CHEN 3101 Lecture Notes - Lecture 16: Saurer, Gibbs Free Energy, Paga

26 views11 pages

mauvedinosaur421

25 Dec 2014

School

Department

Course

Professor

For unlimited access to Class Notes, a Class+ subscription is required.

Document Summary

Volume is additive @ constant t + p. Chen thermo page 1 it should be u + rt: energy + enthalpy, gibbs free energy. Chen thermo page 2 no subscript on the p here. Chen thermo page 3 for 0 <= xi <= 1. -> gases mix spontaneously, we already know this: entropychange in gibbs free energy upon mixing comes from entropy start with this identity remember, this = maxwell relation. Chen thermo page 4 if the change isn"t coming from enthalpy, must be coming from entropy. Pi = pii = p (this = initial condition) then blow a hole in btwn --> pfinal = p. Energy is additive @ constant t + p. T = constant <=> delta u = 0 isothermal <=> adiabatic. Total pressure doesn"t change, but partial pressures decrease b/c have more space to spread out. Simplest case: pure liquid/ideal gas mixture ex: liquid pure water in contact w/ air.

Related Questions

Suppose the (1) + (2) system exhibits liquid-liquid immiscibility. Suppose we are at a state where G1/RT = 0.1 and G2/RT = 0.3. The Gibbs energy of mixing quantifies the Gibbs energy of the mixture relative to the Gibbs energies of the pure components. Suppose the excess Gibbs energy for the (1) + (2) mixture is given by: GE/RT = 2.5 x1 x2

a. Combine this with the Gibbs energy for ideal mixing to calculate the Gibbs energy of mixing across the composition range and plot the results against x1 to illustrate that the system exhibits immiscibility.

b. Draw a tangent to the humps to illustrate that the system is one phase at compositions greater than z1 = 0.854 and less than z1 = 0.145, but will split into two phases with compositions at any intermediate overall composition. Most systems with liquid-liquid immiscibility must be modeled with a more complex formula for excess Gibbs energy. The humps on the diagram are usually offcenter, as in Fig. 14.3 on page 545 in the text. The simple model used for the calculations here results in the symmetrical diagram.

c. When a mixture splits into two phases, the over-all fractions (of total moles) of the two phases are found by the lever rule along the composition coordinate. Suppose 0.6 mol of (1) and 0.4 mol of (2) are mixed. Use the lever rule to calculate the total number of moles which would be found in each phase of the actual system. Designate the (1)-rich phase as the Î² phase.

d. What is the value of the hypothetical Gibbs energy, (expressed as G/RT), of a mixture of 0.6 mol of (1) and 0.4 mol of (2) if the mixture were to remain as one phase? Calculate the Gibbs energy of the total system considering the phase split into two phases, and show that the Gibbs energy is less than the Gibbs energy of the single-phase system.

1. As you know, the equilibrium pH of pure water at 298 K and 1 bar is approximately 7. Based on this, compute the values of (a) the equilibrium constant for the autoionization of water in terms of molar concentrations (Kc ) and (b) the standard Gibbs free energy of reaction in kJ/mol for the autoionization reaction of 1 mole of water, as written in QIII.2 above, at 298K and 1 bar

2. The standard Gibbs free energy for the autoionization of water (QIII.3(b) above) is not zero. Explain why this observation is not in conflict with the 2nd law of thermodynamics, which states that the Gibbs free energy of the reaction should be zero at equilibrium, at constant temperature and pressure.

The canonical partition function of an N-particle, monatomic ideal gas is given by

Q(N, V, T) = 1/N! ( 2*pi*m*K_b* T/h^2)^(3/2N)* (V^N)

Using the definition for the chemical potential ? of a single component system,

?? = ( ????/????) ??,V

find an expression for the chemical potential for a monatomic ideal gas. Then show that the same expression can be derived using the definition of the Gibbs free energy, ?? = ??/?? = 1/?? (?? + ????) where the Helmholtz free energy ?? = ?? ? ????.

CHEN 3101 Lecture Notes - Lecture 16: Saurer, Gibbs Free Energy, Paga

Document Summary

Get access

Related Documents

CHEN 3101 Lecture Notes - Lecture 16: Partial Pressure, Ideal Gas, Stoichiometry

Related Questions