ĐỀ THI VÀ ĐỀ ÔN MÔN HÓA LÝ 1

nd the volume of CO2 gas produced from 100 g of CaCO3 if the CO2 is at a pressure of 746 torr and a temperature of 301 K. Assume the gas to be ideal. 1.10. According to Dalton’s law of partial pressures, the pressure of a mixture of ideal gases is the sum of the partial pressures of the gases. The partial pressure of a gas is defined to be the pressure that would be exerted if that gas were alone in the volume occupied by the gas mixturend the volume of CO2 gas produced from 100 g of CaCO3 if the CO2 is at a pressure of 746 torr and a temperature of 301 K. Assume the gas to be ideal. 1.10. According to Dalton’s law of partial pressures, the pressure of a mixture of ideal gases is the sum of the partial pressures of the gases. The partial pressure of a gas is defined to be the pressure that would be exerted if that gas were alone in the volume occupied by the gas mixturend the volume of CO2 gas produced from 100 g of CaCO3 if the CO2 is at a pressure of 746 torr and a temperature of 301 K. Assume the gas to be ideal. 1.10. According to Dalton’s law of partial pressures, the pressure of a mixture of ideal gases is the sum of the partial pressures of the gases. The partial pressure of a gas is defined to be the pressure that would be exerted if that gas were alone in the volume occupied by the gas mixture

a A sample of oxygen gas is collected over water at 25◦C at a total pressure of 748.5 torr, with a partialpressure of water vapor equal to 23.8 torr If the volume of the collected gas is equal to 454 mL, find themass of the oxygen Assume the gas to be ideal.

b If the oxygen were produced by the decomposition of KClO3, find the mass of KClO3

1.11 The relative humidity is defined as the ratio of the partial pressure of water vapor to the pressure

of water vapor at equilibrium with the liquid at the same temperature The equilibrium pressure of water vapor at 25◦ C is 23.756 torr If the relative humidity is 49%, estimate the amount of water vapor

in moles contained in a room that is 8.0 m by 8.0 m and 3.0 m in height Calculate the mass of the water

1.23 Assuming that the coefficient of thermal expansion of gasoline s roughly equal to that of benzene,

estimate the fraction of your gasoline expense that could be saved by purchasing gasoline in the

morning instead of in the afternoon, assuming a temperature difference of 5◦C

Physical Chemistry 1 Assignments for Midterm (Term 181)

Summary by Dr Nguyen Quang Long (HCMUT, Faculty of Chemical Engineering)

Summary from Physical Chemistry, Robert G Mortimer, 3rd ed., Chapter 1

1.9 Find the volume of CO2 gas produced from 100 g of CaCO3 if the CO2 is at a pressure of 746 torr and a temperature of 301 K Assume the gas to be ideal

1.10 According to Dalton’s law of partial pressures, the pressure of a mixture of ideal gases is the sum

of the partial pressures of the gases The partial pressure of a gas is defined to be the pressure that would be exerted if that gas were alone in the volume occupied by the gas mixture

a Find the volume of 1 mol of ethanol at 10◦C and 1 atm

b Find the volume of 1mol of ethanol at 30◦C and 1 atm

1.33 *

a By differentiation, find an expression for the coefficient of thermal expansion of a gas obeying the van der Waals equation of state

b Find the value of the coefficient of thermal expansion of nitrogen gas at 298.15 K and Vm=24.4 L mol−1

1.36.* Write an expression for the isothermal compressibility of a nonideal gas obeying the Redlich–

Kwong equation of state

1.37 The experimental value of the compression factor Z=PVm/RT for hydrogen gas at T=273.15 K and Vm= 0.1497 L/mol−1 is 1.1336 Find the values of Z predicted by the van der Waals, Dieterici, and

Redlich–Kwong equations of state for these conditions Calculate the percent error for each

1.38 The parameters for the van der Waals equation of state for a mixture of gases can be

approximated by use of the mixing rules:

Where x1 and x2 are the mole fractions of the two substances and where a1,b1,a2, and b2 are the van der Waals parameters of the two substances The quantities a12 and b12 are defined by

a Using these mixing rules and the van der Waals equation of state, find the pressure of a mixture of 0.79 mol of N2 and 0.21 mol of O2 at 298.15 K and at a mean molar volume (defined as V/ntotal) of

0.00350 m3mol−1 Compare your answer with the pressure of an ideal gas under the same conditions

b Using the van der Waals equation of state, find the pressure of pure N2 at 298.15 K and at a molar volume of 0.00350 m3 mol−1

c Using the van der Waals equation of state, find the pressure of pure O2 at 298.15 K and at a molar volume of 0.00350 m3mol−1

