Thermodynamics Exercise - Key Equations

University:
Eastern Michigan University
Course:
HIST 375 | Modern India
Academic year:

2024
Views:

0

Pages:

2
Author:

Navine Saleh

Thermodynamics Exercise - Key Equations Standard conditions: 1 atm pressure for gases and 1 M for solutions. Enthalpy ΔΗ° = ΣηΔΗ° (prod) - ΣηΔΗ°, (reac) + entropy AS = EnS(prod) - EnS°(reac) * ran w=-PAV so that the first law can be written: AE°=q+w=q-PAV At constant pressure, AE°=q,-PAV and AE = AH° - PAV From 141, PV=nRT. If pressure and temperature are maintained constant and the volume of gas in the system changes, the number of moles of gas must have changed, i.e., PAV = (An)RT and therefore, w=-PAV = -(An) RT where Δη = Σηgas, prod - Σηgas reac Either form can be used to calculate work. Either for can be substituted in the AE° equation: AE°=q+w=q-PAV =q-(An)RT There is another new thermodynamic function of use, the Gibbs free energy, G = H-TS. AGAH-TAS and AG°, = AH-TAS, There is an alternate equation for calculating AG°ron that is parallel to those above for AH°rxn and AS°rxn: AG = ΣηAG, (prod) - Ση∆G°, (reac) The Gibbs free energy change is of interest for several reasons. First of all, the sign indicates if the reaction is spontaneous (AG < 0), nonspontaneous (AG > 0), or at equilibrium (AG = 0). It is IMPORTANT to note that a system can be at equilibrium at either standard or non-standard conditions. A liquid in equilibrium with its vapor at any temperature other than the normal boiling point has AG = 0. Only at the normal boiling point, when the vapor pressure of the liquid is equal to one atmosphere, is AG° = 0. (continued...) The second important application of the free energy function involves equilibrium constants. The following equation can be derived: AG = AG+RT In Q If the system is at equilibrium under non-standard conditions, this becomes: 0=AG°+RT In Q and therefore AG°=-RT In K, P since Q = Keq at equilibrium. In the case of a liquid in equilibrium with its vapor, Keq must be a Kp. For our purposes, AH°, and AS° are taken to be independent of temperature. With that in mind, we can substitute in the equation above and derive the relationship between equilibrium constants at two different temperatures: AH-TAS-RT, In K₁ and AH-TAS-RT, In K₂ which can be manipulated to yield the Gibbs-Helmholtz equation: K In() = K₂ ΔΗ° 1 RT 1

Thermodynamics Exercise - Key Equations

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