CHEMICAL THERMODYNAMICS - · PDF fileCHEMICAL THERMODYNAMICS Handbook of Exercises Valentim...

CHEMICAL THERMODYNAMICS
Handbook of Exercises
Valentim Maria Brunheta Nunes
2013

Chemical Thermodynamics _____________________________________________________________________________________
Handbook of Exercises _________________________________________________________________________________
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"A theory is the more impressive the
greater the simplicity of its premises, the
more varied the kinds of things that it
relates and the more extended the area of
its applicability. Therefore classical
thermodynamics has made a deep
impression on me. It is the only physical
theory of universal content which I am
convinced, within the areas of the
applicability of its basic concepts, will never
be overthrown." -- Einstein (1949)
INTRODUCTION
Thermodynamics its a discipline that is very important for many
engineering degree programs like Chemical and Biochemical Engineering,
Environment Engineering or Mechanical Engineering. With the Chemical
Thermodynamics course we intend to introduce the principles of
thermodynamics, and apply them to systems, that are solids, liquids or
gases, with an interest in chemical engineering, dont forgetting
environmental issues. This course is also fundamental in the development of
important calculation techniques in engineering.
This exercise book will serve to accomplish the lectures, and the
problems presented seek to encompass the entire program taught to
prepare students for the final evaluations. The resolution of examinations
of previous academic years may be also quite helpful for the students.

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1st Series of Exercises - Gaseous State
1. Calculate the volume occupied by 3 moles of a perfect gas at 2 bar and
350 K.
2. Calculate the final pressure when 1 mole of nitrogen at 300 K and 100
atm is heated, at constant volume, until attaining 500 K.
3. The mass percentage of dry air at sea level is approximately: N2, 75%;
O2, 23.2% and Ar, 1.3%. What are the partial pressures of each
component when the total pressure is 1 atm?
4. Calculate the pressure exerted by 1 mole of CO2 behaving as (a)
perfect gas and (b) van der Waals gas, when it is confined in the
following conditions: T = 273.15 K and V = 22.414 L (constants of the van
der Waals equation: a = 3.592 atm L2mol-2 and b = 4.26710-2 Lmol-1)
5. Calculate the molar volume of nitrogen at 100 C and 30.5 atm using:
5.1. The perfect gas equation.
5.2. The van der Waals equation (a = 1.35 dm6.atm.mol-2; b = 38.610-3
dm3.mol-1)
5.3. The virial equation: Z = 1 5.310-4 p + 4.810-6 p2, with p in atm.
6. At 300 K and 20 atm, the compressibility factor of a given gas is 0.86.
Calculate (a) the volume occupied by 8.2 mmol of gas (b) the
approximate value of the second virial coefficient at 300 K.

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7. Calculate the pressure exerted by 1 mole of ethane (C2H6) behaving as:
(a) perfect gas; (b) van der Waals gas, when confined in the following
conditions: i) 273.15 K and V = 22.414 L; ii) 1000 K and 100 cm3. Data:
a = 5.489 L2.atm.mol-2 and b = 6.38010-2 L.mol-1.
8. Suggest the pressure and temperature for 1 mole of He to be in
corresponding states with 1 mole of H2 at 1 atm and 25 C. Data: Pc(H2) =
12.8 atm; Tc(H2) = 33.23 K; Pc(He) = 2.26 atm; Tc(He) = 5.2 K.
9. The critical constants of methane are pc = 45.6 atm, Vc = 98.7 cm3.mol-1
and Tc = 190.6 K. Calculate the parameters of the van der Waals
equation for this gas and make an estimative of the molecules radius
(considered as spheres).
10. A sample of 87 mg of an ideal gas at 0.600 bar duplicates its volume and
triplicates its temperature. What will be the final pressure?
11. Two balloons of equal volume and in vacuum are connected by a tube with
negligible volume. The first one its in a thermostatic bath at 200 K and
the other in a bath at 300 K; then it is injected in the system 1 mole of
an ideal gas. What will be the final number of moles in each balloon?
12. One compound made of nitrogen and oxygen as the following variation of
density with pressure at 0 C:
p / atm 0.333 0.500 0.667 1.000
(/p)/g.L-1 .atm-1 1.9694 1.9722 1.9746 1.9804

