Thermodynamics Practice Test - Answer Key

 

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  1. 1 mol of a monatomic ideal gas undergoes the following change:

    PA=3.00atm, VA=15.0L     →PB=3.00atm, VB=55.0L → PC=6.00atm, VC=55.0L

    Calculate w, q, ∆E and ∆H for the process.

    w = – 12.2 kJ
    q = 55.5 kJ
    ΔH = 72.2 kJ
    ΔE = 43.3 kJ

    2.  

     

  2. Determine the mass of CO2 produced by burning enough C3H8 to produce 1.00 x 102 kJ of heat.

    C3H8(g) + 5O2(g)     → 3CO2(g) + 4H2O(g)               ∆Hrxn= - 2217 kJ

    5.96 g CO2

    3.  

     

  3. A piece of iron of mass 20.0g at 100.oC is placed in a vessel containing 50.7g of water at 22.0oC.  Calculate the final temperature of the water.  Assume no energy is lost to the surroundings.  (the heat capacity of iron and water are 0.45 J/goC and 4.184 J/goC, respectively)

    Tf = 25.2 oC

    4.  

     

  4. A 100 mL sample of water is placed in a coffee cup calorimeter.  When 1.0 g of an ionic solid is added, the temperature decreases from 21.5oC to 20.8oC as the solid dissolves.  Which of the following is true for the dissolving of the solid?
    • ∆H > 0
    • ∆H < 0
    • Not enough information.

     

     

  5. Determine the relationship between ∆E and ∆H for the following reaction

    2Na (s) + 2H2O (l)    → 2NaOH (aq) + H2 (g)

    ΔH > ΔE

    6.  

     

  6. For nitrogen gas at 25oC, Cv = 20.8 J/molK and Cp = 29.1 J/molK.  When a sample of nitrogen gas is heated at constant pressure, what fraction of energy is converted to heat?

    0.715

    7.  

     

  7. A 48 g sample of water vapor at 105oC is cooled to a temperature of -5oC at a constant pressure of 1 atm.  Calculate ∆S, ∆E, ∆H, q and w for this process.  The molar heat capacities for solid, liquid and gaseous water are 37.5 J/molK, 75.3 J/molK  and 36.4 J/molK, respectively.  ∆Hvap = 40.7 kJ/mol and ∆Hfus = 6.01 kJ/mol.

    q = ΔH = –145.3 kJ
    w = 8.36 kJ
    ΔE = –136.9 kJ
    ΔS = –414.43 J/K

    8.  

     

  8. What is the maximum amount of work that can be obtained when 0.100 mol Ar(g) in a volume of 1.00 L at 25oC is allowed to expand to 2.00 L?

    wmax = 171.7 J

    9.  

     

  9. 2 moles of an ideal monatomic gas initially at 3.00 atm and 15 L is expanded isothermally from its initial state to a final state (Vf = 25L, Pf = 1.80 atm) in 2 steps as shown below:

    Step 1:  Expand to 20 L at a pressure of 2.25 atm
    Step 2: Expand to 25L at a pressure of 1.80 atm

    Calculate the ratio of the work done in this two-step process to the theoretical maximum amount of work that could be done in a transformation from the initial state to the final state.

    0.88

    10.  

     

  10. Calculate ∆Hfus for gallium (in kJ/mol) using the following experimental data.  10.0 g of liquid gallium at 50.0 oC is placed in a coffee cup calorimeter that contains 50.0 g of water at 10.0oC.  Once the system comes to thermal equilibrium the temperature of the system is 14.1oC.  The heat capacity of calorimeter is 18.4 J/oC.  The heat capacity of both solid and liquid gallium is 0.37 J/goC and gallium melts at 29.8oC.

    ΔHfusion = 5.59 kJ/mol

    11.  

     

  11. In the isothermal reversible expansion or compression of 3.0 moles of an ideal gas at 298K and initial volume of 3.0L, 3.5 kJ of heat is added to the system.  What is the final volume of the gas?

    VF = 4.80 L

    12.  

     

  12. The dissociation of hydrogen

    H2 (g)    → 2H (g)­

      13.  

    • Is spontaneous at any temperature

      •  

    • Is spontaneous at high temperatures

      •  

    • Is spontaneous at low temperatures

      •  

    • Is independent of temperature

      •  

    • Never happens

     

     

  13. Consider the reaction:

    2 HCl(aq) + Ba(OH)2 (aq)    → BaCl2 (aq) + 2H2O(l)       ∆H = -118 kJ

    Calculate the heat when 200.0 mL of 0.500 M HCl is mixed with 300.0 mL of 0.200 M Ba(OH)2.  Assuming that the temperature of both solutions was initially 25.0oC and the final mixture has a mass of 500.0 g and a specific heat capacity of 4.18 J/goC, calculate the final temperature of the mixture.

    Tf = 27.8oC

    14.  

