QUIZZESQUIZZESQUIZZESQUIZZES

CHE 303 W16

PBV

QUIZ #1 PAH

• Find the pressure of a mixture of

• CH4 (0.25 kmol) + n-C4H10 (0.25 kmol)

• at T=250°C and V= 0.241 m3.

• Use the van der Waals EOS.

• (R=0.08314 Bar.m3/kmol.K)

QUIZ #2 OAK

• Find the pressure of a mixture of

• CH4 (0.18 kmol) + n-C4H10 (0.274 kmol)

• at T=238°C and V= 0.241 m3.

• Use the Redlich-Kwong EOS.

• (R=0.08314 Bar.m3/kmol.K)

CH4 nC4H10

a 2.293 13.86

b 0.0428 0.1162

CH4 nC4H10

a 32.11 289.5513.86

b 0.02965 0.0806

Quiz 3: H-x: Water+H2SO4 Mx PAK

• Find the partial molar enthalpy!

• Hwat and Hacid at mass frac. wA=0.60.

• Also find HTOT at wA=0.60 from the relation

between PMH and total H.

Quiz 3: H-x: Water+H2SO4 Mx

• Find the partial molar enthalpy!

• Hwat and Hacid at mass frac. wA=0.65.

• Also find HTOT at wA=0.65 from the relation

between PMH and total H.

Quiz: Use the vdw for pure f0 PAO

• A tank of argon is at T = 77oF and P= 90 atm. Find the

fugacity of the argon (in atm).

• (Use R = 0.7302 atm.ft3/[oR.lbmol] ). For the van-der-

Waals parameters: a= 346.369, b = 0.5171,

• [v=4.044 cuft/lbmol]

• [Units: a = atm(ft3/lbmol)2, b = ft3/lbmol. ]

Quiz: Use the vdW for Mx fi PAR

• A tank of mixture of (mole%)

• 75% argon (1) and 25% ethylene (2) is

• at T= 298.15 K and P= 91.2 bar.

• Find the fugacities of 1 & 2 (use vdW)!

• (Use R = 0.08314 bar.m3/[K.kmol] ).

• For the vdw parameters:

• a1= 1.3681, b1 = 0.032289;

• a2 = 4.56149, b2 = 0.057443.

• [Units of a = bar(m3/kmol)^2, b = m3/kmol. ]

• Molar volume: v = 0.23187 m3/kmol

Summary: van der Waals Eq.

MxFug. for the Redlich-Kwong Eq.

a1 = 0.42748 R2TC15/2/Pc1

b1 = 0.08664 RTc1/Pc1

QUIZOAb

Quiz 1: Use the RK for Mx Psys

• A tank of mixture of (mole%)

• 75% argon (1) and 25% ethylene (2) is

• at T= 298.15 K and v = 0.2092 m3/kmol.

• Find the pressure of the system.

• (Use R = 0.08314 bar.m3/[K.kmol] ).

• For the RK parameters:

• a1= 17.035, b1 = 0.003843;

• a2 = 77.756, b2 = 0.039815.

• [Units of a = bar(m3/kmol)2, b = m3/kmol. ]

Quiz 2: Use the RK for Mx fi• A tank of mixture of (mole%)

• 75% argon (1) and 25% ethylene (2) is

• at T= 298.15 K and P= 91.2 bar.

• Find the fugacities of the components.

• (Use R = 0.08314 bar.m3/[K.kmol],

• v = 0.2092 m3/kmol).

• For the RK parameters:

• a1= 17.035, b1 = 0.003843;

• a2 = 77.756, b2 = 0.039815.

• [Units of a = bar(m3/kmol)2, b = m3/kmol. ]

Quiz: Find activities with RK• Mixture of 75% argon (1) and 25% ethylene (2) is

• at T= 298.15 K and P= 91.2 bar.

• Find the pure fugacities fi0, . (Use the RK Eq.)

• activities ai,

• activity coefficients γi• Given the mx-Fugs: f1 = 60.24 bar, f2 = 14.43 bar.

• (Use R = 0.08314 bar.m3/[K.kmol])

• Pure v10= 0.2302 , v2

0= 0.09896 m3/kmol. .

• For the RK parameters:

• a1= 17.035, b1 = 0.003843 (for argon);

• a2 = 77.756, b2 = 0.039815 (for ethylene).

• [Units of a = bar*sqrt(T)(m3/kmol)2, b = m3/kmol. ]. Mx molar vol. v = 0.2092.

Mx Fugacities from EOS:

Mx Fugacities from EOS: (2)

1

Quiz Hints: Find the activities and their coefficients

• Step 1: Calculate f10, f2

0 for pure 1 & 2.

• (Using RK formulas)

• Step 2: Calculate a1 = f1/ f10, etc.

• Step 3: Calculate γ1 = a1/y1, etc.

QUIZ: PBC-Hw

OBB

• For the same mixture: Benzene (45%)-

Toluene(55%), if the system pressure Psys =

210 kpa, what is the bubble temperature, Tbbl?

• [Hints]: Try the temperatures Tbbl= 391.5,

392.5 and 394 K.

