Question

Maximum number of phases that can be in equilibrium for a 5-component system at constant temperature and pressure is ................... (in integer).

Hint:

Remember this shortcut for the Gibbs Phase Rule: - Standard system: \(F = C - P + 2\) - Constant Pressure OR Temperature: \(F = C - P + 1\) - Constant Pressure AND Temperature: \(F = C - P\) Since F cannot be negative, at constant T and P, the maximum number of phases is simply equal to the number of components.

Answer 1

Step 1: Understanding the Concept:
This question requires the application of the Gibbs Phase Rule. The rule relates the number of degrees of freedom (F) of a system in thermodynamic equilibrium with the number of components (C) and the number of phases (P).
Step 2: Key Formula or Approach:
The Gibbs Phase Rule is given by: \[ F = C - P + 2 \] where:
- \(F\) = Number of degrees of freedom (the number of intensive variables like temperature, pressure, concentration that can be independently varied).
- \(C\) = Number of components.
- \(P\) = Number of phases.
The question specifies that the system is at constant temperature and pressure. This means two of the intensive variables are fixed, which reduces the degrees of freedom. This leads to the condensed or reduced phase rule for this specific condition. The number of non-compositional variables that can be changed is \(F' = F - 2\), and since these are fixed, the remaining degrees of freedom must be \(F' \ge 0\).
A simpler way to think about it is that fixing temperature and pressure uses up the '2' in the standard phase rule. So, for this specific condition, the rule becomes: \[ F' = C - P \] For the system to be in equilibrium, the number of degrees of freedom cannot be negative, so \(F' \ge 0\). \[ C - P \ge 0 \implies C \ge P \] This means the number of phases (P) cannot exceed the number of components (C).
Step 3: Detailed Calculation:
Given:
- Number of components, \(C = 5\).
- Temperature is constant.
- Pressure is constant.
Using the relationship derived above, \(P \le C\), we can find the maximum number of phases. \[ P_{max} = C \] \[ P_{max} = 5 \] Step 4: Final Answer:
The maximum number of phases that can be in equilibrium is 5.
Step 5: Why This is Correct:
The solution correctly applies the Gibbs Phase Rule under the specified constraints of constant temperature and pressure. When these two variables are fixed, the maximum number of coexisting phases becomes equal to the number of components.