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## Concentration calculation from HPLC

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### Concentration calculation from HPLC

Hi there,
Can someone help me confirm the calculations below please:

I extracted 120 mg of my sample (79% moisture) into 10 mL solvent. I then injected an aliquot of the extract into the HPLC and got a concentration of 7 mg/L.
41mg = 7mg/L
=0.17mg/mg of sample
% w/w=17.1

Is my calculation of the concentration in the original sample and the weight percent correct?
Thank you

### Re: Concentration calculation from HPLC

GarryP wrote:
Hi there,
Can someone help me confirm the calculations below please:

I extracted 120 mg of my sample (79% moisture) into 10 mL solvent. I then injected an aliquot of the extract into the HPLC and got a concentration of 7 mg/L.
41mg = 7mg/L
=0.17mg/mg of sample
% w/w=17.1

Is my calculation of the concentration in the original sample and the weight percent correct?
Thank you

Where do the 41 mg come from???

w/w = [concentration of analyte] / [concentration of sample] (both at the same stage of the sample prep e.g. in the vial)

the latter one is
120 mg * (1-0.79) / 0.01 L = 2520 mg/L
So amount is:
7 mg/L / 2520 mg/L = 0.278% w/w (on dried basis)

### Re: Concentration calculation from HPLC

Thank you for your input. The 41mg was a mistake I made in deducing the dry weight content of the sample.

If I want to simply report the concentration in the sample, would that be 7mg/L or do I need to multiply it by 10 mL (the volume in which the sample was extracted) to give 70 mg/L?

### Re: Concentration calculation from HPLC

GarryP wrote:
If I want to simply report the concentration in the sample, would that be 7mg/L or do I need to multiply it by 10 mL (the volume in which the sample was extracted) to give 70 mg/L?

No,no,no, why would the concentration change if you just take more volume of it? Does a small beer have a lower alcohol conc than a big one...?
Also the unit would not be correct if you multiply mg/L * L = mg (L cancels out). Even more mg/L * ml = ug, so 70 mg/l would be totaly wrong.

So in 10ml there are 70ug of analyte, those coming from the 120 mg of sample = amount in the sample "as is" 583*10-6 w/w (=583 ppm)

Same is obtained from previous formula, if you don't correct for the moisture.

### Re: Concentration calculation from HPLC

Something I try to teach my students too:
be strict in using the right terms and check the units

A concentration is always something per volume, so the unit has to be to (something, e.g. g or mol)/L

An amount is mass per mass or unit-peace, so the unit is weight/weight (or pce), e.g g/g or g/tablet

If the unit is just like g, then call it what it is, a mass

further, if not used to it, just write the SI-prefixes as 10^-3 for milli, 10^-6 micro etc, then do the numerics and finaly convert it back to a SI-prefix; e.g mg/l*ml = 10-3g/l*10-3l = 10-6 g = ug

This may help preventing confusion.

### Re: Concentration calculation from HPLC

7 mg/L is concentration determined by the HPLC

7mg/L is the concentration of the 10ml final solution of your extract.

10ml of extract = 0.01L extract

10ml of extract contains (7mg/L) * 0.01L = 0.07mg of analyte

10ml of extract came from 120mg of sample therefore:

120mg sample contains 0.07mg of analyte. which is 0.07mg/120mg

amount of analyte per unit weight of sample = 0.000583mg/1mg which is 0.0583%

Corrected for moisture 0.0583/(1-0.79) = 0.2778%

Just another way to look at the problem.
The past is there to guide us into the future, not to dwell in.

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