An Example of a Gaseous Reaction with Pure Condensed Phase

Consider the reduction of SiO$_2$to Si by heating it at $P=1$ atm. At what temperature will the reduction take place and what will be the pressure of CO (gas) if the reaction takes place at $740^\circ$C?

The pertinent reaction is

$$\input{equations/26-1A}$$ (33-14)

The following reactions are tabulated:

Notice that:

1. The expressions for the molar free energies of reactions take the form: $\Delta \ensuremath{\overline{G}} = \Delta\ensuremath{\overline{H}} - T \Delta \ensuremath{\overline{S}}$ where $\Delta \ensuremath{\overline{H}}$ and $\Delta \ensuremath{\overline{S}}$ are treated as independent of $T$ (This is approximately true if the molar heat capacities are nearly the same.).

2. The appearance of one mole of gas is associated with an entropy production of about 175 $\frac{\mbox{J}}{{}^\circ\mbox{K}}$.

The reaction of interest can be written as:

$$-3 \times ($$First Reaction$$) + ($$Second Reaction$$) + 2 \times ($$Third Reaction$$)$$

or

$$\input{equations/26-2A}$$ (33-15)

so that

$$\input{equations/26-2A-bis}$$ (33-16)

Since $\ensuremath{\overline{\Delta G_{Rx}}} < 0$ at all $T$, the reaction will favor the products.

The total pressure is given by

$$\input{equations/26-3A}$$ (33-17)

Question: Why is $P_{\mbox{O}_2}$ included? Because one can't balance a reaction between carbon monoxide and carbon dioxide without it.

For

$$\input{equations/26-3B}$$ (33-18)

So

$$\input{equations/26-3C}$$ (33-19)

for

$$\input{equations/26-3D}$$ (33-20)

$$\input{equations/26-3E}$$ (33-21)

We conclude that $P_{\mbox{O}_2}$is small compared to $P_{\mbox{CO}}$ and $P_{\mbox{CO}_2}$

$$\input{equations/26-3F}$$ (33-22)

Therefore:

$$\input{equations/26-4A}$$ (33-23)

$$\input{equations/26-4B}$$ (33-24)

Question: Will the fraction of CO go up or down with temperature?