Question

For a binary system at constant pressure, there are two types of invariant reactions:
(i) \( \alpha \leftrightarrow \beta + \gamma \)
(ii) \( \alpha + \beta \leftrightarrow \gamma \)
Analogously, how many different types of invariant reactions may exist under variable temperature and pressure, for a binary system?

• A. 1
• B. 2
• C. 3
• D. 4

Hint:

Always apply Gibbs phase rule carefully—whether pressure is constant or variable changes the degree of freedom and the number of invariant reactions.

Answer 1

The Correct Option is C

For a binary system at constant pressure, the degrees of freedom are given by Gibbs phase rule: \[ F = C - P + 1 \] An invariant reaction corresponds to \( F = 0 \). Two such reactions are possible at constant pressure.
When both temperature and pressure are variable, the Gibbs phase rule becomes: \[ F = C - P + 2 \] For an invariant reaction, \( F = 0 \), so: \[ 0 = 2 - P + 2 \] This allows for three distinct invariant reactions in a binary system. Thus, the total number of invariant reactions under variable temperature and pressure is 3.