CH3103 Lecture Week 9_Fugacity, Chemical Potential.pdf - CH3103 Chemical Thermodynamics Fugacity Chemical Potential and Phase Equilibria Dr Poernomo

CH3103 Lecture Week 9_Fugacity, Chemical Potential.pdf -...

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CH3103: Chemical Thermodynamics Fugacity, Chemical Potential and Phase Equilibria Dr. Poernomo Gunawan School of Chemical and Biomedical Engineering E-mail: [email protected] N1.2-B2-26A
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2 Derive and apply chemical potential as criteria for phase equilibrium. By the end of this lesson, you should be able to: Apply the concept of fugacity for a non-ideal gas system. Explain the concept of fugacity for pure species. Learning Objectives
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3 Chemical Potential In this section, partial molar properties of Gibbs free energy will be discussed, which is also known as chemical potential. Chemical potential plays an important role in describing phase and reaction equilibria. For a mixture containing N species: ? 𝑛 ? = 𝜕(𝑛 ?) 𝜕? 𝑃,? ?? + 𝜕(𝑛 ?) 𝜕? ?,? ?? + 𝑖=1 𝑁 𝜕(𝑛 ?) 𝜕𝑛 𝑖 𝑃,?,? ? ?𝑛 𝑖 ? 𝑛 ? = 𝜕(𝑛 ?) 𝜕? 𝑃,? ?? + 𝜕(𝑛 ?) 𝜕? ?,? ?? + 𝑖=1 𝑁 ? 𝑖 ?𝑛 𝑖
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4 Recall that for any closed system where there is no exchange of matter with the surrounding (constant amount of species): ? 𝑛 ? = 𝑛 ? ?? − 𝑛 ? ?? Chemical Potential Hence: 𝜕(? 𝐺) 𝜕𝑃 ?,? = 𝑛 ? and 𝜕(? 𝐺) 𝜕? 𝑃,? = −𝑛 ? ? 𝑛 ? = 𝑛 ? ?? − 𝑛 ? ?? + 𝑖=1 𝑁 ? 𝑖 ?𝑛 𝑖 We define ? 𝑖 as the chemical potential of species 𝑖 , μ 𝑖 = 𝜕(? 𝐺) 𝜕? ? 𝑃,?,? ? ? 𝑛 ? = 𝑛 ? ?? − 𝑛 ? ?? + 𝑖=1 𝑁 μ 𝑖 ?𝑛 𝑖 Dividing the equation with the total number of mole 𝑛 , ? ? = ??? − ? ?? + 𝑖=1 𝑁 μ 𝑖 ?𝑥 𝑖
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5 ? 𝑛 ? = 𝑛 ? ?? − 𝑛 ? ?? + 𝑖=1 𝑁 μ 𝑖 ?𝑛 𝑖 Using Maxwell relation: 𝜕(? 𝑉) 𝜕? 𝑃,? = − 𝜕(? ?) 𝜕𝑃 ?,? ; therefore 𝜕μ ? 𝜕𝑃 ?,? = 𝜕(? 𝑉) 𝜕? ? ?,𝑃,? ? and 𝜕μ ? 𝜕? 𝑃,? = − 𝜕(? ?) 𝜕? ? ?,𝑃,? ? 𝜕μ ? 𝜕𝑃 ?,? = ? 𝑖 and 𝜕μ ? 𝜕? 𝑃,? = − ? 𝑖 At constant overall composition: 𝒅𝝁 𝒊 = 𝑽 𝒊 𝒅𝑷 − ? 𝒊 𝒅? 𝒅 𝑮 𝒊 = 𝑽 𝒊 𝒅𝑷 − ? 𝒊 𝒅? Chemical Potential
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6 For any irreversible process, we know that: ??
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