Question 13.14.1: 100 g of silica and 100 g of graphite are placed in a rigid ...

The equilibrium attained in the vessel is best seen by constructing the phase stability diagram at 1773 K. In Example 2 in Section 13.4, an isothermal phase stability diagram was constructed using p_{CO}   and p_{CO_2}   as the independent variables. However, in the present problem, the equilibrium values of p_{CO}   and p_{SiO}   are required, and thus, the phase stability diagram at 1773 K will be constructed using p_{CO}   and p_{SiO}   as the independent variables. When CO and SiO exist at equilibrium, the activity of O in the CO equals the activity of O in the SiO. Thus, at a given partial pressure of CO, the activity of C in the CO is fixed, and at a given partial pressure of SiO the activity of Si is fixed. The condensed phases liquid silicon, solid SiC, solid  SiO_2 ,  and graphite can exist in the system, and thus, the number of possible equilibria involving two condensed phases and a gas phase is (4 × 3)/2 = 6. However, as was seen in Example 2 in Section 13.4, Si and C cannot exist in equilibrium with one another. The standard molar Gibbs free energies of formation of the four compounds of interest at 1773 K are

Each of the five equilibria involving two condensed phases and a gas phase must include CO and SiO.
1. Equilibrium among Si, SiO_2 ,  CO, and SiO

The equilibrium is

SiO_2+C=SiO+CO                 (i)

for which \Delta G^\circ _{1773  K}=82,900  J . Thus, for this equilibrium,

which is drawn as line 1 in Figure 13.33. Note that, as both gases occur on the same side of the equation describing the equilibrium, determination cannot be made as to which condensed phase is stable above line 1 and which condensed phase is stable below the line.

2. Equilibrium among  SiO_2 ,  SiC, SiO, and CO

The equilibrium is

2SiO_2+SiC=3SiO+CO                    (ii)

for which \Delta G^\circ _{1773  K}=243,590  J . This gives

which is drawn as line 2 in Figure 13.33. Again, a determination cannot be made as to which condensed phase is stable above the line and which is stable below the line.

3. Equilibrium among  SiO_2 ,  Si, and SiO

This equilibrium is independent of the pressure of CO and is written as

SiO_2+Si=2SiO                  (iii)

for which \Delta G^\circ _{1773  K}=103,700 . Thus,

which is drawn as line 3 in Figure 13.33. Again, indication of the stability of the condensed phases is not given.

4. Equilibrium among Si, SiC, SiO, and CO
The equilibrium is

2Si+CO=SiC+SiO                   (iv)

for which \Delta G^\circ _{1773  K}=36,190  J . Thus, for the equilibrium,

which is drawn as line 4. In this equilibrium, Si is stable relative to SiC above the line, and SiC is stable relative to Si below the line.

5. Equilibrium among SiC, C, SiO, and CO
The equilibrium is

SiC+CO=2C+SiO                 (v)

for which \Delta G^\circ _{1773  K}=77,790  J. Thus,

which is drawn as line 5 in Figure 13.33. As carbon exists at unit activity along this line, SiC is stable relative to graphite above the line and an unstable gas occurs belowthe line.

Inspection of Figure 13.33 shows that

1. SiC is stable relative to Si below the line bc .
2. SiC is stable relative to graphite above the line ed .

3. SiC or SiO_2   are stable below the line bd .

This identifies the area cbde as the field of stability of SiC. It is then seen that (1) Si is stable relative to SiC above the line cb , and (2) Si or SiO_2   is stable below the line ab . This identifies the area abc as the field of stability of liquid Si. Thus, (1) SiO_2   isstable relative to Si above the line ab , (2) SiO_2   is stable relative to SiC above the line bd , and (3) SiO_2   or graphite is stable above the line df .

Thus, the field of stability of SiO_2   lies above the line abdf , and the phase stability diagram is as shown in Figure 13.34. The phase stability diagram shows that graphite and quartz react with one another to produce SiC until the SiO_2 -graphite– SiC equilibrium is reached at the state A , which is the intersection of lines 1, 2, and 5 in

Figure 13.33. Simultaneous solution of the equations of any two of these lines gives the state A as

and

The mass of SiC produced and the mass of graphite consumed are obtained by conducting a mass balance on Si, C, and O. The atomic weights of C, O, and Si are, respectively, 12, 16, and 28.09. Thus, before any reactions begin, the vessel contains 100/60.09 = 1.6642 moles of SiO_2   and 100/12 = 8.3333 moles of C. Thus, the vessel contains 1.6642 moles of Si, 3.3283 moles of O, and 8.3333 moles of C. When reaction equilibrium is attained at 1773 K, the number of moles of CO in the gas phase is calculated as

n_{CO}=\frac{p_{CO}V}{RT}=\frac{0.844\times 20}{0.082057\times 1773} =0.1160  moles

and the number of moles of SiO in the gas phase is

n_{SiO}=\frac{4.315\times 10^{-3}\times 20}{0.082057\times 1773} =5.9310\times 10^{-4}  moles

Thus, the gas phase contains 0.1160 moles of C, 0.1166 moles of O, and 5.9318\times 10^{-4}  moles of Si. Consequently, at equilibrium the solid phases contain

1.6642-5.9318\times 10^{-4}=1.6636  moles of Si

3.3286 – 0.1166 = 3.2120 moles of O

and

8.3333  0.1160 = 8.2173 moles of C

All of the oxygen in the solids occurs in the silica, and thus, 3.2120/2 = 1.6060 moles of silicon in the solids occurs in the silica. The remaining 1.6636 – 1.6060 = 0.0576 moles of silicon in the solids occurs in the SiC. Thus, 0.0576 moles, or 0.0576 × 40.09 = 2.31 g of SiC are formed. The number of moles of graphite consumed equals the number of moles of SiC formed plus the number of moles of CO produced; that is, 0.0576 + 1160 = 0.1736 moles, or 0.1736 × 12 = 2.08 g.

The equilibrium partial pressures of CO_2  and O_2  which are, respectively, 5.9 \times 10^{–5}  and  1.3 \times 10^{–16}  atm, are small enough that the CO_2 and O_2 produced in the gas phase do not need to be included in the mass balance.