"📊 Mathematical Model of UV Degradation in Brine 🌊" | #Sciencefather #researchers #AppliedMathematics

Mathematical Modeling of Octadecylamine and 4-Dodecylmorpholine Degradation in Salt Lake Brine Under UV Light

UV light accelerates the degradation of octadecylamine and 4-dodecylmorpholine in salt brine. 📉 The process follows first-order kinetics, modeled by differential equations. 🔢 Quantum yield measures efficiency, while salt ions and pH influence reaction rates. 🌊 Statistical analysis predicts degradation trends, ensuring accurate environmental impact assessment. 🌞✅

1️⃣ Rate of Degradation and Kinetic Equations 📉

• The degradation follows first-order kinetics, meaning the rate depends on the concentration of the compound: $$\frac{dC}{dt} = -kC$$
• Solving this gives the concentration at time $t$: $$C_t = C_0 e^{-kt}$$
• $C_0$ = initial concentration, $C_t$ = concentration at time $t$, and $k$ = degradation rate constant.

2️⃣ Half-Life Calculation ⏳

• The time for the compound’s concentration to reduce by 50% is: $$t_{1/2} = \frac{\ln 2}{k}$$
• A higher $k$ value indicates a faster degradation process.

3️⃣ UV Absorption and Quantum Yield 🌞🔢

• The efficiency of UV radiation in degrading the molecules is given by: $$\Phi = \frac{\text{Molecules degraded}}{\text{Photons absorbed}}$$
• Higher quantum yield ($\Phi$) means faster and more efficient photodegradation.

4️⃣ Influence of Salt and Environmental Factors 🌊📊

• The degradation rate is modified by ionic strength, pH, and UV intensity: $$\frac{dC}{dt} = -kC f(\text{pH, } I_{UV}, \text{ionic strength})$$
• $I_{UV}$ represents UV intensity, affecting how quickly bonds break.
• Regression analysis is used to determine the best kinetic model based on experimental data.

5️⃣ Graphical and Statistical Analysis 📈

• A first-order reaction shows a linear relationship when plotting $\ln C$ vs. $t$.
• A second-order reaction is linear when plotting $1/C$ vs. $t$.
• Correlation coefficients (R²) help identify the most accurate kinetic model.

✅ Conclusion 🔬

• Mathematical models predict how quickly octadecylamine and 4-dodecylmorpholine degrade under UV light.
• Using differential equations, quantum yield, and regression analysis, we can estimate environmental impact and optimize degradation conditions.

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