Entropy Worksheet - Answer Key

 

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  1. What is a spontaneous process?

    A process that requires no external assistance to occur.

    2.  

     

  2. True or False:          Spontaneous reactions are fast.

    False.  Diamond     →  Graphite is spontaneous but it happens very slowly.  Spontaneity is no indication of speed.

    3.  

     

  3. What is entropy?

    Scientists wondered why some reactions were spontaneous.  Entropy is what they decided to call the reason for spontaneity.  Ultimately entropy is a measure of disorder related to positional probability.  How many ways something can placed in space.

    4.  

     

  4. Why do things tend toward disorder?

      5.  

    • There are more paths to disorder.

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    • Less energy required to be disordered.

     

     

  5. What state of matter has the highest entropy?

    The gaseous phase.

    6.  

     

  6. Determine the sign of ΔS:

      7.  

    • CaCO3(s)→CaO(s) + CO2(g)              +ΔS

      •  

    • N2(g) + 3H2(g)→ 2NH3(g)                  -ΔS

     

     

  7. What is an arrangement versus a microstate?

    An arrangement represents the number of ways a system can be set so that one arrangement is distinct from another.   A microstate, on the other hand, represents the number of ways that a particular arrangement can be reorganized so that it has the same overall “big picture” (macroscopic) appearance. 

    8.  

     

  8. There are multiple equations for entropy.  The first relates it to the number of microstates a system has:

    S = kb ln Ω

      9.  

    • Why is this not a very useful equation?

      Actual gas samples (with multiple molecules of gas) have far too many microstates to account for.

     

     

  9. What would the change in entropy be for the following system change?



               ΔS = - kbln3

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  10. What are the 3 additional equations for entropy, and in which case do you use each?

      11.  

    • Constant Temperature

      ΔST = nR ln (V2/V1) = qreversible

      •  

    • Constant Pressure

      ΔSP = nR ln (T2/T1)

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    • Constant Volume

      ΔSV = nR ln (T2/T1)

     

     

  11. One mole of an ideal gas with a volume of 1.0L and a pressure of 5.0 atm is allowed to expand isothermally into an evacuated bulb to give a total volume of 2.0L.  Calculate w and q. 

    q = 0

     

    w = 0

    12.  

     

  12. The molar heat capacities for CO2 at 298.0K are

    Cv=28.95 J/molK
    Cp=37.27 J/molK

    The molar entropy of CO2 gas at 298.0 K and 1.000 atm is 213.64 J/mol K

      13.  

    • Calculate the energy required to change the temperature of 1.000 mol of CO2 from 298.0K to 350.0K, both at constant volume and at constant pressure.

      qV = 1505.4 J

       

      qP = 1938.0 J          

      •  

    • Calculate the molar entropy of CO2 gas at 350.0K and 1.000 atm.

      S = 219.6 J/K

      •  

    • Calculate the molar entropy of CO2 gas at 350.K and 1.174 atm.

      S = 218.3 J/K                        

     

     

  13. Calculate the entropy change for a process in which 3.00 mol of liquid water at 0°C is combined with 1.00 mol of water at 100.0°C in a perfectly insulated container.  (Assume the molar heat capacity of water is constant at 75.3J/Kmol)

    ΔS = 2.9 J/K             

    14.  

     

  14. When changes in state happen under isobaric conditions.  What relationship is established?

    Because these processes are assumed to be occurring at constant pressure, ∆H = q.

    15.  

     

  15. What are the changes of state for each of the following?

      16.  

    • Fusion is when a solid → liquid

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    • Vaporization is when a liquid → gas.

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    • Sublimation is when a solid → gas

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    • Condensation is when a gas → liquid

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    • Freezing is when a liquid → solid

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    • Deposition is when a gas → solid

     

     

  16. The equation to find the change in entropy during a state change are:

      17.  

    • ΔSfusion =    ΔHfusion     .

       

      Tmelting point

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    • ΔSvaporization =    ΔHvaporization    

       

      Tboiling point

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    • ΔSsublimation =    ΔHsublimation

       

      Tsublimation point

     

     

  17. A sample of ice weighing 1.00 mol, initially at a temperature of -30.0°C, is heated to 140.0°C at a constant pressure of 1.00 atm.  Calculate q, w, ΔH, ΔE, and ΔS. For the process.  The molar heat capacities (Cp) for solid, liquid, and gaseous water are 37.5 J/mol K, 75.3 J/mol K, and  36.4 J/mol K respectively.  The enthalpies of fusion and vaporization are 6.01 kJ/mol and 40.7 kJ/mol, respectively.  Assume ideal gas behavior.

    q = ∆H =  56.8 kJ

     

    w = -3.43 kJ

     

    ΔE = 53.4 kJ

     

    ΔS = 162.7 J/K

    18.  

     

  18. For mercury, the enthalpy of vaporization is 58.51 kJ/mol and the entropy of vaporization is 92.92J/molK.  What is the normal boiling point?

    Tboiling point= 629 K

    19.  

     

  19. What do the following signs/values of ΔSuniv indicate?

      20.  

    • + :   spontaneous

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    • – :   non-spontaneous

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    • 0 :   at equilibrium

     

     

  20. What sign of ΔSsurroundings would be assigned for

      21.  

    • Exothermic:  + ∆Ssurroundings

      •  

    • Endothermic: - ∆Ssurroundings

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