Understanding Degrees of Freedom

This question requires calculating the degrees of freedom ($F$) for the chemical system $M (s) + CO_2 (g) \rightleftharpoons MO (s) + CO (g)$ using Gibbs Phase Rule.

The Gibbs Phase Rule is stated as: $F = C - P + 2$ where:

• $F$ represents the degrees of freedom.
• $C$ is the number of components.
• $P$ is the number of phases.

Determining Number of Phases (P)

Identify the distinct phases present in the equilibrium system:

• Phase 1: Solid $M (s)$.
• Phase 2: Solid $MO (s)$.
• Phase 3: Gaseous mixture of $CO_2 (g)$ and $CO (g)$. A mixture of gases typically constitutes a single phase in phase rule calculations.

Therefore, the total number of phases is $P = 3$.

Determining Number of Components (C)

The number of components ($C$) is the minimum number of constituents needed to define the system.

For the reaction $M (s) + CO_2 (g) \rightleftharpoons MO (s) + CO (g)$, the elemental constituents involved are M, C, and O.

Specifying the amounts of these three elements allows us to define the composition of all phases present ($M$, $MO$, $CO_2$, $CO$).

Therefore, the number of components is $C = 3$.

Calculating Degrees of Freedom (F)

Apply the Gibbs Phase Rule using the determined values of $C$ and $P$:

$F = C - P + 2$

$F = 3 - 3 + 2$

$F = 2$

Result

The number of degrees of freedom for the given reacting system is 2.