a. Write a balanced reaction for equilibrium among the magnesian endmembers pyro
ID: 229008 • Letter: A
Question
a. Write a balanced reaction for equilibrium among the magnesian endmembers pyrope garnet (Mg3Al2Si3O12), spinel (MgAl2O4), forsterite (Mg2SiO4), and enstatite (MgSiO3). (Hint to get started on the balancing: Al bearing minerals will have to be on opposite sides on the equation.)
b. Given the experimental data below, calculate G for your balanced reaction. Is the forward or reverse reaction favored based on your answer?
c. Now calculate S for your balanced reaction using the experimental data given below.
d.In lecture, we saw that one form of the Gibbs Free Energy equation is:
G = H – TS
Knowing G and S for the reaction from the previous questions, you will be able to calculate H for the reaction at 1000ºK. You may have to convert units to make sure things cancel (remember 1kJ equals 1000 J).
e. From the experimental data given below, estimate the equilibrium temperature (Teq) at surface conditions of P=0.1 MPa. So use G = H – TS from the previous question (d) and recall that G=0 at equilibrium. Comment on the significance of your result.
f. Calculate V for the reaction at 298ºK using the experimental data below.
g. Now estimate the equilibrium pressure (Peq) at T = 1000ºK using a new form of the Gibbs Free Energy equation: GPT=0=G + PV. If the reaction did come to equilibrium at that P and T, what would be the effect of increasing pressure? Why?
h. We will want to plot an approximate P-T stability diagram for your reaction. Use the Clapeyron Equation to figure out the slope of the equilibrium line. Plot your equilibrium line on a graph of P vs T. Use the answer from (g) to plot one point on your equilibrium curve. Make sure you label the stability fields on either side of the equilibrium line with the appropriate assemblage based on your written reaction. Recall that high pressure favors the lower volume side of the reaction.
Pyrope Spinel Forsterite Enstatite Gºf, 1000ºK, kJ/mole -5067 -1879 -1772 -1256 Sº, 1000ºK, J/deg-mole 730.8 264.5 277.2 192.9 V, 298ºK, J/MPa 113.17 39.71 43.79 31.47Explanation / Answer
a. Mg3Al2Si3O12 + Mg2SiO4 -> MgAl2O4 + 4MgSiO3
b.now, delGof= delGoproduct - delGoreactant
delGof= (-1879-1256) - (-5067-1772)
=-3135 - (-6839)
= -3135 + 6839
= + 3704KJ/mole
since del Gof is positivethe reaction is favoured in the opposite side. reverse reaction will be favoured.
c. del S = del Sproduct - del Sreactant
= (264.5+192.9) - (730.8+277.2)
= 457.4 - 1008
del S = -550.6 J/deg-mole
d. delG= DelH - T*delS, del S in KJ/deg-mole = -0.5506
3704 = delH - 1000*(-0.5506)
delH= -3153.4 KJ
e. since delG =0 , delH=Teq* delS
Teq= delH/delS
= -3153.4 / -0.5506
Teq = 5727.21 deg
f. del V= Vproduct- Vreactant
= (39.71+ 31.47) - (113.17+43.79)
=71.18- 156.96
delV = -85.78 J/MPa
ignore the negative sign. it is due to the fact that this reaction is not favourable forward. You just need to note the change in volume!
g. at equlibirum del GPT=0, so delG= Peq * delV
Peq= delG/delV
= 3704/0.08578 ( convert delV to KJ/MPa )
= 43180 MPa
if the pressure is increased further the equlibrium will be disturbed and the reaction will move in the opposite direction.
h. sorry my mobile phone clickes pictures above 3MB and chegg picture limit is less than 2MB so i cannot upload the graph
i can tell you that in the clayperon equation -delH/R is the slope when ln P is y and 1/T is x. you can find the equation readily on google or any of your books.
hope this is helful :)
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