Estimate through the use of reaction energetics the true yield coefficient $Y$ in g cells per gram of substrate assuming methanol $(C{H}_{3}OH)$ is the electron donor and nitrate $(N{O}_3)$ is the electron acceptor $($reduced to $N_2).$ Assume nitrate is also used as the nitrogen source, and that the energy transfer efficiency $()$ equals $0\mathrm{.}6.$ Use the step$-$by$-$step approach outlined below. You can assume the $G_s=21\mathrm{.}45k\frac{J}{e}q.$

Determine $G_r($for the energy reaction$).$

a$)109\mathrm{.}4k\frac{J}{e}q$

b$)77\mathrm{.}5k\frac{J}{e}q$

c$)42\mathrm{.}1k\frac{J}{e}q$

d$)-77\mathrm{.}5k\frac{J}{e}q$

e$)-109\mathrm{.}0k\frac{J}{e}q$

f$)$ None of the above $($within $+-5\%)$

Using an energy balance, calculate the value of $A($the number of electron equivalents channeled from the electron donor to the electron acceptor, assuming $1$ electron equivalent is channeled from the electron donor into biomass synthesis$).$

a$)0\mathrm{.}75$

b$)0\mathrm{.}57$

c$)0\mathrm{.}33$

d$)0\mathrm{.}25$

e$)0\mathrm{.}15$

f$)$ None of the above $($within $+-5\%)$

Assuming the above value for A$,$ calculate the true yield coefficient $Y$ in $g$ cells $($as VSS$)$ per gram of COD $($i$.$e$.,$ the COD associated with methanol$).$

a$)0\mathrm{.}75g$ VSS gCOD

b$)0\mathrm{.}50g$ VSS gCOD

c$)0\mathrm{.}38gVS\frac{S}{g},$COD

d$)0\mathrm{.}25g$ VSS $\frac{?}{\text{g}\text{C}\text{O}\text{D}}$

e$)0\mathrm{.}15g$ VSS gCOD

f$)$ Tone of the above $($within $+-5\%)$