in this calculation. I am asked to provide the concentration of a protein and I am given the number of Trp and Tyr residues, 3 and 6, so I have calculated the molar absorptivity as 3*5600+6*1420= 25320 M^-1cm^-1. Is this the correct units for this value?
The path length is 1cm and the absorbance is 0.57 and the MW is 2438Da.
I have
epsilon = 25320 / (g/L)*cm, is this correct?

so if c= A/epsilon, is the calculation just 0.57/25320 = .0000225 moles/Liter, or .0000225M? i cant figure out where to use the MW.

Thanks!

JackBean
Inland Taipan Posts: 5694
Joined: Mon Sep 14, 2009 7:12 pm
what we have:
e = 25320 M^-1 cm^-1 (this is extinction coefficient)
l = 1 cm
A = 0.57
the formula is
A = e . c. l
thus you have
0.57 = 25320 M^-1 cm^-1 . c . 1 cm
0.00002251 M = c
M mean mol/dm^3, thus if you want concentration in mg/ml, which is usually used for proteins, you have to calculate it with the molar weight.
x (the concentration in mg/ml) = c . M
[g/l] = [mol/l] . [g/mol]
http://www.biolib.cz/en/main/

Cis or trans? That's what matters.

protchem12
Garter Posts: 7
Joined: Thu Jan 12, 2012 5:16 pm

### Re: beers law concentration calculation

Ok I believe the reason I am confused is because in chemistry when we say "concentration" we usually mean molarity, or moles per unit volume. Here you are talking about concentration in terms of mass per volume, which I thought was density? Is it different for proteins than solutions?

JackBean
Inland Taipan Posts: 5694
Joined: Mon Sep 14, 2009 7:12 pm
density and weight concentration are something different.
In density you take weight of whole solution and volume of whole solution and use that for calculation.
In weight concentration you take weight only of your solute (in this case proteins, but it can be and is used for any chemical) and volume of whole solution and use that for calculation.
So yes, the units are the same, which may be confusing, but once you grasp different ways to express concentration, it should not be any problem http://www.biolib.cz/en/main/

Cis or trans? That's what matters.

protchem12
Garter Posts: 7
Joined: Thu Jan 12, 2012 5:16 pm

### Re: beers law concentration calculation

Ok thanks- i had no idea concentration was expressed that way. So when talking about protein concentration is one always referring to weight concentration?

JackBean
Inland Taipan Posts: 5694
Joined: Mon Sep 14, 2009 7:12 pm
yes, usually for all biopolymers (i.e. proteins and nucleic acids) is used the concentration in weight per volume. This is because not all proteins/DNA/RNA molecules have the same molar weight. Consider that when you extract proteins from cell, you get many and many different proteins and each have different size. The same is true for RNA or DNA.
http://www.biolib.cz/en/main/

Cis or trans? That's what matters.

protchem12
Garter Posts: 7
Joined: Thu Jan 12, 2012 5:16 pm
So let me write out the entire question, I want to see if you guys get the same answer as me.
When a pure peptide containing 3 Trp, 6 Tyr, and 1 Phe is placed in a UV/Vis spectrometer, the absorbance measured is 0.57. If there is 1mL of solution in a 1cm path-length cuvette, calculate the approximate concentration of the peptide if the molecular weight is 2438 Da.
I got 9.1624 x 10 -6 mg/ml. is this correct??

JackBean
Inland Taipan Posts: 5694
Joined: Mon Sep 14, 2009 7:12 pm
you have neglected the Phe in your calculation, didn't you?
http://www.biolib.cz/en/main/

Cis or trans? That's what matters.

protchem12
Garter Posts: 7
Joined: Thu Jan 12, 2012 5:16 pm

### Re: beers law concentration calculation

no-
Calculation of ε:
Trp: 3 x 5600 = 16800 + Tyr: 6 x 1420= 8520 + Phe 1x197 = 25517 M-1 cm-1
0.57= 22517 c (1)
c=.000022338 mol/ml
c=( .000022338/2438)/ml = 9.1624 x 10 -6

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