     

  14. Consider what you know about the following reaction

    H2O(g)    → H2O(l)

    At 25oC and 1 atm pressure determine:

      15.  

    • The sign of ∆H:       

       

      -ΔH

      •  

    • The sign of ∆S:       

       

      -ΔS

      •  

    • The sign of ∆G:       

       

      -ΔG.

      •  

    • Is the reaction exothermic or endothermic? 

       

      exothermic

      •  

    • Is the reaction spontaneous?    

       

      This reaction is spontaneous at 25oC.

      •  

    • Is the process reversible or irreversible?        

       

      Irreversible.

      •  

    • Is the reaction entropically or enthapically favorable?     

       

      Enthapically.

     

     

  15. At its melting point of 1132.2oC (at 1 atm) it takes 15.48 kJ to melt a mole of solid uranium.  What are the values of ∆H, ∆S, ∆G of the phase change at this melting point?

    ΔH = 15.48kJ
    ΔS = (15480J) / (1405.4K) = 11.01 J/K
    ΔG = 0

    16.  

     

  16. Determine the value of ∆G for an isothermal compression of one mole of an ideal gas.

      17.  

    • ∆G >0

      •  

    • ∆G <0

      •  

    • ∆G=0

     

     

  17. The boiling point of methanol is 64.7oC and the enthalpy of vaporization is 71.8kJ/mol.  What is ∆S when 2.15 moles of methanol are condensed?

    -457 J/K

    18.  

     

  18. The following exothermic reaction occurs at constant pressure

    2 Na (s)  +   2 H 2 O (l)       →  2  NaOH  (aq)  +    H2   (g)

      19.  

    • What is the sign of work?

       

      Negative

      •  

    • What is the sign of heat?

       

      Negative.

      •  

    • What is the sign of ∆H?

       

      Negative.

      •  

    • What is the sign of ∆E?

       

      Negative.

     

     

  19. The standard enthalpy of formation of H2O(l) at 25oC is -285.8 kJ/mol.  Calculate the ∆E for the following reaction at 25oC and 1 atm.

    H2O(l)    → H2(g) + ½ O2 (g)

    ΔE =282 kJ

    20.  

     

  20. Compounds A and B have the same mass, but compound B has 2 more atoms in its structure.  Which of the statements is true?

      21.  

    • Cv for compound A is greater than Cv for compound B.

      •  

    • Cv for compound A is greater than Cv for compound B.

      •  

    • Cv for compound A is less than Cv for compound B.

      •  

    • Cp for compound A is greater than Cp for compound B.

      •  

    • Cp for compound A is less than Cp for compound B.

      •  

    • A and C

      •  

    • B and D

     

     

  21. Given the following 2 reactions at 298 K and 1 atm, which of the following statements is true?

    1.  N2 (g) + O2 (g)    → 2NO (g)                                    ∆H1

     

    2.  NO (g) + ½ O2 (g)    → NO2 (g)                          ∆H2

      22.  

    • ∆Hf for NO2 (g) = ∆H2

      •  

    • ∆Hf for NO(g) = ∆H1

      •  

    • ∆H1 = ∆H2

      •  

    • ∆Hf for NO2 (g) = ∆H2 + ½ ∆H1

      •  

    • None of these

     

     

  22. A system is expanded isothermally in one step at a temperature of 200K, resulting in 200 J of work done.  Determine the relative value of ∆S.

      23.  

    • ∆S>1.00 J/K

      •  

    • ∆S<1.00 J/K

      •  

    • ∆S = 1.00 J/K

     

     

  23. A 1.00 g sample of rocket fuel hydrazine, N2H4, is burned in a bomb calorimeter containing 1200. g of water.  The temperature of the water and the bomb calorimeter rises from 24.62oC to 28.16oC.  Assuming the heat capacity of the empty bomb calorimeter is 837 J/oC, calculate the heat of combustion of 1 mol of hydrazine in the bomb calorimeter.  (The specific heat of water is 4.184 J/goC).

    ∆H = -665 kJ

    24.  

     

  24. The enthalpy of fusion of ice is 6.020 kJ/mol.  The heat capacity of liquid water is 75.4 J/moloC.  What is the smallest number of ice cubes at 0oC, each containing 1 mol of water, necessary to cool 500. g of liquid water initially at 20oC to 0oC?

    7 ice cubes

    25.  

     

  25. Given the equation

    S(S) + O2 (g)     → SO2 (g)                                 ∆H = -296 kJ

    Which of the following statements are true?

    I.          The reaction is exothermic.

     

    II.        When 0.500 mol of sulfur is reacted, 148 kJ of heat energy is
    released.

     

    III.       When 32.0g of sulfur is burned, 2.96 x 105 J of energy is released.

      26.  

    • All are true.

      •  

    • None are true.

      •  

    • I and II are true.

      •  

    • I and III are true.

      •  

    • Only II is true.

