Problem 1: A mixture of nitrogen and butane exists in gaseous equilibrium equilibrium at 171° C and 13.79 MPa. Calculate the fugacity of both components when nitrogen makes up 35 mass % of the mixture. Data: B N2-N2 = -1.24 * 10-5 BBut-But = -4.32 * 10-5 and and figure 7.4-1
A very good problem that looks simple but is actually fairly complex. The statement is a little vague and the solution requires assumptions that may not be completely obvious.
Problem 2: The following data was collected collected for a gaseous mixture of compounds D and E for the virial coefficients of a truncated eq n. of state. BDD (m3/mol) BEE (m3/mol) BDE (m3 /mol) Temp (° C) 25 -1.85*10-4 -1.69*10-4 -2.10*10-4 35 -1.37*10-4 -1.27*10-4 -1.85*10-4 a. Calculate the fugacity of D at 27° C at 500 kPa for XD = 0.60 b. Discuss the effect of temperature on the fugacity of D over the range from 25° C to 35° C. Hint Hint : One additional fugacity will be sufficient.
As opposed to problem 1, this one is completely straightforward but uses the exact same equations. Which one forces you to use more logic? Part b is an an excellent idea but without wit hout knowing kn owing the th e identity ident ity of D and E we can say very little other than the fugacity went up or down.
Problem 3: Given: P=10 bar T=373.15 K fET =9.6 =9.62 29 bar bar f BU=8.628 bar A mixture containing 30 mol % ET and 70 mol % BU, calculate the fugacity of ET and BU in the mixture using: Good idea of comparing between a. Lewis- Randall rule an approximation and an EOS. b. Virial EOS with Calculations are straightforward. -4 3 BET-ET = -1.15*10 m /mol BET-BU = -2.15*10-4 m3/mol BBU-BU = -4.22*10-4 m3 /mol c. Compare the results of parts A and B and explain which one will be more accurate.
Problem 4 Compute the vapor fugacities of substance A and substance B in an equimolar mixture at 150° C at 1 bar. State all assumptions. assumptions. (a) Using the Lewis-Randall rule. (b) Using the Virial Equation of State. (c) Compare results and tell which technique is more accurate and why? At what conditions are these techniques not accurate and give an example of more accurate technique?
YIKES! This is a grading nightmare. Basically we are asked to assume the pure component fugacities for part a then merely copy an equation for part b since we aren't given any numbers for virial coefficients. Part c is im oss ossible ible to do beca because use an an
Data : at T=423.15K, BA-A=α m3/mol , BB-B= β m3/mol , BA-B= Κ m3/mol
answer is justifiable based on assumptions and we have no numerical results to compare. This is a FUMBLE.
Problem 5 A mixture of 20% CO 2 , 35% O2 , and 45% N2 by mole is held in a room. The temperature of the room is 500 K. Interesting idea using an a) Assuming the gas obeys the given EOS for partial expression for partial molar volume. I wouldn't want to be in a molar volume, calculate the fugacity of each component room at 40 bar. In part a) how is of the mixture in the room if the total pressure is 40 bar. the result different for different EOS: species? Seems like you'll get the 3RT exact same answer for each Vi = where a= 4.0 bar component. Part b is not very (P − a ) specific. Could go the easy route b) Then find the pure component fugacity for each using the Lewis-Randall rule but component. part a implies that there is an EOS c) Is your estimating in (b) a good one? What factors involved. Some of us might try to back ou t phi and t hen pure comp. would affect it? fugacity.
Problem 6 One day, thermodynamic genius Stanley Sandler was Finally something besides A & doing some recreational gas mixture experiments when he B! Question suffers from the discovered a new physical law. He found that the partial same ambiguity as in problem molar volume of "gobuckeyes" in a closed system of 5. Those who assume L-R will gobuckeye and "beatmichigan" was dependent on the total be done in 5 minutes, t hose who don't will take 30. pressure via the relationship: RT Vg = P + P Using this equation, find the fugacity of pure gobuckeyes at a temperature of 373.15K, a pressure of 20MPa, mole fraction of gobuckeye yg=0.5
Problem 7 A) Assuming a mixture obeys the EOS: aRT b + V = P P with mixing rules: a
= ∑ xi a i i
and
b=
∑
xi bi
i
Derive the fugacity coefficient for a component in a binary mixture. B) Calculate the partial molar gibbs free energy of component 1 at 298 K and 2 bar if 0.3 moles of 1 is mixed with 1.34 moles of component 2 given the following information:
This is good although a bit scary initially (mainly because of that ugly wo rd "derive"). Part B is challenging and could have a few pitfalls along the way if you take a wrong path. The twist giving U=f(T) is interesting.
a1 = 4.63 (mol) a2 = 3.42 (mol) UIG = 2.42 + 0.324 T + 9.35 T2
b1 = 0.486 m3 /bar b2 = 0.827 m3 /bar
Problem 8 Components A&B mix at 20 bar, 298 K to form two gas phases. Phase 1 is pure component A and phase 2 is 30% A and 70% B by mole. The molar Gibbs free energy of phase 2 is 100 J/mol and the partial molar Gibbs free energy of component B is 39 J/mol. The pure component A molar Gibbs free energy is 120 J/mol. Assume that pure component A behaves ideally at system pressure. Do not assume equilibrium conditions.
Hmmm, 2 gas phases? Well let's throw out our instincts and continue. We are given a lot of information but I'm worried about the last statement regarding equilibrium - it was scribbled as an addendum on the question. If the 2 phases aren't in equilibrium I don't know if the probl em can be solve d.
a) Find the partial molar Gibbs free energy of component A in phase 2. b) Explain how the assumption in the problem statement allows you to make a simplification to the problem in order to solve part c. (Hint: What does it allow you to do with respect to fugacities?) c) Find the fugacity of Component A in the mixture.
