Gibbs Formation Energy of Silicon Carbide from Silicon and Graphite at 1700°C

Overview

This MIT OCW lecture uses a silicon carbide problem to illustrate how equilibrium thermodynamics applies to reacting systems with gases and condensed phases. The phase diagram reveals three solid phases (silicon, silicon carbide, carbon) and one liquid phase, with a peritectic reaction forming silicon carbide from a silicon-containing melt and graphite.

Key insights

• There is a gas phase present even when solids are visible, indicating a multi-phase equilibrium.
• The carbon chemical potential in silicon carbide equals that in graphite due to equilibrium with the vapor phase.
• The silicon partial pressure is effectively the total pressure because carbon vapor is negligible for these refractory materials.
• The Gibbs formation energy is computed from a delta mu expression and a simple pressure ratio, yielding a negative value near -1.56 kJ/mol.

Overview and Problem Setup

The instructor presents a practical thermodynamics problem that merges concepts from previous lectures on reacting systems with gases and condensed phases. In a vacuum oven, pieces of silicon carbide and graphite are placed, the system is evacuated to 0 Pa, then heated to 1700°C. Observations show both solids present and a total pressure of 4.0 Pa, implying the presence of a gas phase. The core question asks for the Gibbs free energy of formation of silicon carbide at 1700°C, defined as the Gibbs energy of SiC minus the energies of silicon and carbon in their reference states, scaled by the reaction stoichiometry.

"The key to solving such problems, is to ask who is in equilibrium with whom," - Instructor

The Thermodynamic Framework

Mathematically, the formation energy is written in terms of chemical potentials: ΔfG°(SiC) = μSiC° − μSi°(ref) − μC°(ref). Using the fact that μSiC can be split into μSi and μC within the SiC phase, and that carbon in SiC is in equilibrium with graphite, the carbon term cancels. The remaining piece is the silicon chemical potential relative to its reference state. This is obtained from the condition that silicon in SiC is in equilibrium with silicon vapor, so μSi in the gas equals μSi in SiC, which is μSi(ref) + RT ln(PSi/PSiSat). The ratio of actual to saturation pressure is the critical driver of ΔfG°.

"Carbon in silicon carbide is in equilibrium with carbon in graphite, which means the chemical potential of carbon in SiC equals that in graphite," - Instructor

Solution and Numerical Result

The total pressure is given as 4.0 Pa. The problem setup and literature data imply that the vapor phase is dominated by silicon rather than graphite, so the silicon partial pressure approximates the total pressure: PSi ≈ 4.0 Pa, while PSat(Si) at 1700°C is about 4.4 Pa. The carbon term cancels as explained, leaving the silicon term as the sole contributor to the Gibbs formation energy. The calculation yields ΔfG°(SiC) = RT ln(4.0/4.4) = RT ln(0.91). With T = 1700°C (1973 K) and R = 8.314 J mol−1 K−1, this gives ΔfG°(SiC) ≈ −1.56 × 10^3 J mol−1 (approximately −1.6 kJ/mol). The negative value indicates the formation of silicon carbide is thermodynamically favorable under these conditions.

"The silicon partial pressure is basically the same as the total pressure, in other words, the vapor is essentially pure silicon," - Instructor

Strategy and Takeaways

The instructor emphasizes a general strategy for solving thermodynamics problems: always identify the species that exchange mass and determine which phases are in chemical equilibrium with which other phases. In this Si–C system, the key equilibria involve the vapor phase and the condensed phases SiC and graphite, while solid silicon is not in equilibrium with the vapor in this setup because its vapor pressure is far below the measurement precision. This approach underpins a wide range of reacting systems with gases and condensed phases and illustrates how to translate observations into ΔG-based conclusions.

Quotes included above are paraphrased from the lecture and presented for emphasis in context.