The oxygen partial pressure at which a metal and its oxide coexist in equilibrium. It is found from ΔG° = RT ln pO₂; above it the metal is oxidized, and below it the oxide is reduced.
Japanese name: 平衡酸素分圧
Equilibrium oxygen partial pressure appears in 2 practice questions across 1 topic, including Thermodynamics of materials.
Field: Thermodynamics of materials
For 2M + O₂ → 2MO written per 1 mol of O₂, if the metal and oxide are pure solids, the equilibrium constant is 1/pO₂. From ΔG° = −RT ln K it follows that ΔG° = RT ln pO₂, so the equilibrium oxygen partial pressure is found from the standard value alone. For example, for a reaction with ΔG° = −400 kJ/mol, at 1200 K log pO₂ = −400000/(2.303 × 8.314 × 1200) ≈ −17.4, that is, about 4×10⁻¹⁸ bar. When the metal or oxide is in an alloy or solid solution and its activity is not 1, the activity is included in the equilibrium constant.
The equilibrium oxygen partial pressure is extremely low for metals whose oxides are stable. For example, at 1000°C the ΔG° of 4/3 Cr + O₂ → 2/3 Cr₂O₃ is about −530 kJ/mol, and the equilibrium oxygen partial pressure is of the order of 10⁻²² bar. Even in a vacuum of 1 Pa, by contrast, the oxygen partial pressure of the remaining air is as much as about 2×10⁻⁶ bar, far higher. So even in vacuum or in high-purity inert gas, the surfaces of alloys containing Cr, Al, Ti and similar elements oxidize when heated. In bright heat treatment of such metals, reducing gases such as hydrogen are used to lower the effective oxygen partial pressure of the atmosphere.
Lowering the oxygen partial pressure directly to something like 10⁻²⁰ bar is difficult, so in practice the oxygen partial pressure of an atmosphere is set by the ratio in mixed gases of H₂/H₂O or CO/CO₂. From the equilibrium 2H₂ + O₂ → 2H₂O, fixing the ratio of H₂O to H₂ fixes the oxygen partial pressure at that temperature. In industrial furnaces, the amount of water vapor in hydrogen is controlled through the dew point, and the lower the dew point, the lower the oxygen partial pressure. Which metals oxidize can be judged by comparing the oxygen partial pressure of the atmosphere with each metal's equilibrium oxygen partial pressure, and selective oxidation, in which only the easily oxidized components of an alloy oxidize at the surface, is treated with the same idea.
The oxygen partial pressure in atmospheres and molten metals can be measured with oxygen sensors using a zirconia solid electrolyte. When gases with oxygen partial pressures p₁ and p₂ are on the two sides of the zirconia, oxide ions move and an electromotive force E = (RT/4F) ln(p₁/p₂) arises, where F is the Faraday constant. At 1000 K each order of magnitude difference in oxygen partial pressure gives about 49.6 mV, so with air on the reference side even extremely low oxygen partial pressures can be measured as a voltage. Such sensors are used to control the air–fuel ratio from car exhaust, in probes that measure the oxygen content of molten steel in steelmaking, and to control the atmosphere of heat-treatment furnaces.
Answer: C. About 3×10⁻¹⁶ bar
At equilibrium ΔG = ΔG° + RT ln(1/pO₂) = 0, so ΔG° = RT ln pO₂. Then log pO₂ = ΔG°/(2.303RT) = −298000/(2.303 × 8.314 × 1000) ≈ −15.6, and pO₂ ≈ 3×10⁻¹⁶ bar. If the oxygen partial pressure of the atmosphere is higher than this, Ni is oxidized; if it is lower, NiO is reduced. About 1×10⁻³⁶ bar mistakes ΔG°/RT ≈ −35.8 for a common logarithm instead of a natural logarithm. About 2×10⁻⁸ bar takes ΔG° per mol of NiO (−149 kJ/mol), drops the exponent 1/2 on pO₂, and sets it equal to RT ln pO₂.
Answer: B. About 22 times
At equilibrium ΔG° = −RT ln K, with K = a(Cr₂O₃) to the power 2/3 ÷ (a(Cr) to the power 4/3 × pO₂). At the same temperature ΔG° and K are the same, so with a(Cr₂O₃) = 1, a(Cr) to the power 4/3 × pO₂ is constant. Therefore pO₂ = p₀ × 0.10 to the power −4/3 ≈ 21.5 p₀, about 22 times. Cr in the alloy becomes harder to oxidize to the extent that its activity is lowered, and a higher oxygen partial pressure is needed. About 10 times takes the coefficient 4/3 of Cr as 1, and about 100 times takes it as 2. In this way, the activities of alloying elements and the oxygen partial pressure let you judge which element is selectively oxidized at the surface of a stainless steel.
They refer to the same thing. In the reaction in which an oxide decomposes into metal and oxygen, the oxygen pressure at equilibrium is called the dissociation pressure of the oxide. If the oxygen partial pressure of the atmosphere is below it, the oxide decomposes (is reduced); if above, the metal oxidizes. The equilibrium pressure of the gas from decomposing carbonates and similar compounds is also called the dissociation pressure.
For most metal oxidation reactions ΔS° is negative, so as temperature rises ΔG° approaches 0 and the equilibrium oxygen partial pressure increases. In other words, oxides decompose more readily at higher temperature. For example, raising the temperature from 1000 K to 1200 K increases the equilibrium oxygen partial pressure of Ni/NiO by about four orders of magnitude.
Because the activity of the metal is less than 1, the oxygen partial pressure in equilibrium with the oxide is higher than for the pure metal. In other words, a metal in an alloy oxidizes less readily in the same atmosphere than the pure metal. Conversely, when the oxide is in a solid solution and its activity is small, the oxide forms more readily.
Activity Stainless steel Chemical potential Ellingham diagram Entropy of mixing Gibbs energy Regular solution Spinodal decomposition