Question

In a binary system of A and B, if a liquid of 30% A is co-existing with a solid of 75% A, for an overall composition of 40% A, the fraction of liquid is given by

• A. 0.78
• B. 0.87
• C. 0.22
• D. 0.27

Hint:

The lever rule is used in phase diagrams to determine the relative fractions of phases in a two-phase region.

Answer 1

The Correct Option is C

The fraction of liquid in a binary system is determined using the lever rule, which is given by the following formula: \[ f_L = \frac{C_S - C_0}{C_S - C_L} \] where: - \( C_0 = 40% \) (overall composition of A), - \( C_L = 30\% \) (composition of A in the liquid phase), - \( C_S = 75% \) (composition of A in the solid phase). Step 1: Applying the Lever Rule \[ f_L = \frac{75 - 40}{75 - 30} = \frac{35}{45} = 0.22 \] 

Step 2: Conclusion The fraction of the liquid phase in equilibrium is 0.22, making **option (C) 0.22** the correct answer.