# The time-dependent pH value in a fermentation

I want to know if someone has supporting tips or solutions to my problem: In biotechnology, fermentations are used to grow microorganisms. These need a specific media/broth in which temperature, pH, substrate and many other factors conclude to an optimum. Only if the surrounding broth is in optimal condition for the individual microorganism, the microorganism will grow as best as possible.

In my media the broth is buffered with $$[\ce{HA}] = \ce{H2PO4^-}$$ and $$[\ce{A-}] = \ce{HPO4^2-}$$.

While the fermentation is running the pH is corrected by $$2\ M\ \ce{NaOH}$$ which is pumped into the broth. Via balances, the weight is recorded and the input can be calculated.

I know the initial concentrations of my buffer solutions and the concentration of the base that is dropped into at every minute of record.

How can I calcute the pH for an individual timepoint in my aqueous fermentation? My tries via the Henderson-Hasselbach-formula did not work so far... (Neglecting other surroundings such as stirring, the other media components, the biomass' metabolites, temperature influence on the pKs, etc.),

• I guess you are aiming to control the $p^H$. Are pH probes + a feedback/feedforward control system not possible? – Eashaan Godbole Jul 16 '19 at 14:17
• I need to calculate the pH at different times troughout the process to be able to implement a pH-model on a calculation/formula. It should be used to compare it to the probes and control system.Furthermore to the model made from probes + feedback/feedforward control system. – Capt.Krusty Jul 16 '19 at 16:39