1.43 The critical temperature of xenon is 289.73 K, and its critical pressure is 5.840 MPa (5.840×10 Pa)

a Find the values of the van der Waals constants a and b for xenon

b Find the value of the compression factor,Z, for xenon at a reduced temperature of 1.35 and a reduced pressure of 1.75

1.48 j Assume that the van der Waals equation of state can be used for a liquid Calculate the molar

volume of liquid water at 100◦C and 1 atm by the van der Waals equation of state (Get a numerical approximation to the solution of the cubic equation by a numerical method.) Compare your answer with the correct value, 18.798 cm3mol−1

Chapter 2 : First Law of Thermodynamics

Summary from Physical Chemistry, Robert G Mortimer, 3rd ed., Chapter 2

2.1 Calculate the work done on the surroundings if 1 mol of neon (assumed ideal) is heated

from 0◦C to 250◦C at a constant pressure of 1 atm

2.2 Calculate the work done on the surroundings if 100 g of water freezes at 0 ◦C and a

constant pressure of 1 atm The density of ice is 0.916 g cm-3 and that of liquid water is 1 g cm

−3

2.3 Calculate the work done on 100.0 g of benzene if it is pressurized reversibly from 1.00

atm to 50 atm at a constant temperature of 293.15 K

2.4 Calculate the work done on the surroundings if 1 kg of water is heated from 25 ◦C to 100◦C at a constant pressure of 1 atm

2.10 Calculate the amount of heat required to bring 1 mol of water from solid at 0◦C to gas at

100◦ C at a constant pressure of 1 atm Calculate w for the process

2.12 The normal boiling temperature of ethanol is 78.5◦C, and its molar enthalpy change of vaporization at this temperature is 40.3 kJ mol−1 Find q and w if 3 mol of ethanol are vaporized

at 78.5◦C and a constant pressure of 1 atm

2.14 Calculate q and w if 2 mol of helium is heated reversibly from a volume of 20 L and a

temperature of 300 K to a volume of 40 L and a temperature of 600 K The heating is done in such a way that the temperature remains proportional to the volume

2.15 The normal boiling temperature of ethanol is 78.5◦C, and its molar enthalpy change of vaporization at this temperature is 40.3 kJ mol−1 Find q and w if 3 mol of ethanol are reversibly vaporized at 78.5◦C and a constant pressure of 1 atm Neglect the volume of the liquid

compared with that of the vapor

2.21.* Consider the following three processes: (1) A sample of 2 mol of helium gas is

isothermally and reversibly expanded from a volume of 10 L and a temperature of 400 K to a volume of 40 L (2) The same sample is reversibly cooled at a constant volume of 10 L from 400

K to a temperature of 300 K, then expanded reversibly and isothermally to a volume of 40 L, and then heated reversibly from 300 K to 400 K at a constant volume of 40 L (3) The same sample is expanded irreversibly and isothermally at a temperature of 400 K from a volume of 10

L to a volume of 40 L with a constant external pressure of 1 atm Calculate ∆U,q, and w for each process

2.22 1 kg of water is pressurized isothermally at 298.15 K from a pressure of 1 atm to a

pressure of 10 atm Calculate w for this process State any assumptions

2.24 A sample of 3 mol of argon is heated from 25 ◦C to 100◦C, beginning at a pressure of 1 atm (101,325 Pa)

a Find q,w, and ∆U if the heating is done at constant volume

b Find q,w, and ∆U if the heating is done at constant pressure

2.25 Find the final pressure if 2 mol of nitrogen is expanded adiabatically and reversibly from a

volume of 20 L to a volume of 40 L, beginning at a pressure of 2.5 atm Assume nitrogen to be ideal with CV, m = 5R/2

2.26 A sample of 1 mol of neon gas is expanded from a volume of 5 L and a temperature of

400 K to a volume of 8 L

a Find the final temperature if the expansion is adiabatic and reversible Assume that the gas is ideal and that CV=3nR/2=constant

b Find ∆U,q, and w for the expansion of part a

c Find ∆U, q, w, and the final temperature if the expansion is adiabatic but at a constant

external pressure of 1 atm, starting from the same state as in part a and ending at the same

volume as in part a

d.Find ∆U, q, and w if the expansion is reversible and isothermal, starting at the same state as

in part a and ending at the same volume as in part a State any assumptions and

approximations

2.27 Find the final temperature and the final volume if 2 mol of nitrogen is expanded

adiabatically and reversibly from STP to a pressure of 0.6 atm Assume nitrogen to be ideal with

CV, m=5R/2

2.28 1 mol of carbon dioxide is expanded adiabatically and reversibly from 298.15 K and a

molar volume of 5 L mol−1 to a volume of 20 L mol −1

a Find the final temperature, assuming the gas to be ideal withCV, m=5R/2 = constant

b Find the final temperature, assuming the gas to be described by the van der Waals equation with CV, m=5R/2 = constant

