practice final(1)

8/23/2019 Practice Final(1)

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CHEM 131

FINAL EXAM

F. Paesani Winter 2011

NAME

STUDENT ID

1. /25 5. /20

2. /10 6. /15

3. /12 7. /13

4. / 8 8. /12

TOTAL FINAL /115

NOTE: Your REASONING and ANSWERS MUST be clear to me. Guesswork,

or apparent guesswork, will not earn credit.

TOTAL NUMBER OF PAGES INCLUDING THIS COVER PAGE: 21.

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CHEM 131

1. 25 pointsThis problem has five parts, one part for each of Chapters 6-10. YOU NEED ONLY

ANSWER T OR F. Correct choice = 1 points, no choice = 0 points, incorrect choice= -0.25 points. Be careful: pure guessing is a very bad idea because you losepoints for incorrect choices.

Chapter 6 - Reaction Equillbirum in Ideal Gas Mixtures.

The chemical potential of ideal gas i in an ideal gas mixtureat temperature T and partial pressure Pi equals the chemicalpotential of pure gas i at temperature T and pressure Pi.

of a pure ideal gas goes to as P 0and goes to + as P.

The entropy of a mixture of N2 and O2 gases (assumed ideal)is equal to the sum of the entropies of the pure gases,each at the same temperature and volume as the mixture.

When the ideal-gas reaction A + B C + D has reachedequilibrium, it must hold that nC + nD = nA + nB.

For an ideal-gas reaction KP for the reverse reaction

is the negative ofKP for the forward reaction.

KP for a particular ideal-gas reaction is a function of temperaturebut is independent of pressure and of the initial compositionof the reaction mixture.

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CHEM 131

Chapter 7 - One Component Phase Equilibrium.

Since the three possible phases are solid, liquid, and gas, the maximumpossible value of the number of phases p in the phase rule is 3.

The number of degrees of freedom f is the number of variables neededto specify the thermodynamic state of a system.

The normal boiling point is the temperature at which the vapor pressureof a liquid equals 1 atm.

The enthalpy of vaporization of a liquid becomes zero at the criticalpoint.

When three phases coexist in equilibrium in a one-component system,one must be a gas, one must be a liquid, and one must be a solid.

For a one-component system, the most stable phase at a given Tand P is the phase with the lowest Gm.

Chapter 8 - Real Gases.

The parameters a and b in the van der Waals equation for CO2have the same values as in the Redlich-Kwong equation for CO2.

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CHEM 131

Chapter 9 - Solutions.

The volume of a solution at T and P equals the sum of the volumes ofits pure components at T and P.

i is a partial molar quantity.

Intermolecular interactions are negligible in an ideal solution.

If B is a component of a solution, B cannot be greater than

B.

For equilibrium between an ideal solution and an ideal vapor, themole fraction xB of component B in the solution must be equal to the

mole fraction yB of B in the vapor.

In an ideally dilute solution, i =

i + RT ln xi for all components.

Chapter 10 - Nonideal Solutions.

When a solution component is in its standard state, its activity is 1.

ai and i are extensive properties.

For a solute in a solution, II,B = I,B.

The activity ai is never negative.

Activity coefficients may be positive or negative.

The ionic charge z+ in an electrolyte solution does not affect the valueof the mean ionic activity coefficient .

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CHEM 131

2. 10 points - Problems about ideal gas equilibria

(a) 5 pointsFor the gas-phase reaction 2SO2 + O2 2SO3, observed mole fractions for acertain equilibrium mixture at 1000 K and 1767 torr are xSO2 = 0.310, xO2 =0.250, and xSO3 = 0.440. Find K

0p and G

0 at 1000 K, assuming ideal gases.(R = 8.314 J/mol-K, 1 bar = 0.987 atm = 750 torr.)

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(b) 5 pointsFor the ideal-gas reaction A + B 2C + 2D, it is given that G0500 = 1250

cal/mol. If 1.000 mol of A and 1.000 mol of B are placed in a vessel at 500 K andP is held fixed at 1200 torr, find the equilibrium amounts ni of all the components.R = 1.987 cal/mol-K. If H0 = 2000 cal/mol, calculate K0p at 800 K when P isheld fixed at 1200 torr (H0 can be assumed to be constant in this temperaturerange). Will the equilibrium amount of C be larger than at 500 K?(1 bar = 750 torr.)

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CHEM 131

3. 12 points - Problems about one-component phase equilibria

(a) 4 pointsAt the normal melting point of Hg, -38.9 C, its enthalpy of fusion is 2.82 cal/mol,the density of the solid is 14.193 g/cm3, and the density of the liquid is 13.690g/cm3. Find the melting point of Hg at 500 atm.(R = 1.987 cal mol1 K1 = 82.06 cm3 atm mol1 K1).

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CHEM 131

(b) 4 pointsThe normal boiling point of diethyl ether is 34.5C and its vapHm at the normal

boiling point is 6.38 kcal/mol. Find the vapor pressure of ether at 25.0

C usingappropriate approximations. (R = 1.987 cal mol1 K1, 1 atm = 760 torr.)

