Thermodynamics Problem (which is more stable)

[Jacobpm64]

My thermodynamics professor gives us the theory during lectures, and then we are given problems to try to solve for homework. I always have trouble applying the theory for the first couple problems. I have a few problems of this type, and once I get through one of them, I should be able to do the other ones. It's just a matter of trying to figure out how to bring the theory into application.

 

Anyway, here's the question and my thoughts (I haven't worked anything out like this before, so my thoughts may sound ridiculous, just let me know):

 

Two forms of solid phosphorus are white (a cubic crystal) and red (a triclinic crystal). The [math] \Delta H^{\circ} [/math] for the reaction: red -> white is 17.57 kJ/mol at 298.2 K and 1.00 atm. The absolute entropies for the two forms at 298.2 K are: white, [math] S^{\circ} [/math] = 41.09 J/K-mol and for red, [math] S^{\circ} [/math] = 22.80 J/K-mol. The densities of the two forms are : white, 2.342 g/mL and red, 1.823 g/mL.

 

a) Which form is more stable at 298 K?

For this question, don't we just look at the form with the greater absolute entropy? In this case, the white form is more stable because it has a greater absolute entropy.

 

b) Increasing pressure favors which form? Explain.

I'm guessing this has something to do with Helmholtz free energy since pressure is not constant (so we can't use Gibbs free energy). So if I look at the equation [math] \Delta A = \Delta E - T \Delta S [/math], I don't think I can get anything out of here. I don't know what equation to look at!

 

c) Increasing temperature favors which form? Explain.

I'm having the same problems as part (b). Even if I look at the Gibbs free energy [math] \Delta G = \Delta H - T \Delta S [/math], I still don't get anything (I don't think). Any help would be appreciated on how to think about this.

 

d) What is the percent of the red form present at 400 K and 1.00 atm?

Well, this is constant temperature and pressure, so, I will use Gibb's free energy.

[math] \Delta G = \Delta H - T \Delta S [/math]

Now, I can figure out [math] \Delta S [/math] by subtracting the two absolute entropies. I also have [math] \Delta H [/math] and T. So, plugging all this in, I get

[math] \Delta G = 17570 J/mol - 298.2 K * (41.09 J/K.mol - 22.80 J/K.mol) [/math]

[math] \Delta G = 12,115.922 J/mol [/math]

I have no idea what that tells me about the percent of the red form present though.

 

Any help on how to think about these would be greatly appreciated. Thanks!