2.29 A sample of 20 g of acetylene, C2H2, is expanded reversibly and adiabatically from a

temperature of 500 K and a volume of 25 L to a volume of 50 L Use the value of CV, m obtained from the value in Table A.8 for 500 K with the assumption that acetylene is an ideal gas

a Find the percent difference between this value of CV, m that you obtain and 5R/2

b Find the final temperature

c Find the values of ∆U, q, and w for the process

2.30

a A sample of 2 mol of argon gas is adiabatically and reversibly expanded from a temperature

of 453.15K and a volume of 15.0 L to a final temperature of 400.0 K Find the final volume, ∆U,

w, and q for the process Assume argon to be ideal and assume that CV, m= 3/2R

b Consider an irreversible adiabatic expansion with the same initial state and the same final volume, carried out with P(transferred)=1 atm Find the final temperature, ∆U, w, and q for this process

2.31

a Find the final temperature, ∆U, q, and w for the reversible adiabatic expansion of O2 gas from 373.15 K and a molar volume of 10 L to a molar volume of 20 L Assume the gas to be ideal with CV, m= 5R/2

b Repeat the calculation of part a for argon instead of oxygen Assume that CV, m=3R/2

c Explain in physical terms why your answers for parts a and b are as they are.

2.32

a 2 mol of O2 gas is compressed isothermally and reversibly from a pressure of 1 atm and atemperature of 100 ◦ C to a pressure of 3 atm Find ∆U,q,w, and ∆H for this process State anyassumptions or approximations Assume that the gas is ideal

b The same sample is compressed adiabatically and reversibly from a pressure of 1 atm and atemperature of 100.0◦ C to a pressure of 3 atm Find ∆U,q, and w for this process State anyassumptions or approximations Assume that CV, m=5RT /2 and that the gas is ideal

2.35 A sample of 1 mol of water vapor originally at 500 K and a volume of 10 L is expanded

reversibly and adiabatically to a volume of 20.0 L Assume that the water vapor obeys the van der Waals equation of state and that its heat capacity at constant volume is described by Eq (2.4-25) withα=22.2JK−1 mol−1 and β=10.3×10 −3 JK−2 mol−1

a Find the final temperature

b Find the value of w and ∆U

c Compare your values with those obtained if water vapor is assumed to be an ideal gas and itsheatcapacity at constant pressure is constant and equal to its value at 500 K

2.36

a A sample of 2 mol of H2 gas is reversibly and isothermally expanded from a volume of 20 L

to a volume of 50 L at a temperature of 300 K Find q,w, and ∆U for this process

b.The same sample of H2 gas is reversibly and adiabatically (without any transfer of heat)expanded from a volume of 20 L and a temperature of 300 K to a final volume of 50 L Find thefinal temperature Find q,w, and ∆U for this process

2.37 A sample of 2 mol of N2 gas is expanded from an initial pressure of 1 atm and an initial

temperature of 450 K to a pressure of 0.4 atm

a Find the final temperature if the expansion is adiabatic and reversible Assume thatCV=5nR/2, so that γ=7/5=1.400

b Find ∆U,q, and w for the expansion of part a

c Find ∆U,q,w, and the final temperature if the expansion is adiabatic but at a constant externalpressure of 0.400 atm, starting from the same state as in part a and ending at the same volume

as in part a

d Find ∆U,q, and w if the expansion is reversible and isothermal, ending at the same pressure

as in part a

2.40

a The Joule–Thomson coefficient of nitrogen gas at 50 atm and 0◦C equals 044 K atm −1.Estimate the final temperature if nitrogen gas is expanded through a porous plug from a

pressure of 60.0 atm to a pressure of 1.00 atm at 0◦C

b Estimate the value of (∂Hm/∂P)T for nitrogen gas at 50 atm and 0◦C State any assumptions

2.41 A sample of 3.00 mol of argon is heated from 25.00◦C to 100.00◦C, beginning at a

pressure of 1 atm (101,325 Pa)

a Find q,w,∆U, and ∆H if the heating is done at constant volume

b Find q,w,∆U, and ∆H if the heating is done at constant pressure

2.42

a Calculate ∆H and ∆U for heating 1 mol of argon from 100 K to 300 K at a constant pressure

of 1.00 atm State any assumptions

b Calculate ∆H and ∆U for heating 1 mol of argon from 100 K to 300 K at a constant volume of30.6 L

c Explain the differences between the results of parts a and b

2.44 Supercooled steam is condensed irreversibly but at a constant pressure of 1 atm and a

constant temperature of 96.5 ◦C Find the molar enthalpy change State any assumptions and approximations

