Question

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. At -76.9°C, ΔG for this process is less than zero.

2. The sign of ΔS for this process is positive.

3. Above -76.9°C, the sign of ΔG for this process is negative.

4. The sign of ΔH for this process is positive.

5. The α phase has the less ordered crystalline structure.

6. At -76.9°C, both solid phases can coexist indefinitely.

Answer 1

P4(s, α) --> P4(s, β)

1. As said in question, the these two forms are in equilibrium at -76.9°C . Therefore ΔG for this process should be zero.Hence the statement is false.

2. There is relatioship , ΔG = ΔH - TΔS
If ΔH and ΔS have different signs, ΔG can never be zero (considering that T is always positive). Thus ΔH and ΔS must have the same sign. Now consider the fact that when ΔS is positive, ΔG becomes more negative (more favourable) with increasing temperature.

Since this reaction goes the other way around, ΔS is negative. it means that the alpha phase has higher entropy than the beta phase; the alpha phase has the less ordered structure.

since the ΔS is negative.,therefore the above statement is False.

3. The process is spontaneous below -76.9 °C, ΔG must be negative. Therefore the above statement is False.

4.The sign for ΔH for this process is Negative as expalined in part # 2.Hence the statement is False.

5. since ΔS is negative. it means that the alpha phase has higher entropy than the beta phase; the alpha phase has the less ordered structure. Hence the statement is true

6. At -76.9 °C the two phase are in equilibrium. Like water/ice at exactly 0 °C.Hence the statement is true