Question $1)$

a$)$ Construct a half reaction for the oxidation of hydrogen sulfide to elemental sulfur $($S$).$ Write the half reaction on one electron equivalent basis.

b$)$ Use the free energies of formation in lecture slides$/$handout to calculate the standard free energy change $($all reactants and products at standard conditions except pH which is $7),\backslash$Delta Go$,$ for the above half reaction $($Half reaction in Question $1).$

c$)$ Confirm if the energy reaction mediated by Halothiobacillus sp is thermodynamically feasible at standard conditions and pH $7.$

d$)$ Calculate fso and feo.

e$)$Construct a complete stoichiometry for the reaction mediated by Halothiobacillus sp that includes synthesis of Halothiobacillus sp cells with empirical formula C$5$H$7$O$2$N$.$ These cells utilize ammonium as a nitrogen source.

f$)$ Estimate the following kinetic parameters at bioreactor operating temperature of $38$oC;

yield, Y $($in units of g cells$/$g total hydrogen sulfide$),$ maximum specific growth rate, mu $($in units

of $1/$day$)$

g$)$ doubling time for the cells, td $($in units of days$)$

Monod half$-$saturation constant, Ks $=25$ mg$/$liter$,$ Death rate $($decay$)$ coefficient, b$=0\mathrm{.}1$ d$-1$ at $38$oC and Neglect substrate consumption for maintenance.

For above calculations assume that $1$ electron equivalent is transferred from donor to acceptor$/$ g cells$/$day at $20$ oC$.$ Now consider the treatment of $1000$ m$3/$day of wastewater containing $150$ mg$/$l of total hydrogen sulfide in a continuously fed stirred tank bioreactor $($CSTR$)$ utilizing Halothiobacillus cells operated at $38$ oC and $1$ atmosphere pressure and at steady state.

In addition to kinetic parameters calculated in Question $6$ above, you can also use

The growth and substrate utilization kinetics for these cells follow Monod equation and hydrogen sulfide is the limiting substrate.

h$)$ Write steady state mass balance equations in the CSTR bioreactor for

Microbial cells $($use notation X$)$ b$)$ Total hydrogen sulfide concentration $($use notation SH$2$S$)$ c$)$ Elemental sulfur concentration $($use notation SS$)$

Define all other notations used in the above mass balance equations.

i$)$ Determine the operating dilution rate to convert $99\%$ of the hydrogen sulfide in the feed

stream. For steady state operation calculate the Volume of reactor Volume of air required for aeration at $22$ oC and $1$ atm pressure c$)$ Mass of elemental sulfur produced daily