     

     

  26. For the reaction

    H2O (l)       →  H2O (g)

    ∆H is more positive that ∆E by 2.5 kJ/mol.  This quantity of energy can be considered to be

      27.  

    • The heat flow required to maintain a constant temperature.

      •  

    • The work done in pushing back the atmosphere.

      •  

    • The difference in the H-O bond energy in H2O(l) compared to H2O(g).

      •  

    • The value of ∆H itself.

      •  

    • None of the above

     

     

  27. A rigid insulated box contains 20.0 g of He (g) at 25.0oCand 1.00 atm in one compartment and 20.0 g of N2 (g) at 115oC and 2.00 atm in the other compartment.  These compartments are connected by a partition that transmits heat.  What is the final temperature in the box at thermal equilibrium?   (Cp (He) = 20.81 J/mol K; Cp (N2) = 29.01 J/mol K)

    Tf = 315.2K – 273.15 = 42.2oC

    28.  

     

  28. One mole of an ideal gas at 25oC is expanded isothermally and reversibly from 125.0 L to 250. L.  Which statement is correct?

      29.  

    • ΔSgas = 0

      •  

    • ΔSuniv = 0

      •  

    • ΔSsurr = 0

      •  

    • ΔSgas = ΔSsurr

      •  

    • More than one of the above is correct.

     

     

  29. A machine employs the reversible isothermal expansion of 1 mol of an ideal gas from 4.50 L to 15.0 L.  At 25oC, the machine performs 3.00 kJ of work.  What percent of the maximum possible work is the machine producing?

    Could not possibly produce 3000J of work as it is more than the theoretical maximum.

    30.  

     

  30. Calculate ΔG for the isothermal compression of 1 mol of an ideal monatomic gas from 1.4 atm to 5.6 atm at 24oC.

    ΔG = 3.40 kJ

    31.  

     

  31. Water expands when it freezes.  How much work does 100. g of water do when it freezes at 0oC and pushes back the metal wall of a pipe that exerts an opposing pressure of 1070 atm?  The densities of water and ice at 0oC are 1.00 g/cm3 and 0.92 g/cm3, respectively.

    w = -0.9 kJ

    32.  

     

  32. ΔSsurr is ____________ for exothermic reactions and ___________ for endothermic processes.

      33.  

    • Favorable, unfavorable

      •  

    • Unfavorable, favorable

      •  

    • Favorable, favorable

      •  

    • Unfavorable, unfavorable

      •  

    • Cannot tell

     

     

  33. A 100 mL sample of water is placed in a coffee cup calorimeter.  When 1.0g of an ionic solid is added, the temperature decreases from 21.5oC to 20.8oC as  the solid dissolves.  Which of the following is true for the dissolving of the solid?

      34.  

    • ΔH < 0

      •  

    • ΔSuniv > 0

      •  

    • ΔSsys <0

      •  

    • ΔSsurr > 0

      •  

    • None of these

     

     

  34. Assume that the enthalpy of fusion of ice is 6020 J/mol and does not vary appreciably over the temperature range from 270 – 290K.  If 1.20 mol of ice at 0oC is melted by the heat supplied from surroundings at 284K, what is the entropy change in the surroundings in J/K?

    ΔS = 26.5 J/K

    35.  

     

  35. For the vaporization of a liquid at a given pressure,

      36.  

    • ΔG is positive at all temperatures

      •  

    • ΔG is negative at al temperatures

      •  

    • ΔG is positive at low temperatures but negative at high temperatures (and zero at some temperature).

      •  

    • ΔG is positive at high temperatures but negative at low temperatures (and zero at some temperature).

     

     

  36. Given the following data, calculate the normal boiling point for formic acid (HCOOH)

    ΔHof (kJ/mol)                                   So (J/mol K)

     

    HCOOH (l)                               -410                                        130­

     

    HCOOH(g)                       -363                                         251

    Tmp = 388 K

    37.  

     

  37. Calculate the change in molar entropy of an ideal gas when it is compressed isothermally to one-third its initial volume.

    ∆S = –9.1 J/mol K

    38.  

     

  38. Calculate the change in entropy when the volume of 2.00 mol Ar(g) is increased from 5.00 L to 10.00 L while the temperature increases from 100.K to 300K.  Assume ideal behavior. Cv(Ar) = 12.47 J/molK

    ∆S = 38.9 J/K

    39.  

     

  39. Consider the combustion of propane

    C3H8 (g) + 5O2 (g)    → 3CO2 (g) + 4 H2O(l)                ∆H = -2221 kJ

    Assume that 1.3 x 108 J of heat is produced by the combustion of propane.  What mass of propane must be burned to furnish this amount of energy, assuming the heat transfer process is 60% efficient?

    4309.7 g C3H8

    40.  

     

  40. The boiling point of methanol is 64.7oC and the enthalpy of vaporization is 71.8kJ/mol.  What is ∆S when 2.15 moles of methanol are vaporized?

    456.9 J/K

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