• Prove that it is the bubble point temperature

Tbbl! Make the sum = 1.0!

Example 5-1-1

Bubble point T =? yi = ?

• Determine the temperature and composition of the first

bubble created from a saturated liquid mixture of benzene

and toluene containing 45 mole percent benzene at 200 kPa.

Benzene and toluene mixtures may be considered as ideal.

Use Antoine Equation for vapor pressure:

CALC #1 Benzene Benzene Toluene Toluene Benzene Toluene Σyi=1

|==>210 kPa T K lnVap1 Vap1(kPa) lnVap2 Vap2(kPa) K1 K2 SumKixi

Ben (Boil T) 377.31 5.298364 200.0093 4.429957 83.92783 0.952425 0.399656 0.648402

380 5.369431 214.7407 4.50934 90.86179 1.022575 0.432675 0.69813

390 5.623917 276.9721 4.793517 120.7252 1.318915 0.574882 0.909697

391.1 5.651014 284.5798 4.823768 124.433 1.355142 0.592538 0.93571

391.3 5.655922 285.98 4.829247 125.1167 1.36181 0.595794 0.940501

391.5 5.660824 287.3855 4.83472 125.8034 1.368502 0.599064 0.945311

391.7 5.665721 288.7962 4.840187 126.493 1.37522 0.602347 0.95014

391.8 5.668168 289.5036 4.842918 126.8389 1.378589 0.603995 0.952562

392.1 5.675498 291.6336 4.851101 127.8811 1.388731 0.608958 0.959856

392.3 5.680378 293.0603 4.856549 128.5797 1.395525 0.612284 0.964743

392.5 5.685253 294.4922 4.86199 129.2812 1.402344 0.615625 0.969648

394 5.721633 305.4032 4.9026 134.6393 1.454301 0.64114 1.007062

QUIZ: PBE-Hw

• For the same mixture: Benzene (45%)-

Toluene(55%), if the system pressure Psys =

210 kPa, what is the dew temperature, Tdew?

• And xi?

• [Hints]: Try the temperatures Tdew= 393K, and

400 K, and 402K.

• Prove that it is the dew point temperature

Tdew! Make the sum (yi/Ki)= 1.0!

CALC #2 Benzene Benzene Toluene Toluene Benzene Toluene Σxi=1

<T Dew> T K lnVap1 Vap1(kPa)lnVap2 Vap2(kPa)K1 K2 SumKixiPsys, kPa = 391.5 5.660824 287.3855 4.83472 125.8034 1.368502 0.599064 1.246926

210 393 5.697414 298.0956 4.875566 131.0483 1.419503 0.624039 1.198367y1 394 5.721633 305.4032 4.9026 134.6393 1.454301 0.64114 1.167274

0.45 400 5.86414 352.1793 5.06165 157.8508 1.677044 0.75167 1.000033y2

0.55

0.268329 0.731704x1 x2

PBH

OBD

385

QUIZ

PBH

Psys=

200

kPa

PBO

QUIZ:OBFPBO

Also find xi !

Rachford-Rice

Ans. (Quiz OBF)

PBQ

QUIZ: OBIPBQ

• For a liquid mixture of 41.2 mol% ethanol (1) and

n-hexane (2).

• Find the activity coefficients γi from the Van Laar

equations:

• Compare those from the Wilson equations:

PBS

QUIZ: Construct P-x-y PBS

• For mixture of n-pentane (1) and n-heptane

(2) at T= 260oF, construct the P-x-y diagram.

You can use two pressures P1= 50 psia and

P2= 100 psia.

• The vapor pressures for nC7 = 31.6 psia (at

x1=0), for nC5 = 148.7 psia (at x1=1.0). Read the

Ki values from the nomograph.

Hints

• Read nomographs: Ki (at P1 & P2)

• Calculate xi and yi

• Plot on P-x1 and P-y1.

Excel Cal (Q)OBK P-x-y nC5+nC7303W15QUIZ

DATA K oC oFT 400 126.85 260.3

Antoine eq logP(mmHg)= A- B/(ToC+C)n-pentane6.85296 1064.84 232.012n-heptane6.89677 1264.9 216.544

CALC.1 log(10)

Vap-PlogPmmHg mmHg psia atm

C53.88569

17685.83

8 148.6603 10.11295

C73.21324

61633.97

8 31.60457 2.149971

CALC.2Read Ki from nomograph

Select P1,P2… psia K5 K7

P1= 50 2 0.5P2= 100 1.45 0.35

CALC.3Cal. xi,yi

Psia 31.6 50 100 148.66x1 0 0.333333 0.590909 1y1 0 0.666667 0.856818 1

0

20

40

60

80

100

120

140

160

0 0.2 0.4 0.6 0.8 1

P (

psi

a)

x1 or y1

Pxy: nC5+nC7P-x: Bubble

P-y: Dew

0

20

40

60

80

100

120

140

160

0 0.2 0.4 0.6 0.8 1

P (

psi

a)

x1 or y1

Pxy: nC5+nC7

P-x: Bubble P-y: Dew