Thermodynamics fundamentals - Part 2

Still working on thermodynamics problems....

 

We have the change in Gibbs free energy for the following reactions (every compound is a separate phase:

$Al_2O_3(s)+SiO_2(s)=Al_2SiO_5(s)$ $\Delta G^{\circ}=-8320-0.4T$ $J$

 

$3Al_2O_3(s) +2SiO_2(s)=Al_6Si_2O_{13}(s)$ $\Delta G^{\circ}=22770-31.8T$ $J$

a) Compute $\Delta G^{\circ}$ for the following reactions:

 

$3Al_2SiO_5=Al_6Si_2O_{13}+SiO_2$

 

$Al_6Si_2O_{13}=2Al_2SiO_5+Al_2O_3$

 

also compute the temperatures for which $\Delta G^{\circ}=0$

 

b) Plot the phase diagram for the system $SiO_2\cdot Al_2O_3$ between 45 and 65% mol percent $Al_2O_3$ at atmospheric pressure and the temperatures computed on a9)

c) For the reaction $3Al_2SiO_5=Al_6Si_2O_{13}+SiO_2$, $\Delta V>0$ ¿How would the coexistence temperature of these phases change if pressure increases?

The solution can be found on this Juypter notebook.

You can also check part one of this series here.

Thermodynamics fundamentals

 Recently I have been reading Principles of extractive metallurgy , I'm currently at the starting chapters, mostly thermodynamics review. I will create an entry for every chapter with a couple of solved problems. 

So for this week these are the exercises:

1) For the reaction $H_2\text{(g, 1 atm)}+\frac{1}{2}O_2\text{(g, 1 atm)}=H_2O\text{(l)}$, $\Delta H^{\circ}_{298}=-285.9$ kJ and $\Delta G^{\circ}_{298}=-238$ kJ.

a) Compute $\Delta S^{\circ}_{298}$

b) The reaction can proceed at 298 K and 1 atm in a reversible way, for example, in a fuel cell, or in a completely irreversible form, that is, by combustion with no other work besides volume. Compute for both cases the heat $q$ absorbed from the environment and, for case a), the work $w'$ done on the environment. Show that your results are in agreement with the second law of thermodynamics.

Now I will try using a jupyter notebook for storing the solutions, I think the possibility of combining text and code could be useful for problems that requires several calculations.

The solution can be found here.