Hand Calculating Concentration

Discussions about GC-MS, LC-MS, LC-FTIR, and other "coupled" analytical techniques.

3 posts Page 1 of 1
Hi all,

I'm trying to hand-calculate the concentration of an analyte using just the raw data but I'm having trouble finding the right approach.

I have an 8 point internal standard calibrated compound using quadratic regression forced through zero as the calibration model.

I can do the math to calculate if I do not force through zero but I'm stuck on how to evaluate if "c", the intercept, by forcing it to zero.

Any ideas? Thank you.
Regards,

Christian
EDIT

I have a calculator that correctly calculates concentration using av RF, linear, and quadratic, as well as inverse weighted and inverse square weight.

The only thing I cannot seem to figure out is how to program it to force through zero.
Regards,

Christian
I use Newton's Method for this sort of thing. It's an iterative procedure that you can read about in any freshman calculus book. Basically it goes like this for:

R = a1*C + a2*C^2 (could be any polynomial function)

Newton's Method is:

Cn+1 = Cn - (a1*Cn + a2*Cn^2 - Ro)/(a1 + 2*a2*Cn)

Ro is the instrument response for your unknown. a1 and a2 are the regression constants from your calibration curve. You input Ro and the regression constants and keep changing Cn until Cn+1 converges to the answer. The function is only valid over the calibrated range. If your response is outside the calibrated range, you can't use it.

I usually start at zero and walk up in my iterations. For instance, if I put in zero, the Newton's Method expression might say 10.3. Then I put in 10.3 and it might say 12.6. Then I put in 12.6 and it might say 13.1. Then 13.1 might say 13.2. If +/- 0.1 is within the precision of my measurement, I'm probably done.

For R = a0 + a1*C + a2*C^2, Newton's Method is:

Cn+1 = Cn - (a0 + a1*Cn + a2*Cn^2 - Ro)/(a1 + 2*a2*Cn)

The denominator on the right-hand side is basically the derivative of the calibration function with respect to concentration (the slope of the line tangent to the curve at the point).

Good luck.
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