# Falghane Week 14/15

## Purpose

The purpose of this assignment was to model the chemostat used in Tai et al. (2007) using MATLAB.

## Methods

1. Use the Arrhenius equation (rate = A*exp(-B/(R*T)) to model the temperature dependence of the chemostat reaction.

• Ea was found from the slope between ln(k) and 1/temp (K) and finding B which equaled Ea.​
• Equation: A = k/ e^-(Ea/RT) was then used to solve for A​
• Then Arrhenius Equation: rate = A*exp(-B/(R*T ) was used to find rates at temperatures 15, 20, 25 in Kalvin. ​
• Then the New Rates were added to MATLAB to model temperature dependence of the chemostat reaction​

2. Investigating the glucose efficiency/ waste constant

• The values of E for glucose-limited and ammonium-limited conditions were noted.
• For each temperature (12, 30), the function E(y) that matches the two points of (y,E) data was found.
• The chemostat_2nutrient_dynamics.m file was modified to use the functions created.
• The resulting simulation was compared to the previous one.

## Results

• Determing the A & B constants:
• B found to be 69,840.59 from B = (Rln(k1/k2))/(1/T1-1/T2).
• A found to be 4.979 * 10^11 from A = k/ e^-(Ea/RT).
• Rate values:
• r(15°C) = (4.979 x 10^11)e^(-69840.59)/((8.314)(288.15)) = 0.1087
• r(20°C) = (4.979 x 10^11)e^(-69840.59)/((8.314)(293.15)) = 0.1787
• r(25°C) = (4.979 x 10^11)e^(-69840.59)/((8.314)(298.15)) = 0.289
• Efficiency constant Investigation
• Original: E = 1/Y New equation: where E = my + b
• y = residual glucose
• point intercept m = (y-y)/(x-x) was used to determine m and thenew value was plugged into E = my + b to determine b
• 12°C: E = 0.363y + 14.11
• m = (14.3-20)/(0.5045-16.22) = 0.363
• b=14.11
• 30°C: E = 0.7y + 14.25
• m = (14.3-25)/(.0541-15.33) = 0.7
• b=14.25

## Acknowledgments

• I worked with my homework partner, Edward Ryan R. Talatala to complete this assignment.
• I also worked with Austin to work on the efficiency constant investigation.