Modeliranje kemijskih reakcija

undergraduate thesis

• Title (english): Modelling chemical reactions
• Author: Relja Ivan Dular
• Mentor: Ivica Gusić (mentor)
• Committee member: Ivica Gusić (predsjednik povjerenstva)
• Committee member: Miroslav Jerković (član povjerenstva)
• Committee member: Petar Kassal (član povjerenstva)
• Granter: University of Zagreb; Faculty of Chemical Engineering and Technology; Zagreb
• Defense date and country: 2019-09-20, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Opisan je matematički model za kinetiku kemijskih reakcija. Model je primijenjen na jednostavne enzimske reakcije pri kojima supstrat uz pomoć enzima kao katalizatora prelazi u produkt, poznat kao Michaelis-Menteničin model. Zasnivanje modela temelji se na brzini kemijske reakcije i analizi brzine promjene koncentracije tvari koji sudjeluju u reakciji. Matematički gledano to je sustav od četiri obične diferencijalne jednadžbe. Sustav je nelinearan pa nije izgledno njegovo egzaktno rješavanje. Zato se u ovoj radnji rješenje provodi numerički. Koristi se programski paket MATLAB te analizira ovisnost modela o izboru parametra i utjecaj početnih uvjeta. Rezultati su prikazani grafički tako da krivulje pokazuju promjenu koncentracije pojedinih tvari u vremenu. Zaključuje se da su rezultati modela u skladu s uobičajenim fenomenima enzimskih reakcija.

Abstract (english)

Here is described a mathematical model for kinetics of chemical reactions. The model is applied to simple enzyme reactions that require the use of enzymes as catalysts for converting a substrate into a product, known as Michaelis-Menten model. The design of the model is based on the chemical reaction rate and the analysis of the rate of change of concentration of the substances involved in the reaction. Mathematically, it is a system of four ordinary differential equations. The system is not linear, so its exact solution is not plausible. Therefore, in this final thesis the solution is implemented numerically. The MATLAB software is used to analyze the model's dependence on parameter selection and the impact of initial conditions. The results are presented graphically, so that the curves indicate the change in the concentration of individual substances over time. It is concluded that the model results are consistent with the common phenomena of enzymatic reactions.

• Keywords: modeliranje kemijskih reakcija; diferencijalna jednadžba; MATLAB
• Keywords (english): modeling chemical reactions; differential equation; MATLAB
• Language: croatian
• URN:NBN: urn:nbn:hr:149:145600
• Study programme: Title: Applied Chemistry - Undergraduate study; specializations in: Environmental chemistry and green technologies, Advanced materials and technologies, Applied organic chemistry; Course: Applied organic chemistry; Study programme type: university; Study level: undergraduate; Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) primijenjene kemije (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) primijenjene kemije)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Closed access
• Created on: 2023-02-14 11:33:44