Formation of lactic acid from glucose is realized in a...

Formation of lactic acid from glucose is realized in a continuous culture by Streptococcus lactis. The following information was obtained from experimental studies. $$ \begin{aligned} &S_{0}=5 \mathrm{~g} / 1, \mu_{m}=0.2 \mathrm{~h}^{-1}, K_{S}=200 \mathrm{mg} / 1, k_{d}=0.002 \mathrm{~h}^{-1}, Y_{X S}^{M}=0.4 \mathrm{~g} X / \mathrm{g} S, Y_{P / S}=0.2 \mathrm{~g} P / \mathrm{g} S, \\ &q_{P}=0.1 \mathrm{~g} P / \mathrm{g} X-\mathrm{h} . \end{aligned} $$ a. Plot the variations of $S, X, P, \mathrm{DX}$, and DP with dilution rate. b. Determine (graphically) the optimum dilution rate maximizing the productivities of biomass (DX) and the product (DP).

Formation of lactic acid from glucose is realized in a continuous culture by Streptococcus lactis. The following information was obtained from experimental studies.
$$
\begin{aligned}
&S_{0}=5 \mathrm{~g} / 1, \mu_{m}=0.2 \mathrm{~h}^{-1}, K_{S}=200 \mathrm{mg} / 1, k_{d}=0.002 \mathrm{~h}^{-1}, Y_{X S}^{M}=0.4 \mathrm{~g} X / \mathrm{g} S, Y_{P / S}=0.2 \mathrm{~g} P / \mathrm{g} S, \\
&q_{P}=0.1 \mathrm{~g} P / \mathrm{g} X-\mathrm{h} .
\end{aligned}
$$
a. Plot the variations of $S, X, P, \mathrm{DX}$, and DP with dilution rate.
b. Determine (graphically) the optimum dilution rate maximizing the productivities of biomass (DX) and the product (DP).

Key Concepts

Optimum Productivity

Optimum productivity in a continuous culture refers to the identification of an ideal dilution rate that maximizes the output, whether it is biomass or a specific product. Determining this optimum involves balancing microbial growth and substrate utilization to maximize the overall production while avoiding detrimental effects like wash-out.

Microbial Growth Kinetics

Microbial growth kinetics describes the relationship between the growth rate of microorganisms and substrate concentration, often modeled by the Monod equation. Key parameters include the maximum specific growth rate and the half-saturation constant, which indicate how rapidly cells can multiply and the substrate concentration needed for significant growth, respectively.

Specific Production Rate

The specific production rate quantifies the rate at which a product is formed per unit of biomass. This parameter is crucial in bioprocess optimization as it provides insights into the metabolic activity of the culture and helps in adjusting operational conditions to enhance the production of desired compounds.

Continuous Culture

Continuous culture is a mode of microbial cultivation in which fresh medium is continuously added while culture liquid is simultaneously removed at the same rate. This method maintains cells in a steady state, allowing for constant environmental conditions such as nutrient concentration and growth rate, which is crucial for studying microbial kinetics, substrate utilization, and product formation.

Dilution Rate

The dilution rate, defined as the rate at which fresh medium is introduced relative to the culture volume, is a critical operational parameter in continuous culture. It directly influences substrate concentration, biomass concentration, and product formation; varying the dilution rate can help optimize the productivity of desired outputs while avoiding wash-out of the microbial cells.

Yield Coefficients

Yield coefficients represent the efficiency of substrate conversion into biomass or product. They are defined as the amount of biomass or product formed per unit of substrate consumed. These coefficients are essential in bioprocess engineering to predict product yields and to design systems that maximize productivity.

Transcript

00:01 In the given question, we have been provided a reaction in which glucose get converted into two moles of lactic acid.

00:09 Okay.

00:10 Two moles of lactic acid.

00:13 And we have been provided the value of delta h, c, b and s for both the compounds.

00:20 Okay.

00:21 So we have to calculate delta g of this reaction at two different temperature, 298 kelvin, and at 310 kelvin.

00:33 Further, we also have to calculate the value of delta h of the reaction and delta s of this reaction at 310 kelvin.

00:46 So, first of all, for calculating this, we will require delta h of this reaction, which will be equal to twice the delta h formation of lactic acid minus delta x formation of glucose okay which is provided to us in the given table so we can use the value so it is 2 in minus 673 .6 plus 1 into 1273 .1 so our value will come out in kilojou per mole and that is 74 .1 kilojoule per mole with a negative sign okay, similarly we can calculate the delta s of the reaction at 298 .1 .5 kelvin.

01:36 Okay, these both are at 298 .1 .15 kelvin.

01:44 Okay.

01:44 So that will be equals to twice s not of lactic acid minus s not of glucose.

01:56 Okay.

01:57 So we have the values.

01:58 So that is twice into 192 .1 minus 209 .2.

02:05 So this will come out to be 175 jule kelvin inverse, mole inverse.

02:12 Now with the help of this, we can calculate the delta g of the reaction at 298 .15 kelvin, which will be equal to delta h of the reaction at the same temperature, plus.

02:29 P delta s of the reaction at the same temperature.

02:34 Now our delta h is minus 74 .1, while our endropy isn't jule.

02:41 So we will convert it into kilojoule by multiplying it by 10 to the power minus 3.

02:47 Okay, so our answer will come out to be minus 73.

02:51 Okay, we have to also multiply it by temperature.

02:54 So the temperature is 298 .15.

02:57 Okay, so our delta g.

02:59 At this temperature is minus 73 .7 kilojoule per mole.

03:04 Okay, we can further, this is our part b, okay, this is our answer for part a...