2.45 The enthalpy change of fusion of mercury is 2331 J mol−1 Find ∆H for converting 100.0

g of solid mercury at−75.0◦C to liquid mercury at 25.0◦C at a constant pressure of 1.000 atm Assume that the heat capacities are constant and equal to their values in Table A.6 of the appendix

2.46 Find ∆H if 100.0 g of supercooled liquid mercury at −50.0 ◦ C freezes irreversibly at constant temperature and a constant pressure of 1.000 atm The enthalpy change of fusion at the normal melting temperature is 2331 J mol −1 Assume that the heat capacities are constant and equal to their values in Table A.6 of the appendix

2.47 Find the value of q and the value of ∆H if 2 mol of solid water (ice) at−10◦C is turned into liquid water at 80◦C, with the process at a constant pressure of 1 atm Assume that the heat capacities are constant and equal to their values in Table A.6 of the appendix

Summary from Thermodynamics - An engineering approach, Yunus A Çengel, 5th ed., Chapter 3

Summary from other sources

1 Is it true that it takes more energy to vaporize 1 kg of saturated liquid water at 100°C than itwould at 120°C?

2 Which process requires more energy: completely vaporizing 1 kg of saturated liquid water at 1atm pressure or completely vaporizing 1 kg of saturated liquid water at 8 atm pressure?

3 Complete this table for H2O:

4 Complete this table for refrigerant-134a:

Chapter 3 - Second Law of Thermodynamics

Summary from Physical Chemistry, Robert G Mortimer, 3rd ed., Chapter 3

Summary from Thermodynamics - An engineering approach, Yunus A Çengel, 5th ed., Chapter 6 & 12

6-48 A house that was heated by electric resistance heaters

consumed 1200 kWh of electric energy in a winter month If

this house were heated instead by a heat pump that has an

average COP of 2.4 , determine how much money the home

owner would have saved that month Assume a price of

8.5¢/kWh for electricity.

6-71 A Carnot heat engine operates between a source at

1 000 K and a sink at 300 K If the heat engine is supplied

with heat at a rate of 800 kJ/min, determine (a) the thermal

efficiency and (b) the power output of this heat engine.

Answers: (a) 70 percen t , (b) 9 33 kW

6-72 A Carnot heat engine receives 650 kJ of heat from a

source of unknown temperature and rejects 250 kJ of it to a

s i nk at 24 ° C Determine (a) the tempe r at u re of the source and

(b) the t h erm a l efficiency of the heat engine.

12-60 Determine the enthalpy change and the entropy

change of nitrogen per unit mole as it undergoes a change of

state from 225 Kand 6 MPa to 320 Kand 12 MPa, (a) by

assuming ideal-gas behavior and (b) by accounting for the

deviation from ideal-gas behavior through the use of general­

ized charts.

12-61 Dete1mine the enthalpy change and the entropy

change of CO2 per unit mass as it undergoes a change of state

from 250 Kand 7 MPa to 280 Kand 12 MPa, (a) by assum­

ing ideal-gas behavior and (b) by accounting for the deviation

from ideal-gas behavior.

12-62 Methane is compressed adiabatically by a steady-flow

compressor from 2 MPa and - 10 ° C to 10 MPa and l l 0 ° C at a

rate of 0.55 kg/s Using the generalized charts , determine the

required power input to the compressor Answer: 133 kW

12-75 Show that

Cv = -T C�),G�t and C - T -(aP) (av)

-P - aT , aT p

12-76 Estimate the c" of nitrogen at 300 kPa and 400 K,

using (a) the relation in the above problem and (b) its defini­

tion Compare your results to the value listed in Table A-2b.

12-77 Steam is throttled from 4.5 MPa and 300 ° C to 2.5

MPa Estimate the temperature change of the steam during

this process and the average Joule-Thomson coefficient.

Answers: - 26 3 ° C , 13 1 ° C /M Pa

12-78 A rigid tank contains 1.2 m 3 of argon at -100 ° C and

1 MPa Heat is now transferred to argon until the temperature

in the tank rises to 0 ° C Using the generalized charts, deter­

mine (a) the mass of the argon in the tank, (b) the final pres­

sure, and (c) the heat transfer.

Answers: (a) 35 1 kg, (b) 1531 k Pa , (c) 1251 kJ

6-76 In tropical climates, the water near the surface of the ocean remains warm throughout the year as a result of solar energy absorption In the deeper parts of the ocean, however, the water remains at a relatively low temperature since the sun's rays cannot penetrate very far It is proposed to take advantage of this temperature difference and construct a power plant that will absorb heat from the warm water near the surface and reject the waste heat to the cold water a few hundred meters below Determine the maximum thermal effi­ ciency of such a plant if the water temperatures at the two respective locations are 24 and 3 ° C

24°c OCEAN

3°c

Boi er

Pump

Turb i ne