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The measurement and what it assumes

Absorbance is proportional to concentration, to path length and to the extinction coefficient. Rearranged, concentration is absorbance divided by the product of the other two, and that is the whole calculation.

The assumptions behind it are that the sample is in the instrument's linear range, that the only thing absorbing at that wavelength is your peptide, and that the coefficient you are using belongs to the species actually in the cuvette. Each of those fails in a recognisable way.

Staying in the linear range

Below about 0.1 absorbance the signal approaches the instrument's noise. Above about 1.5 the detector receives so little light that small errors in the transmitted intensity become large errors in the calculated absorbance, and stray light begins to dominate.

A reading outside that window should be brought back inside by diluting or by changing the path length. Correcting it arithmetically does not work, because the departure from linearity is not a fixed factor.

Path length and microvolume instruments

A standard cuvette has a 1 cm path. Microvolume instruments that hold a drop of sample between two surfaces use paths of a millimetre or less, and some of them report a value already normalised to 1 cm while others report the raw reading.

Which of the two your instrument does is worth establishing once, because the difference is a factor of ten or more and produces a plausible-looking wrong answer rather than an obviously wrong one.

The two ways the mass concentration goes wrong

The first is a unit error. Molar concentration multiplied by molecular weight in grams per mole is already grams per litre, which is the same number as milligrams per millilitre. Multiplying by a further thousand, as this calculator once did, overstates the mass concentration by exactly that factor.

The second is using the wrong molecular weight. If the material was weighed out as a salt, the salt's weight is the right one; if the extinction coefficient was calculated from the sequence, the free base weight matches it. Mixing the two introduces an error of ten to twenty percent.

How the Beer-Lambert conversion works

One division for the molar concentration and one multiplication for the mass concentration, with the dilution factor applied once so that both figures describe the same sample.

c (mol/L)  = A / (epsilon x path length)
c in stock = c in cuvette x dilution factor
c (mg/mL)  = c (mol/L) x molecular weight (g/mol)

worked: A=0.5, eps=1490, l=1 cm, MW=1419.5
        c = 0.5 / 1490 = 3.36e-4 M
        c = 3.36e-4 x 1419.5 = 0.476 mg/mL
  1. Divide absorbance by the coefficient and the path. Gives the molar concentration in the cuvette. This is the only place the instrument reading enters the calculation.
  2. Apply the dilution factor. Multiplied once, and applied to the molar and mass figures alike so that both describe the original sample rather than one describing the cuvette and the other the stock.
  3. Multiply by molecular weight for mass concentration. Moles per litre times grams per mole is grams per litre, which is numerically identical to milligrams per millilitre. No further scaling is applied, and applying one is the thousandfold error this calculator used to make.
  4. Report both cuvette and stock figures. When a dilution factor is in play, the concentration in the cell and the concentration in the original sample are both shown, so the arithmetic can be followed rather than trusted.
  5. Refuse an impossible input. A zero extinction coefficient returns no result rather than infinity. A peptide with no chromophore cannot be measured this way, and reporting a number would be worse than reporting nothing.

What this method cannot tell you

  • •It assumes only the peptide absorbs at the wavelength used. Nucleic acid, aromatic buffer components and turbidity all inflate the reading.
  • •It assumes the reading is inside the instrument's linear range. Outside it, the relationship between absorbance and concentration is not proportional and no arithmetic recovers the true value.
  • •It assumes the extinction coefficient matches the species in the cell, including its oxidation state.
  • •It says nothing about purity. Impurities that absorb are counted as peptide; impurities that do not are invisible.

Where the numbers come from

UV concentration calculator: frequently asked questions

Absorbance equals the extinction coefficient times the path length times the concentration. Rearranged, concentration is absorbance divided by the other two.

It holds while the sample is dilute enough that molecules absorb independently of each other, which is what defines the linear range.

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