Exam 2 Flashcards
What are the natural variables of entropy?
V and U, since its coefficients in dS = PdV + (1/T)dU are simple thermodynamic quantities
Sketch out a generalized phase diagram.
sketch https://chem.libretexts.org/Textbook_Maps/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Physical_Properties_of_Matter/States_of_Matter/Phase_Transitions/Phase_Diagrams
What is the triple point?
point on a phase diagram at which the three states of matter: gas, liquid, and solid coexist
What is the critical point?
point on a phase diagram at which the substance is indistinguishable between liquid and gaseous states
Sketch out the phase diagram for water and CO2.
sketch https://chem.libretexts.org/Textbook_Maps/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Physical_Properties_of_Matter/States_of_Matter/Phase_Transitions/Phase_Diagrams
State Raoult’s Law.
the vapor pressure of a solvent above a solution is equal to the vapor pressure of the pure solvent at the same temperature SCALED by the mole fraction of the solvent present
Write out the generalized, undifferentiated form of the Helmholtz free energy.
A = U - TS
The sign of the Helmholtz free energy change denotes
the direction of a spontaneous process in a system at constant volume and temperature (i.e. if da <= 0)
Sketch out a diagram of Helmholtz free energy versus time.
sketch Dineli’s Exam 4 Notes, page 21
Write out the differentiated form of the Helmholtz free energy, and show the steps to get there.
ΔA = ΔU - TΔS
Write out the generalized, undifferentiated form of the Gibbs free energy.
G = H - TS
The sign of the Gibbs free energy change denotes
the direction of a spontaneous process in a system at a constant pressure and temperature (i.e. if dG <= 0)
Sketch out a diagram of the Gibbs free energy versus time.
sketch Dineli’s Exam 4 Notes, page 21
Derive the Maxwell relation for A.
derive Dineli’s Exam 4 Notes, page 22
Write out the equation for U.
U = q + w
What are the natural variables of U?
S and V
What is the differential expression for U?
dU = TdS - PdV
What is the Maxwell relation for U?
(∂T/∂V)S = -(∂P/∂S)V
Write out the equation for H.
H = U + PV
What are the natural variables of H?
S and P
What is the differential expression for H?
dH = TdS + VdP
What is the Maxwell relation for H?
(∂T/∂P)S = (∂V/∂S)T
Write out the equation for A.
A = U - TS
What are the natural variables of A?
V and T
What is the differential expression for A?
dA = -PdV - SdT
What is the Maxwell relation for A?
(∂P/∂T)V = (∂S/∂V)T
Write out the equation for G.
G = H - TS
What are the natural variables of G?
P and T
What is the differential expression for G?
dG = VdP - SdT
What is the Maxwell relation for G?
(∂V/∂T)P = -(∂S/∂P)T
How do we calculate ΔG if we know the volume and the initial and final pressures?
ΔG = V*(Pf - Pi)
How do we calculate ΔG if we know the entropy and the initial and final temperatures?
ΔG = -S*(Tf - Ti)
What is the relationship between ∂G, ∂P, and V?
(∂G/∂P)T = V
What is the relationship between ∂G, ∂T, and S?
(∂G/∂T)P = -S
Write out the equation for the pressure dependence of G at constant T. Identify each component.
ΔGrxn = ΔG° + RT*lnQ — Dineli’s Exam 4 Notes, page 25
Write out the expression for Q.
write out Dineli’s Exam 4 Notes, page 25
Write out the formula for the temperature dependence of G at constant P. This expression leads us to what equation?
(G/T) = (H/T) - S, leads us to the Gibbs-Helmholtz equation
Write out the Gibbs-Helmholtz equation.
write out Dineli’s Exam 4 Notes, page 25
Write out the secondary version of the Gibbs-Helmholtz equation.
write out Dineli’s Exam 4 Notes, page 25
Which equation do we use when comparing the Gibbs energy of a reaction at two temperatures?
Gibbs-Helmholtz equation, secondary version
Write out the generalized ICE table for A + B —> Y + Z.
write out Dineli’s Exam 4 Notes, page 26
Write out the equation for chemical potential at constant temperature and pressure.
write out Dineli’s Exam 4 Notes, page 26
When a reaction system is in equilibrium, ΔG =
0
At equilibrium, what is true about Q and Kp?
Q = Kp
Write out the equation for ΔG° given Kp.
ΔG° = -RT*ln(Kp)
Write out the expression for Kp.
write out Dineli’s Exam 4 Notes, page 27
How can you calculate ΔGrxn without calculating ΔG°?
ΔGrxn = RT*ln(Q/Kp)
If Q < Kp, what is true about ΔG and the direction of the reaction?
ΔG < 0 and the reaction will shift to the right
If Q > Kp, what is true about ΔG and the direction of the reaction?
ΔG > 0 and the reaction will shift to the left
The equilibrium constant Kp is a function of
T and T only
What is Le Chatelier’s principle?
if a chemical reaction at equilibrium is subjected to a change in conditions that displaces it from equilibrium, then the reaction adjusts toward a new equilibrium state
Draw a graph of reaction extent versus pressure.
draw Dineli’s Exam 4 Notes, page 29
What is Kc?
equilibrium constant with concentration terms
Write out the expression for Kc.
write out Dineli’s Exam 4 Notes, page 30
Write out the relationship between Kp and Kc. What assumptions do we make?
write out Dineli’s Exam 4 Notes, page 30; P° = 1 bar and c° = 1 mol/L
Write out the equation relating Kp and two different temperatures. What is the name of this equation?
write out Dineli’s Exam 4 Notes, page 31; Van’t Hoff equation
Write out the equation for the chemical potential of substance i.
write out Dineli’s Exam 4 Notes, page 32
What is the physical interpretation of the partial molar Gibbs quantity?
a measure of how G changes when ni is changed while keeping T, P and other mole numbers fixed
Write out the equation relating the chemical potential of a substance i and the chemical potential of its pure form. Identify each component.
write out Dineli’s Exam 4 Notes, page 32
Write out the equations for G, S, and Vsoln for a liquid-liquid mixture.
write out Dineli’s Exam 4 Notes, page 33
Write out the Gibbs-Duhem equation.
write out Dineli’s Exam 4 Notes, page 33
Write out the Gibbs-Duhem equation for volume.
write out Dineli’s Exam 4 Notes, page 33
At equilibrium, what is the relationship between the chemical potential of the solution and the chemical potential of the vapor?
