Yeast growth with ammonia as $N-$source can be described using the following equation:

$CH4O+aO2+bNH3cCH1\mathrm{.}7500\mathrm{.}462N0\mathrm{.}207+d2O+eCO2.$

You want to estimate the cooling requirements per $kg$ methanol to estimate the cooling costs.

You expect, that the realistic yield is $38\%$ of the theoretical maximal possible biomass yield $($YXS$,$max$).$ The process is performed at $30C$ in a stirred tank reactor. The power input from the stirrer is neglected. In the process, you loose about $59kg$ water per ton substrate consumed due to evaporation. $hv,30C$ is $2430\mathrm{.}7k\frac{J}{k}g.$ The biomass contains $5\%$ ash.

Substitute values:

If you fail to solve the yield or oxygen requirement, use the following substitute values. Make sure that you state that you have used the substitute value!

Realistic yield: $0\mathrm{.}4\frac{g}{g}.$ Oxygen consumed: $0\mathrm{.}5kg.$

Interims results.

Please put your interims results in this table. Be aware, that the values appear in random order and do not necessarily reflect the calculation path. Read the questions first before filling the table!!! The subscript "max" indicates the values derived from the maximal theoretical yields.

Variable Result $-$ Variable Result

$yCH30OH$ Answer

MWbiomass $[$g$/$mol$]$ Answer

$a[mo\frac{l}{m}ol]$ Answer

c realistic $mo\frac{l}{m}ol$ Answer

$MWCH30H[\frac{g}{m}ol]$ Answer

MO$2kg$ Answer

$Hrxn[kJ]$ Answer

cmax $[$mol$/$mol$]$ Answer

YXS$,$max $[$g$/$g$]$ Answer

NO$2[$mol$]$ Answerycells Answer

$MH2O,$ev $[$kg$]$ Answer

Questions:

Please give your results with $4$ significant digits. Take care about the units!!!

a$)$ What is the $($realistic$)$ biomass yield?

$Y\frac{x}{S}[\frac{g}{g}]$: Answer

b$)$ What amount of oxygen is consumed per gram substrate $($YO$/$S$)?$

Hint: remember that the stoichiometric coefficient a is the molar equivalent to YO$/$S$.$

YO$/$S $[$g$/$g$]$: Answer

b$)$ What is the most appropriate energy balance? Please refer to the numbers in your formulary!

Energy balance:

$2\mathrm{.}24$

$2\mathrm{.}30$

$2\mathrm{.}31$

$2\mathrm{.}32$

$2\mathrm{.}47$

c$)$ What are the cooling requirement per kg substrate?

Cooling requirement per kg substrate: Qper kg substrate $kJ$ : Answer

d$)$ Would a change to an air driven reactor increase the cooling requirements? Explain your response in $1-2$ sentences in the text field below.

A change to an STR would increase the cooling requirements. Answer

Usage of substitute values:

I used the substitute value for the realistic yield: Answer

I used the substitute value for the oxygen consumed: Answer