Two crystalline phases of white phosphorus are known. Both contain P4 molecules,
ID: 637723 • Letter: T
Question
Two crystalline phases of white phosphorus are known. Both contain P4 molecules, but the molecules are packed together in different ways. The a phase of the solid (P4 density 1.82 g/cm2) is always obtained when molten phosphorus crystallizes below the melting point (44.1 °C). However, when cooled below -76.9 °C, the a phase spontaneously converts to the B phase (P4; density 1.88 g/cm3). P4(s, a)P4(s, B) Indicate which of the following statements are true or false, with regard to the above process. ?At-76.9°CAG for this process is less than zero. The a phase has the more ordered crystalline structure The sign of AS for this process is negative. At-76.9°C, both solid phases can coexist indefinitely The sign of ?? for this process is positive. Above-76.9°C, the sign of 0G for this process is positive cf Section 10.7 "Free Energy pp 368-71 in Zumdahl Chemical Principles 8th ed.Explanation / Answer
Statement 1 -
Equilibrium temperature T = - 76.9 °C
Gibbs free energy
?G = ?H - T?S
At equilibrium (T)
?G = 0
Statement 1 is false
Statement 2 -
Density of beta phase > density of alpha phase
Beta phase has the more ordered crystalline structure
Statement 2 is false
Statement 3 -
Since the beta phase has more ordered than alphas phase, there must be entropy loss. Entropy decreases as the order improves.
Entropy is negative for this process
Statement 3 Is true
Statement 4 -
Equilibrium temperature T = - 76.9 °C
?G = 0
Both solid phases can coexist indefinitely
Statement 4 is true
Statement 5 -
At equilibrium T = - 76.9 + 273 = 196.1 K
?H = T?S
?S for process < 0
Therefore
?H < 0
Statement 5 is false
Statement 6 -
T > (-76.9)°C
Let the temperature be T" > T
?G = ?H - T"?S
From the equillibrium relation
?G = T?S - T"?S = ?S(T - T")
?S < 0
(T - T") < 0
?G > 0
Statement 6 is true
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