How to calculate carbon to phosphorus stoichiometric ratios using results from ICP-MS and CHN analyzer?

I run a few chemostats to manipulate the carbon to phosphorus ratio (C:P) of algae, which is later feed to an invertebrate. I used Inductively coupled plasma mass spectrometry (ICP-MS) and Inductively coupled plasma atomic emission spectroscopy (ICP-OES) to run samples to measure P and I used CHN analyzer to measure C. Afterwards, I discussed the results with the techs that run those machines and they helped me calculate mol of P in the sample per unit dry weight. Yesterday I showed the C:P ratios of 6 algae samples to my advisor and she said that they were way too P-enriched that they would be toxic to the invertebrate - many of our invertebrates in our dietary experiments that have been feed this algae live throughout the whole experiments. She said that I likely had a calculation error and I should look at my work again. I want back and wrote down everything that I did with the techs and tried out a few things that I thought might fix the problems - none of them worked. So here I am, asking you all to provide me with help.


Before I go into the math, I want to make my preparation work is clear. I performed 2 acid digestions on 6 different algae samples with several replicates. Since we did not know the P concentration of the algae beforehand, we used a variety of weights during the first digestion and ran the samples on ICP-OES. Once we had an idea of the P concentration from the ICP-OES we decided we would run some of the same samples on the ICP-MS and also do another acid digestion, with some tweaks, and ran those samples on ICP-MS. To clarify, we ran 3 “High-P” algae samples and 3 “Low-P” algae samples. The preparation for the CHN analyzer was easy: 1) weighed algae, 2) put them into tin caps, and 3) tossed them into the analyzer.
Without further ado, I will now describe what calculations I have done.


ICP-MS calculations


We calculated the P concentration ppm of the algae by using the P (no gas) counts per second (CPS) value. First, we made a calibration “curve” (aka a linear regression) with the blank and standards. To make the calibration curve we had to make a scatterplot with the standards (10 ppb, 100 ppb, and 1000 ppb standards) and added a line of best fit. We then used the slope and intercept of that graph and input the sample’s P (no gas) CPS value in the equation [slope \* CPS + or - intercept]. Then we calculated our dilution factor: we divided the algae sample weight but the final algae sample weight. To clarify, for the ICP-MS results we digested a small amount of algae (0.20 g) and digested them. Afterwards, we diluted this situation with deionized water until our sample weight reached 100 grams. The P concentration ppm was calculated as [calibration CPS value \* dilution factor / 1000]; the values range from 300 to 2500. **Here, I am unsure why the value was divided by 1000.**


ICP-OES calculations


We calculated the P concentration ppm of the algae by using the P 185.878 value - if I recall we looked at some figures to determine which option was the best, but I cannot explain our choices anymore than that. Again first, we made a calibration “curve” (aka a linear regression) with the blank and standards. To make the calibration curve we had to make a “blank correction”, here we subtracted the blank from the 1, 5, and 10 ppb standards. We plotted those corrected values on a scatterplot and added a line of best fit. Then we used the slope and intercept of that graph and input the sample’s P 185.878 value in the equation [slope \* P 185.878 value + or - intercept]. Then we calculated our dilution factor: we divided the algae sample weight but the final algae sample weight. For the ICP-OES results we digested a small range of algae (0.004 to 0.1 g) and digested them. Afterwards, we diluted this situation with deionized water until our sample weight reached 4 - 8 grams. The P concentration ppm was calculated as [calibration P 185.878 value \* dilution factor]; the values range from 573 to 3306. **Here, I would like to suggest that perhaps the division by the 1000 in the ICP-MS calculations was a correction for the 100 grams used.** The ICP-MS solution was close to water.


Average of P mol/ g of sample calculations


Next, I wanted the mol of P in the sample per unit dry weight, so we multiplied the P concentration ppm by the atomic mass (31) and divided by 1000000 to convert from ug/mol to g/mol. **I am confused about this conversion – these algae samples were in grams so how can this result be converted from ug/mol to g/mol?** I then took the average of P mol / g of sample for each algae sample. A range of Low P algae was 0.01 to 0.025; the range of the High P algae was 0.054 to 0.075.


CHN analyzer calculations


We started with the % of C in the sample. We multiplied %C by the sample weight (micrograms) to receive micrograms of C. Then we divided micrograms of C by atomic mass (12.011) to receive the ug / mol of C. We took that value and divided it by the sample weight (micrograms) to cancel out the micro(grams) so we receive C mol / g of sample. Our end result was the average of C mol/ g of sample – we averaged the algae samples. The range of the samples were 1.79 to 3.09.


C:P calculations


We divided the average of C mol/ g of sample by average of P mol / g of sample to calculate C:P.


Those are all the calculations that we did! Please let me know if you need example charts. I also recognize that this was one of my first times digesting algae so I may have made a mistake with the digestions, but I want to make sure that I did not convert anything incorrectly. I am not a chemist so I could make very easy mistakes an that fact that I am confused by some calculations is probably telling. **If you all do not have suggestions on how to calculate C:P from ICP-MS and CHN please let me know if you know of any video or pdfs that can help me with this!** I want to be sure I did this right before I try to run these digestions again.


