I would like to know if there's a way to calculate the concentration of transcripts based on their transcripts per million value (TPM). I have seevral spikes (small RNA samples) for which the concentration and the molar mass is known. Is there any way to get the values of mol/L for all the transcripts?
You are right, that is kinda unrealistic, during the library preparation there is selection and amplification steps that will alter any real concentration for your sample. Ideally, you can calculate the molecular weight using the sequence composition, then multiply by your read count and divide by the initial volume, you can use the spike sequences to calibrate/test that.
I guess the result will be nowhere near the initial concentration. RNA extraction, conversion to cDNA, fragmentation, adapter ligation, PCR, all the cleanup steps in between. A lot of source of bias.
The above answers are technically correct in highlighting the many ways in which this answer might be wrong. However, for most transcripts these issues are not a serious problem. Have a look at the many (many) papers that have used ERCC standards for quantification of RNA abundance. I have used ERCC standards to quantify transcripts across many RNA seq experiments and have correlated abundance values based upon the calculation you propose to other measures of abundance that did not involve all the technical steps of an RNAseq experiment and find them to be highly correlated.
I know it might be a bit unrealistic. By the way, I forgot to mention that the total ARN concentration is also known.