Spontaneity of Solid Phase Change

Two crystalline phases of white phosphorus are known. Both contain P4 molecules, but the molecules are packed together in different ways. The α phase of the solid (P4; density≅1.82 g/cm3) is always obtained when molten phosphorus crystallizes below the melting point (44.1 °C). However, when cooled below -76.9 °C, the α phase spontaneously converts to the β phase (P4; density≅1.88 g/cm3).

P4(s, α) --> P4(s, β)
Indicate which of the following statements are true or false, with regard to the above process.

1. Below -76.9°C, the sign of ΔG for this process is negative.
2. The sign of ΔS for this process is negative.
3. At -76.9°C, ΔG for this process is less than zero.
4. At -76.9°C, the two solid phases cannot coexist.
5. The α phase has the more ordered crystalline structure.
6. The sign of ΔH for this process is negative.

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  1. Your thoughts/rationale please.

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  2. 1. i think is true because its spontaneous so dG is negative
    2. false I'm guessing false cuz if low-temperature dS is positive
    3. true
    4. I'm not sure about this I'm guessing false?
    5. I don't understand this one. I'm guessing false
    6. true

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  3. actually if its spontaneous low temp it would be negative for dS and dH so 2. i think true

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  4. I agree with 1.
    I agree with the second answer for 2. My thought is that the density is lower at very cold T. If density is lower it means d = m/v ; therefore, volume must be lower so the crystal is packed closer together so it is more ordered thus dS is - and statement is true.
    I agree with 3.
    I agree with your guess on 4. Remember that ice and liquid water co-exist at 0o C, the melting point of water. Same thing should apply at -76.9 in my opinion.
    I think your guess is right for 5 since the answer to 2 was that the b crystal @ -79.4 C was more compact and more ordered.
    I agree with 6. dG = dH - TdS. dS is - so -TdS is + so dH must be - for dG to be -.

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