µj(sol) = µj(vap)
What is the formula to calculate µj(vap)? Identify each component.
write out Dineli’s Exam 4 Notes, page 34
What is the formula to calculate µ*j(vap)? Identify each component.
write out Dineli’s Exam 4 Notes, page 34
What is the formula to calculate µj(sol)? Identify each component.
write out Dineli’s Exam 4 Notes, page 35 + 36
Write out the equation for the chemical potential of an ideal solution in the context of Raoult’s law, using activity.
write out Dineli’s Exam 4 Notes, page 36
Write out the equation for the chemical potential of a non-ideal solution in the context of Raoult’s law, using activity.
write out Dineli’s Exam 4 Notes, page 36
What is Dalton’s law?
total pressure of a system is the sum of the partial pressures exerted by each gas in the system
What is Henry’s Law?
the amount of dissolved gas is proportional to its partial pressure in the gas phase
Write out the formula for activity.
write out Dineli’s Exam 4 Notes, page 36
Write out Henry’s Law for an ideal solute.
write out Dineli’s Exam 4 Notes, page 36
Write out Henry’s Law for a non-ideal solute.
write out Dineli’s Exam 4 Notes, page 36
What is the generalized equation for equilibrium systems consisting of gases, solids, liquids, and/or solutions? Identify each component.
write out Dineli’s Exam 4 Notes, page 37
What is the standard reference state for a gas and the corresponding expression for activity?
chemical potential of an ideal gas at 1 bar; aj = Pj/P°
What is the standard reference state for a solvent and the corresponding expression for activity?
Raoult’s Law reference/state — chemical potential of pure component j; aj = Pj/P* and aj = γ*xj
What is the standard reference state for a solute?
Henry’s Law reference/state — chemical potential of an ideal solution at unit molality or unit molarity
What are the three activity coefficient scenarios for the standard/reference state of a solute?
mole fraction scale; molality scale; molarity scale
Write out the activity expressions for the mole fraction scale.
write out Dineli’s Exam 4 Notes, page 37
Write out the activity expressions for the molality scale.
write out Dineli’s Exam 4 Notes, page 37
Write out the activity expressions for the molarity scale.
write out Dineli’s Exam 4 Notes, page 37
Write out the expression for the extended Debye-Huckel equation. Identify each component.
write out Dineli’s Exam 4 Notes, page 38
Write out the expression for ionic strength. Identify each component.
write out Dineli’s Exam 4 Notes, page 38
What is the relationship between ΔS-bar-trans, ΔH-bar-trans, and T?
write out Dineli’s Exam 4 Notes, page 38
Write out the two variants of the Clapeyron equation.
write out Dineli’s Exam 4 Notes, page 38
What is the Clapeyron equation?
relates the slope of the two-phase boundary line in a phase diagram
Why can’t we use the Clapeyron equation for liquid-to-gas or solid-to-gas transitions?
because the molar volume of a gas varies strongly with pressure
The Clapeyron equation is restricted to which transitions?
solid to liquid
Write out the two variants of the Clausius-Clapeyron equation.
write out Dineli’s Exam 4 Notes, page 39
What are the three colligative properties discussed in this unit?
lowering of vapor pressure; freezing point depression; boiling point elevation
What is the simple formula for freezing point depression?
ΔTfus = Kf * m
In addition to P and T, what else does G depend on?
the number of moles of each species in the system
(∂G/∂P)T =
V
How do we convert the activities of two ionic species into their concentrations?
(αx+)(αy-) = (cx+)(cy-)*(γ+/-)^2 [combined lecture notes, page 9]
What is the phase rule?
degrees of freedom = 3 - (# phases in coexistence)
The solid-gas coexistence line gives vapor pressure as a function of
temperature
The solid-liquid coexistence line gives melting point as a function of
pressure
(∂G/∂T)P =
-S
The Clausius-Clapeyron equation is used for which transitions?
liquid-gas, solid-gas
Write out the derivation for the Clausius-Clapeyron equation.
write out [combined lecture notes, page 12]
Draw a graphical representation of the Clausius-Clapeyron equation. What is the slope of the line?
draw [combined lecture notes, page 12]; slope = -ΔHvap/R
What is the physical interpretation of partial molar volumes?
if you mix two substances, the total volume of the combined mixture might change because of intermolecular forces
Transfer dn1 moles of species 1 from solution to vapor. How does the free energy of the system change?
write out [combined lecture notes, page 14]
What is the physical interpretation of Raoult’s Law?
surface composition is bulk composition
What is the complex formula for freezing point depression?
write out [combined lecture notes, page 16]
What is the complex formula for boiling point elevation?
write out [combined lecture notes, page 16]
What is the simple formula for boiling point elevation?
ΔTvap = Kb * m
What is the simple formula for osmotic pressure?
pi = R * T * c
