Question

For a chemical system with 5 phases at the invariant point, the number of possible univariant reactions in pressure-temperature space is ____ (answer in integer).

Hint:

Use F = C - P + 2 with F = 0 to find the components, then count how many ways one phase can be dropped from the full set of five.

Answer 1

Correct Answer: 5

Step 1: Start from the phase rule.
The phase rule reads $F = C - P + 2$. At an invariant point both pressure and temperature are pinned down, so $F = 0$, which gives $P = C + 2$.

Step 2: Find the number of components.
With $P = 5$ phases at the invariant point, the components work out to $C = 5 - 2 = 3$, a three component system, the kind seen in classic petrologic diagrams.

Step 3: Think about what a univariant reaction is.
Moving away from the invariant point along a curve means one degree of freedom is allowed, $F = 1$. By the same phase rule logic, a curve with $F = 1$ can only involve $P - 1$, that is 4, of the phases at a time, since $1 = 3 - 4 + 2$ checks out. So every reaction curve is the full phase list with exactly one phase dropped.

Step 4: Count the drop-one-phase combinations.
Choosing which single phase to drop from 5 phases gives
\[ \binom{5}{4} = 5 \]
different combinations, and each combination is one univariant reaction, so there are 5 reaction curves meeting at the invariant point, matching the Schreinemakers rule that the number of univariant curves equals the number of phases at the invariant point.

Step 5: Conclude.
\[ \boxed{5} \]