Question

Consider a two-phase mixture of ammonia and water in equilibrium. Can this mixture exist in two phases at the same temperature but at a different pressure?

Short answer

Answer: Yes, it is possible for the two-phase mixture of ammonia and water to exist in two phases at the same temperature but at different pressures.

Step-by-step solution

Define the problem

The problem asks whether a two-phase mixture of ammonia and water can have the same temperature but different pressures while remaining in equilibrium.

Examine the Phase Rule

The phase rule is a tool we can use to determine the number of independent intensive properties we can vary while maintaining phase equilibrium: F = C - P + 2 where F is the degrees of freedom, C is the number of components, and P is the number of phases. In this case, we have a binary mixture (C = 2) and two phases (P = 2).

Calculate Degrees of Freedom

Using the phase rule, we can determine the degrees of freedom for the given system: F = 2 - 2 + 2 = 2 Thus, there are two independent intensive properties that can be varied while maintaining equilibrium.

Define the Two Independent Intensive Properties

The two independent intensive properties for our system are typically chosen as temperature and pressure (T, P).

Conclusion

Since we have 2 degrees of freedom in our system, we can independently vary both temperature and pressure while still maintaining the two-phase equilibrium. In other words, it is indeed possible for the two-phase mixture of ammonia and water to exist in two phases at the same temperature but at different pressures.