A. Spontaneity of Solid Phase Change Two crystalline phases of white phosphorus

Question

A. 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).

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

true false  The sign of S for this process is positive.
true false  The phase has the less ordered crystalline structure.
true false  At -76.9°C, both solid phases can coexist indefinitely.
true false  The sign of H for this process is negative.
true false  At -76.9°C, G for this process is greater than zero.
true false  Below -76.9°C, the sign of G for this process is negative.

B. Free Energy of Reaction -- Temperature Dependence

The above reaction is used in the industrial production of hydrogen cyanide. Consider the relevant thermodynamic data from the appendices of your text. (The tabulated values H°fand S° are for 25°C. For the purposes of this question assume that H° and S° are invariant with temperature. This is not actually true but would generally be a reasonable approximation over "small" temperature ranges.)

a) Calculate H° for this equation.

-939.8 kJ

b) Calculate S° for this equation.

165 J/K

c) Calculate G° at 787°C, for this equation.

Cant figure this one out!

d) Are the following statements about this process True or False?

The high temperature required for this process is needed for thermodynamic reasons.
The equilibrium position for this reaction is further to the right at higher temperatures.
This reaction is endothermic at 1000°C.
Thermodynamically, this reaction is spontaneous at any temperature.
At temperatures significantly lower than 1000°C this reaction is spontaneous.

Explanation / Answer

c) DG0 = DH0-TDS0

    T = 787 c = 787+273.15 = 1060.15 k

DG0 = -939.8 - (1060.15*165*10^-3)

      = -1114.72 kj

as DH = -ve, DS = +ve, the reaction is spontaneous at all temperatures.

d)

The high temperature required for this process is needed for thermodynamic reasons.(False)

The equilibrium position for this reaction is further to the right at higher temperatures.(false)

This reaction is endothermic at 1000°C. (false)

Thermodynamically, this reaction is spontaneous at any temperature. (True)

At temperatures significantly lower than 1000°C this reaction is spontaneous. (false)

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