Spontaneity of Solid Phase Change Two crystalline phases of white phosphorus are

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 phase of the solid (P4; density1.82 g/cm3) is always obtained when molten phosphorus crystallizes below the melting point (44.1 °C). However, when cooled below -76.9 °C, the phase spontaneously converts to the phase (P4; density1.88 g/cm3).

P4(s, ) --> P4(s, )

Indicate which of the following statements are true or false, with regard to the above process.

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

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

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

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

5. The phase has the less ordered crystalline structure.

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

Explanation / Answer

P4(s, ) --> P4(s, )

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

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

Since this reaction goes the other way around, S 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 S is negative.,therefore the above statement is False.

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

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

5. since S 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

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