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Spontaneous Reactions

  1. May 21, 2012 #1
    1. The problem statement, all variables and given/known data
    At 2600 K, ΔG° = 775 kJ for the vaporization of boron carbide:
    [itex]B_{4}C (s) ⇔ 4 B (g) + C (s)[/itex]

    Find ΔG and determine if the process is spontaneous if the reaction vessel contains 4.00 mol of [itex]B_{4}C (s)[/itex], 0.400 mol of [itex]C (s)[/itex], and [itex] B (g)[/itex] at a partial pressure of 1.0 x 10^-5 atm. At this temperature, R T = 21.6 kJ

    2. The attempt at a solution

    I first tried to find the reaction quotient but quickly realized that they did not give me the volume for this vessel. Thus, I just plugged everything into the reaction quotient (products/reactants) and got Q = 1*10^-21.

    Then I plugged that into the ΔG = -RT*ln(Q) equation:

    ΔG = -RT*ln(Q)
    ΔG = -(21.6 J * 1000)*ln(1*10^-21)
    ΔG = 1.044*10^6 J = 1044 kJ

    The answer on the back of the book says that ΔG is in fact -270 kJ; how is this the answer? What mistake did I do in my calculations?
     
  2. jcsd
  3. May 21, 2012 #2

    Borek

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    Staff: Mentor

    Please write the reaction quotient.
     
  4. May 21, 2012 #3
    [itex]Q=\frac{(pB)^4*[C]}{[B_{4}C]}[/itex]
     
  5. May 21, 2012 #4

    Borek

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    Staff: Mentor

    What do you know about solids in this context?
     
  6. May 21, 2012 #5
    Um all I can figure out is that the solids are within a closed vessel and that the temperature also appears to be 2600 K since 21.6kJ/8.314 = 2600. The only issue regarding the solid is that I don't know what the volume is, which is prohibiting me from finding the concentration mol/L.

    The only other thing is that maybe I have the wrong idea of how concentration of a solid works?
     
  7. May 21, 2012 #6

    Borek

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    Staff: Mentor

    Activity of solids is assumed to be 1, so they are not present in the reaction quotient.
     
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