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12.1. Calculate the molar mass of the compound and suggest the
correspondent molecular formula.
12.2. Calculate the 2nd virial coefficient at 0 C.
13. Deduce the relation between pressure and density for a perfect gas
with molar mass M. Confirm graphically that dimethyl ether at 25 C
behaves like a perfect gas at low pressures and calculate the
correspondent molar mass of gas.
p/torr 91.74 188.98 273.3 452.8 639.3 760
/ g.L-1 0.225 0.456 0.664 1.062 1.468 1.734
2nd Series of Exercises The First Law of Thermodynamics
14. Two moles of an ideal gas at 500 K are isothermally and reversibly
compressed until a final volume that is 1/10 of the initial volume.
Calculate: (a) U (b) H (c) work done by the gas (d) heat absorbed by
the gas.
15. Two moles of an ideal gas for which Cp = 40 JK-1mol-1 are heated from
300 to 400 K, (a) at constant pressure and (b) at constant volume.
Calculate in each case (i) U, (ii) H, (iii) work done by the gas and (iv)
heat absorbed by the gas.
16. One mole of an ideal gas expands from 10 L and 0 C to 20 L and 100 C.
Taking CV = 20 JK-1mol-1, calculate U, W and Q for each of the

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following alternative steps for the whole process: (a) Isothermic and
reversible expansion at 0 C from 10 L to 20 L, followed by a constant
volume heating until 100 C and (b) Heating of 10 L at constant volume
until 100 C, followed by an isothermic and reversible expansion until
20 L.
17. A given quantity of an ideal gas occupies 1 dm3 at 1 atm and 300 K. It is
subject to the following transformations:
(a) Heated at constant pressure until attaining the volume of 2 dm3.
(b) Heated at constant volume of 2 dm3 until the pressure attains 2 atm.
(c) Cooled at constant pressure until the volume decreases to 1 dm3.
(d) Cooled at constant volume until the pressure attains 1 atm.
Calculate the sum for the 4 steps for (i) U, (ii) H, (iii) Q e (iv) W
18. A sample of 4.5 g of methane occupies 12.7 L at 310 K. Calculate the
work done by the gas when it expands isothermally against an external
constant pressure of 200 torr until the volume increases 3.3 L.
Calculate the work if the expansion was reversible.
19. Two moles of a gas suffers a reversible and isothermic expansion at
300 K from 1 dm3 to 10 dm3. Calculate the work considering (a) a
perfect gas (b) the gas obeys the van der Waals equation, with a = 1.36
atm dm6 mol-2 e b = 3.18310-2 dm3mol-1.
20. Write an expression for dV, considering V as a function of p and T.
Deduce an expression for dlnV in terms of the isobaric thermal
expansion coefficient and the isothermic compressibility coefficient.

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21. In order to project a given refrigerator we need to know the decrease
of temperature due to the adiabatic expansion of a refrigerant gas.
For a given Freon, JT = 1.2 K atm-1. What is the decrease of pressure
necessary to produce a decrease of temperature of 5.0 K?
22. Calculate the amount of heat we have to furnish to 500 g of O2 in
order to increase the room temperature from 298 K to 500 K, at
constant pressure, knowing that:
Cp (O2) = 7.16 + 110-3 T 0.40105/T2 cal K-1mol-1
23. Consider one mole of nitrogen (Cp = 29.4 JK-1mol-1) at 300 K and 1 atm
that suffers a reversible adiabatic compression until 400 K. Calculate:
(a) The final pressure
(b) Work, W, heat, Q and the internal energy change of the gas.
24. The following figure shows two reversible processes 1-2-3 and 1-4-3 in
which a mole of Freon changes from state T1, p1 to the state T2,p3. The
curves T1 and T2 are isotherms, and the vertical lines are isochoric (V
constant). Show that the heat involved in the two processes is
deferent, assuming that the Freon is a perfect gas.
V
1
2
3
4
T1
T2
p

Chemical Thermodynamics ______________________________

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