Physical Chemistry Exam 3 (Ch.6-Ch.10)

Why is the magnitude of the boiling point elevation less than that of the freezing point depression?

1. The chemical potential of the vapor has a steeper slope than the chemical potential of the solid 2. Larger difference between solid-liquid coexistence curve and the solid solution coexistence line when compared to the liquid-vapor coexistence line and the solution-vapor coexistence line

Phase Rule

F = 3 - p; F is DOF and p is # of phases present

Give the state function, total derivative, and natural variable definitions in terms of the partial derivatives of the Gibbs free energy state function. In addition, give the Maxwell relations.

G(T,P) State Function: G=H-TS; G=U+PV-TS Total derivative: dG=-SdT+VdP Natural Variable: dG=(dG/dT)P *dT+(dG/dP)T+dP Maxwell Relations: (dS/dP)T=-(dV/dT)P

Decreases with increasing temperature. Most changes in gas state, not significant for liquids or solids

Gibbs-Helmholtz Energy

The entropy of two liquids is increased if they mix. How can immiscibility be explained in terms of thermodynamic state functions?

Given a binary solution, miscible ideal solutions can be described with no differences in the interactions between A-A, B-B, and A-B. Entropy of mixing substance A and B is spontaneous if the substance is miscible. If the interactions between A-A and B-B are greater than the reactions between A-B, the entropy is non spontaneous and the solutions are described as immiscible. For immiscible substances, the enthalpy of mixing and volume of mixing would not be expected to equal - as it does for miscible solutions.

Is a whale likely to get the bends when it dives deep into the ocean and resurfaces? Answer this question by considering the likelihood of a scuba diver getting the bends if he or she dives and resurfaces on one lung full of air as opposed to breathing air for a long time at the deepest point of the dive.

Henrys law suggests that a solubility of a gas in a solution is dependent upon the partial pressure of the pure substance. Atmospheric pressure increases with decreasing altitude. High levels of dissolved nitrogen in the blood cause a decompression sickness termed "the bends". It would be unlikely that the whale would have the bends.

Provide the formulas for Kc and Kp

Kc = [products]ⁿ/[reactants]ⁿ Kp = Kc∙RTⁿ

Explain why chemists doing quantitative work using liquid solutions prefer to express concentration in terms of molality rather than molarity?

Molality does not depend upon temperature as it is given in moles of solute per kg of solvent. Molarity is defined as moles of solute per L of solution. Volume is temperature dependent. Mass is temperature independent.

Define K and Q. What happens when Q > K

Q - the reaction quotient K - the equilibrium constant When Q is larger than K the reaction is not at equilibrium and some products will be converted to reactants

Provide Raoult's Law and Henry's Law

Raoult: Pi = (xi)(Pi*) Henry's: Pi = (xi)(kHi)

What information can be obtained from a tie line in a P-Z phase diagram

Tie lines are horizontal lines that connect liquid to vapor-liquid phases and vapor-liquid to vapor phases. These lines help determine the mole fraction of each component in both liquid (x) and vapor (y) phases in the binary solution

Provide the formula for finding volume of binary solution when given partial volumes

V =n1v1(P,T,n1,n2)+ n2v2(P,T,n1,n2) lowercase v are partial volumes, should have line over them

What is the formula for the compressibility factor, z? What happens if Z > 1 Z < 1

Z = PVm/RT Z>1: real gas exerts more pressure than ideal gas Z< ideal gas exerts more pressure than real gas

Provide the formula for: Average Composition

Zx = (nx)/(n total)

Provide the formula for activity

a solvent = Psolvent/P*solvent

Provide the formula for mean ionic activity

a+/-^v = a+^v+ * a_^v_ a+/- = (a+^v+*a_^v_)^1/v

What formulas do you need to calculate the molecular weight?

n,solute=m(solute) * mass(solution) m,solute = mass in grams/n,solute

Provide the formula for osmotic pressure

pi = (n solute * RT)/V

What does the clausius-claperyon equation solve for? Provide it.

the CC equation solves for the slope of the coexistence lines. m = dP/dT = ∆Sm/∆Vm

What is fugacity?

the effective pressure a real gas exerts (fleetness)

Relating chemical potential to activity - Provide Henry's law

u*H(solute) = u*(solute) + RT ln (kHsolute/P*solute)

Relating chemical potential to activity - Provide Raoult's law

ui(solution) = ui* + RTln(ai)

Provide the formula for activity coefficient

y solvent = a solvent/x solvent

Provide the formula for mean activity coefficient

y+/-^v = y+^v+*y_^v_

What is the formula for ∆Gmix and ∆Smix?

∆Gmix = nRT * xi ln xi ∆Smix = - (∆Gmix/T)

A solution is characterized by ∆Gmixing<0 and ∆Smixing>0. is the formation of this solution spontaneous or nonspontaenous

∆S,mix > ∆G,mix < 0 for a spontaneous process

Provide the formula for boiling point elevation

∆Tb = (Kb)(m solute)

What formulas do you need to calculate the freezing point density?

∆Tb=Kb(m) - solve for m ∆Tf=-Kf(m)

Provide the formula for freezing point depression

∆Tf = (-Kf)(m solute) where m=molality (kg/mol)

Why is it not possible to measure the Gibbs energy of solvation of Cl- directly?

Because solutions are electrically neutral. The solution containing both cationic and anionic portions is the only value that can be experimentally measured.

transport occurs from a region of high chemical potential to one of low potential, until a mixture has the same value of chemical potential in all regions

Chemical potentials

What do chemical potentials show?

Chemical potentials show how the Gibbs energy of a system changes as a substance is added to it

Explain why colligative properties depend only on the concentration and not on the identity of the molecule

Colligative properties depend on changes in the entropy of the solution when the solution is dissolved, which is determined by the concentration of the solution not their identity or structure.

Provide the formula for mean ionic molality

m+/-^v = m+^v+*m_^v_ m+/- = (v+^v+*v_^v_)^1/v * m

Provide the formula for how activity and activity coefficients relate to Henrys law

ai = PiH/kiH yi= ai/xi

Gives the Gibbs-Duhem equation. What does it tell us?

dU2=(-n1dU1)/(n2) tells us that the chemical potential of 2 components in a binary solution are dependent on one another, if you know one you can figure out the other