Problem 9 Data for two components, A & B, in a gas mixture are given below: Property Component A Component B Pressure = 1 bar Temp = 373.15 K Number of Moles 10.0 25.0 Pure comp. fugacity 0.981 bar 0.995 bar 3 Second virial coeff. (Bii) -3.21e-4 m /mol -1.60e-4 m3/mol Cross virial coeff (BAB) -2.63e-4 m3 /mol Back to good old A & B (they're nothing if not reliable). Why do I have to calculate pure component fugacities in part a when they are given in the problem? Am I supposed to calculate them using the Virial Equn also?
a) Calculate the fugacities of the two components in a mixture by calculating pure component fugacities with virial EOS and the Lewis-Randall rule. b) Calculate the fugacities of the two components in a mixture using the truncated virial equation of state. c) Which of these calculations would you expect to be more accurate? why?
Problem 10 Equation 7.2-13, from Sandler’s Chemical and Engineering Thermodynamics, states that
v
ln
f i (T , P , y ) yi P
=
V = Z v RT / P
1 RT
∫
V = ∞
RT ∂ P − N N ∂ V i T ,V , N ≠
j 1
Compute the fugacities of ethane and butane in a 35:65 mixture at 373.15K and 10 bar. Since pressure is relatively low, use the truncated virial equation of state to solve for your answer. The following are given:
d V − ln Z v
This problem violates both the intent and the spirit of the exercise. The only thing different between this and Illustration 7.4-2 on p 408 is the composition. I expect better. I'm docking 2 points from the quiz score of each member of this group.
Virial EOS: Z mix
=
1+
Bmix (T , y ) V
,
where Bmix (T , y ) =
∑∑ y y B (T ) i
i
j
ij
j
at 373.15 K, Bethane-ethane = -1.15*10-4 m3/mol B butane-butane = -4.22*10-4 m3/mol Bethane-butane = -2.15*10-4 m3/mol
Problem 11: a) Estimate the fugacity of both gases in a mixture of 23% napthalene and 77% isopentane at 8MPa and 405 K using the Lewis Randall rule. (Assuming both are gases at the given conditions). b) What kind of accuracy would you expect from this model? c) Propose an alternative model, which would be more accurate, and OUTLINE the necessary steps to solve the problem. DO NOT actually solve it.
Straightforward question IF I can find the pure component fugacities of these species. A little help in this regard would be appreciated because I suspect that naphthalene will be difficult to get. Part c is a great level 5 question but requires a lot of time unless we copy an idea from the book. A modification might be to outline the steps using an equation of state and discuss why it would be more accurate.
Problem 12: Seventy-six (76) moles of methane and 90 moles of CO2 gas are mixed in a 1 L tank at 273.15 K and 10 bar. At this temperature and pressure, the pure component fugacities of each component are: f v CO2 = 9.629 bar f v CH 4
= 8.753 bar
Given the following parameters, BCH 4 − CH 4 and BCH 4− CO2
= −4.65 ⋅ 10
= −6.27 ⋅ 10 −4
−4
m3
mol m3
,
BCO2 − CO2
mol solve for the fugacities of each component using,
a) the Lewis-Randall rule.
= −8.16 ⋅10
−4
m3 mol
,
Straightforward application of principles used in class. Short concise question with proper information given. Not extremely creative but functional. Good test of basic skills.
b) the virial equation of state method.
Problem 13: a) What is the significance of the fugacity of a gas? What does φ ’s deviation from 1 reflect about the gas? Explain φ >1 and φ <1. b) Calculate the fugacities of pure Cl2 and F2 at 230 K and 15 bar, and then at 30 bar. Assume virial EOS is valid. BCl 2
= −457
cm3 mol
,
B F 2
= −32
cm 3 mol
Very well done. Sets up the significance of the calculation with some discussion. There do seem to be a lot of calculations. Seems like I'm calculating fugacity at 2 different pressures f or no apparent reason. Could the same thing be accomplished by calculating at one pr essure? Of course, I'm expecting the result to give me one φ>1 and one φ<1 to reinforce part a but I don 't know if that will happen.
c) Find the fugacities of Cl2 and F2 in a mixture of 100g Cl2 and 100g F2 at 230 K and 15 bar, and then at 30 bar. Assume the Lewis-Randall rule is correct. g MW Cl 2 = 69.9 , MW F 2 mol
= 38
g mol
Problem 14: In a magical pressure container, I combined 17 kg of butane and 20 kg of methane. Last night, this magical container was left in my house where ignorant roommates left the thermostat on too high and the vessel heated up to Huffing butane, now THAT's 100° C. The next morning, after waking up in a appealing. Note how the temperature pool of my own sweat, I thought it would be cool to change is only implied and by giving take a big whiff of the butane mixture and calculate only one T and P we are forced to do the calculations assuming these are the the fugacities of each component of the mixture at conditions. However, by opening the 10 bar. a) Calculate the fugacities using the LewisRandall approximation.
container to smell, won't the pressure be 1 bar? Yes, someone will ask that very question. Be a little more specific.
b) Calculate the fugacities using the Virial Equation of State.
c) Are the two answers similar? Why or why not?
Necessary data: MW(methane) = 16 g/mol MW(butane) = 58 g/ mol f butane (373.15 K, 10 bar) = 8.628 bar f methane (373.15 K, 10 bar) = 9.90296 bar BMe-Me = -6.6*10-5 m3/mol BBu-Bu = -0.00117 m3/mol BMe-Bu = -2.45*10-4 m3/mol Hint: You really shouldn’t sniff butane.