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CHEM 131

(c) 4 pointsThe vapor pressure of water at 25C is 23.76 torr. Suppose that 0.360 g ofH2O is placed in an empty rigid container at 25

C. What phase(s) are presentat equilibrium if the volume of the container is V = 10.0 L? What phase(s) arepresent at equilibrium if the volume of the container is V = 20.0 L? Assume thevapor to be an ideal gas. Make sure I understand how you get your answers.(R = 82.06 cm3 atm mol1 K1, 1 atm = 760 torr.)

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CHEM 131

4. 8 points - Problem about real gasesFor ethane, Pc = 48.2 atm and Tc = 305.4 K. Calculate the pressure exerted by 74.8 g

of C2H6 (molar mass = 30 g/mol) in a 200-cm3 vessel at 37.5

C using(a) 3 pointsthe ideal-gas law

(b) 5 pointsthe van der Waals equation

P =RT

Vm b

a

V2m

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CHEM 131

5. 20 points totalThroughout this problem the temperature is kept at T = 308K. Also, I

want numerical answers for all parts. A container is divided into two separatecompartments. One contains liquid acetone (A) in equilibrium with its vapor. Thevapor pressure is 347 torr. The other compartment contains liquid chloroform (C) inequilibrium with its vapor at 273 torr. (R = 8.314 J/mol-K.)

(a) 3 pointsWe now remove the partition so that the liquids mix. The composition of theresulting solution in mole fractions is 80% acetone and 20% chloroform, xA = 0.8and xC = 0.2. If this were an ideal solution, what would be the partial vaporpressures of each component and the total vapor pressure in equilibrium with theliquid solution?

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CHEM 131

(b) 3 pointsSuppose that the vapor also behaves ideally. What are the mole fractions of

acetone and chloroform in the vapor?

(c) 3 pointsCalculate the molar free energy of mixing of the ideal solution. R = 8.314 J/mol-K.

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CHEM 131

(d) 3 pointsThe solution with 80% acetone and 20% chloroform is not really ideal. Instead, itis better described as ideally dilute. The Henrys Law constant for chloroform isK = 165 torr. Calculate the partial vapor pressures of each component and thetotal vapor pressure in equilibrium with the liquid solution.

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(e) 4 pointsCalculate the molar free energy of mixing of this ideally dilute solution.

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(f) 4 pointsAlas, the solution is neither ideal nor ideally dilute, since one observes non-negligible deviations from both behaviors. The actual ratio of partial pressure toHenrys constant for the chloroform in this solution is pc/K= 0.21 and the ratio ofthe partial pressure to the vapor pressure of pure liquid acetone is pA/p

A = 0.72.Calculate the activity coefficients for acetone and for chloroform in this solutionaccording to convention II (for the chloroform, use the mole fraction convention,i.e., dont change to molality units).

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CHEM 131

6. 15 points - Problems about real solutions (nonelectrolytes)At 35C the vapor pressure of chloroform is 295.1 torr and that of ethanol is 102.8 torr.

A chloroform-ethanol solution at 35

C with xeth = 0.200 has a vapor pressure of 304.2torr and a vapor composition ofyeth = 0.138. R = 8.314 J/mol-K.

(a) 5 pointsCalculate I and aI for chloroform and for ethanol in this solution.

(b) 5 pointsCalculate i

i for each component in this solution in J/mol.

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CHEM 131

(c) 5 pointsCalculate G for the mixing of 0.200 mol of liquid ethanol and 0.800 mol of liquidchloroform at 35C.

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CHEM 131

7. 13 points - Problems about real solutions (electrolytes)Consider the strong electrolyte MgCl2.

(a) 4 pointsGive the following numerical values (rather than a formula) for this electrolyte:+, , z+, z, .

(b) 4 pointsExpress in terms of+ and , and ai in terms of and mi, exhibiting explicitexponents and coefficients.

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(c) 5 pointsCalculate the ionic strength of a 0.2-mol/kg aqueous solution of MgCl2 at 25 Cknowing that the fraction of Mg2+ ions that associate with Cl ions to form ionpairs is 1 = 0.35. Note that the ion pair is charged.Useful equation for this problem:

Im =1

2

j

z2jmj

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CHEM 131

8. 12 points totalShort unrelated questions.

(a) 4 pointsSuppose that the ideal-gas reaction A+B C+D has reached equilibrium. Allquantities below are the values at equilibrium. Only two of the following relationsare true. Tell me which ones. (1) nC + nD = nA + nB; (2) PC + PD = PA + PB;(3) nA = nB; (4) nC = nA; (5) nC = nD; (6) if only A and B are present initially,then nC = nA; (7) if only A and B are present initially, then nC = nD; (8) if onlyA and B are present initially, then nC + nD = nA + nB; (9) A + B = C + D.

(b) 4 points

Which has the higher vapor pressure at -20

C, ice or supercooled liquid water?Explain using quantitative arguments.

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CHEM 131

(c) 4 pointsConsider an aqueous solution of the weak acid HCN. The system has five chemicalspecies, H2O, HCN, H

+, OH, and CN, and two independent reactions:

H2O H+ + OH

HCN H+ + CN

Find the number of degrees of freedom f for this system, and tell me whichintensive variables you would use to specify the state of the system. I mustunderstand your reasoning.

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