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.
Your thoughts/rationale please.
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
actually if its spontaneous low temp it would be negative for dS and dH so 2. i think true
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 -.
To determine the truth of each statement, we need to understand the concepts of Gibbs free energy (ΔG), entropy (ΔS), enthalpy (ΔH), and phase transitions.
1. ΔG is related to the spontaneity of a process. If ΔG < 0, the process is spontaneous. At -76.9 °C, the α phase spontaneously converts to the β phase. So statement 1 is true.
2. ΔS is a measure of the disorder or randomness of a system. The β phase has a higher density (more ordered packing of P4 molecules) compared to the α phase. When a substance undergoes a phase transition from a less ordered phase to a more ordered phase, ΔS is negative. Therefore, statement 2 is false.
3. ΔG is the difference between the Gibbs free energy of the products and the reactants. At -76.9 °C, the α phase converts to the β phase spontaneously. In this case, the reaction is exothermic, so ΔH is negative. As ΔG = ΔH - TΔS (temperature multiplied by ΔS), if ΔH is negative and ΔS is negative, ΔG can be either positive or negative depending on the temperature (T) value. So statement 3 is false.
4. At -76.9 °C, the α phase spontaneously converts to the β phase. This means that both solid phases can coexist. Therefore, statement 4 is false.
5. The α phase has a lower density compared to the β phase. Since density is related to the packing and arrangement of molecules, the α phase has a less ordered or less dense structure compared to the β phase. So statement 5 is false.
6. As mentioned earlier, the α to β phase transition is exothermic, meaning it releases heat. In exothermic reactions, ΔH is negative. So statement 6 is true.
To summarize:
1. True
2. False
3. False
4. False
5. False
6. True