CHEM 481 Lecture Notes _Engle 2nd - Chapter 6_

# CHEM 481 Lecture Notes _Engle 2nd - Chapter 6_ - Chapter 6...

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Last printed 4/3/2010 3:13 PM 4-1 Chapter 6- Chemical Equilibrium NOTE : You should read AND understand Section 5.1 and 6.7 (Standard Reaction Entropies and Gibbs Energies). I do not plan on covering this material in class. H ELMHOLTZ AND G IBBS E NERGIES To use S as a signpost for spontaneous change, we need to analyze both the system and the surroundings. This is cumbersome Better to have a quantity that focuses on just the system. To get that quantity, start with the Second Law of Thermodynamics. Tot sys sur dS 0 dS dS 0 > +> When change occurs at Constant T ... sur sur sur dq dq dS TT == Heat that enters surroundings is (-) of heat that leaves the system. This gives, sys dq dS 0 T −> This equation is written entirely in terms of the system “Clausius Inequality” We can take this further by considering two different types of processes. .. Constant Volume Helmholtz Energy (A) Constant Pressure Gibbs Energy (B) Constant Volume : If heat is transferred at constant V V dq dq dU dU dS 0 T TdS dU 0 or dU TdS 0 −< Define a new quantity Helmholtz Energy AUT S =− ⇒ dA dU TdS =−

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Last printed 4/3/2010 3:13 PM 4-2 dA 0 dU TdS 0 < −< For spontaneous change (C onstant V,T ) Comment : You might be tempted to say that system tends towards minimum energy and maximum entropy. But you would be wrong. This is still just a statement about entropy one term reflects the system, and the other reflects the surroundings. Constant Pressure: If heat is transferred at constant P P dq dq dH == (no non-expansion work) dH dS 0 T TdS dH 0 −> or dH TdS 0 Define a new quantity Gibbs Energy GHT S =− dG dH TdS dG 0 dH TdS 0 < For spontaneous change ( Constant P,T) Comments: 1.) The change in Helmholtz energy (dA) is equal to the maximum amount of work that can be obtained from a process (See Justification 3.2 in Atkins 8 th ed). 2.) The change in Gibbs Freen energy (dG) is equal to the maximum amount of non-expansion work that can be obtained from a process (See Justification 3.3 in Atkins 8 th ed). NOTE : You should read AND understand Section 3.6 (Standard Reaction Gibbs Energies). I do not plan on covering this material in class.
Last printed 4/3/2010 3:13 PM 4-3 F UNDAMENTAL E QUATIONS (P URE S UBSTANCES ) Starting with the 1 st Law of Thermodynamics, dU dq dw =+ where dq TdS = and dw PdV =− (if we consider only reversible PV-work) dU TdS PdV Comment: Because this equation only involves state functions, it applies to both reversible and irreversible processes. 1. Equations of State: Examination of the form of dU, suggests that the “natural” variables are: UU ( S , V , { n } ) = V,n S,n dU dS dV SV ∂∂ ⎛⎞ ⎜⎟ ⎝⎠ Compare the two forms of dU to obtain Equations of State (i.e. equations that relate different state variables. V,n U T S = S,n U P V = − 2. Maxwell Relation: Because dU is exact, mixed derivatives must be equal… VS V S S V T P V S =⇒ = (at const composition) We can develop similar expressions using the other thermodynamic properties, H, A, and G as starting points.

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CHEM 481 Lecture Notes _Engle 2nd - Chapter 6_ - Chapter 6...

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