Phase Equilibria and Phase Rule MCQ Quiz in தமிழ் - Objective Question with Answer for Phase Equilibria and Phase Rule - இலவச PDF ஐப் பதிவிறக்கவும்

CONCEPT:

Pressure vs Volume Plot for Various Phase Transitions

• The pressure vs volume (P vs V) plot shows the relationship between the pressure exerted by a system and its corresponding volume during different phase transitions.
• The slope (magnitude) of the P vs V plot reflects how much the pressure changes when the volume changes, with steeper slopes indicating greater pressure changes per unit volume change.
• The slopes differ across phase transitions due to the compressibility and nature of the phases involved:
  • Solid-Vapor transition: This involves significant changes in volume as the solid transitions directly to the vapor phase. Since solids are highly incompressible, the pressure changes rapidly with small volume changes, resulting in a steep slope.
  • Liquid-Vapor transition: This involves the vaporization of a liquid, which usually leads to large volume changes as the liquid becomes vapor. The liquid is more compressible than solids, and the volume change is significant, leading to a moderate slope.
  • Solid-Liquid transition: This transition involves the melting of a solid into a liquid, where both phases are relatively incompressible. The pressure change is small because the volume change between the solid and liquid phases is minimal, resulting in a gentle slope.

EXPLANATION:

• Solid-Vapor Transition (e.g., Sublimation): When a solid transitions directly to a vapor (sublimation), there is a significant decrease in density. Since solids are nearly incompressible, a small change in volume results in a large pressure change, leading to the highest slope among the phase transitions.
• Liquid-Vapor Transition (e.g., Boiling): During vaporization, a liquid changes to vapor. Liquids are more compressible than solids, so the pressure change is less drastic for the same volume change compared to a solid-vapor transition. Thus, the slope is moderate compared to solid-vapor transitions.
• Solid-Liquid Transition (e.g., Melting): The solid-liquid transition occurs when a solid melts into a liquid. Both solids and liquids are relatively incompressible, and the volume change during this transition is typically small. As a result, the pressure changes less dramatically, leading to the smallest slope.

CALCULATION OF SLOPE MAGNITUDE:

• Solid-Vapor: Since solids have low compressibility and vapors occupy much larger volumes, the slope is the steepest. The change in pressure per unit change in volume is large.
• Liquid-Vapor: The liquid phase has higher compressibility than solids, and vaporization causes large volume increases. However, the pressure changes are moderate, resulting in a slope lower than solid-vapor but higher than solid-liquid.
• Solid-Liquid: Since both phases are almost incompressible and the volume change is minimal, the slope is the gentlest, meaning the pressure changes very little with volume change.

CONCLUSION:

• The correct option is: Option 3: solid-vapor > liquid-vapor > solid-liquid

Concept:

The lever rule is a technique used in phase diagrams to calculate the relative amounts of each phase present in a two-phase region. It is particularly useful in determining the fraction of components in different phases at equilibrium in binary systems.

• Definition: The lever rule is a graphical tool that uses the composition axis of a phase diagram to determine the relative amounts of two coexisting phases in a two-phase region.

• Application: The rule applies to a binary system where two phases are present, and it helps determine the quantity of each phase based on their compositions.

• Principle: The fraction of each phase is inversely proportional to the distance from the overall composition to the phase boundaries on the composition axis.

• Formula: The lever rule formula for the fraction of the phenol-rich phase is:

  • , where X_phenol represents mole fractions.

Explanation: 

• Using the lever rule, the fraction of the phenol-rich phase in the two-phase region can be calculated as:

  • ​

• Substitute the values:

  • ​

• Solving for

Conclusion:

The total amount of phenol and water present in the phenol-rich phase at 40°C is approximately 8.2 moles

Solution (2)

When liquid water presents in equilibrium with ice then the degree of freedom may be calculated by following formula,

P + F = C + 2

where, P = number of phases, F = degree of freedom

and C = number of components

Here, P = 2 and C = 1 

∴ F = C + 2 - P = 1 + 2 - 2

F = 1(one degree of freedom) 

Concept:

Phase Diagram

A phase diagram is a graphical representation of the various phases of a substance or mixture of substances that coexist in thermodynamic equilibrium, and undergo phase changes under different working conditions, such as temperature, pressure, or volume.

Explanation:

Therefore, the correct option is 4.

CONCEPT:

Phase Diagram and Lever Rule

• A phase diagram is used to determine the composition of phases at equilibrium at a given temperature and the composition of the mixture.
• In this case, the system consists of a mixture of hexane and nitrobenzene, where the α-phase is hexane-rich, and the β-phase is nitrobenzene-rich.
• To calculate the number of moles of hexane in the α-phase, we use the lever rule, which helps find the amount of each phase when a mixture lies in the two-phase region.
• The lever rule is applied using the formula:
  where  and are the compositions of nitrobenzene in the β-phase and α-phase, respectively, and is the overall composition of nitrobenzene in the mixture.

EXPLANATION:

• From the phase diagram, at 300 K:
  • (nitrobenzene composition in α-phase) ≈ 0.3
  • (nitrobenzene composition in β-phase) ≈ 0.8
  • (overall nitrobenzene composition in the mixture) = 0.4
• Now, applying the lever rule:
• Thus, 80% of the mixture is in the α-phase.
• To find the number of moles of hexane in the α-phase:
  • Total moles of hexane = 0.6 mol
  • Moles of hexane in the α-phase =  mol
• Since the α-phase is hexane-rich, the fraction of hexane in the α-phase will be slightly higher. From the options, the closest match for the number of moles of hexane in the α-phase is 0.56 mol.

CONCLUSION:

• The correct answer is: Option 1: 0.56 mol

CONCEPT:

Phase Diagram of Fe₂Cl₃ - Water System

• A phase diagram depicts the stable phases of a mixture as a function of temperature and composition.
• Eutectic Point:
  • The point at which a mixture of substances melts or solidifies at a single, fixed temperature, which is lower than the melting points of the individual components.
  • In a eutectic system, multiple eutectic points can exist depending on the complexity of the mixture.
• For the Fe₂Cl₃ (ferric chloride) - water system, the number of eutectic points indicates the different compositions where eutectic mixtures form.

EXPLANATION:

Ferric chloride forms four different stable crystalline hydrates (new compounds) having congruent melting points i.e., these are stable upto their melting points. The names of four hydrates of ferric chloride formed, their
composition and the corresponding melting points are summarised as under:

The formation of these compounds (hydrates) increases the number of areas
and eutectic points in the phase diagram. However, it does not introduce any
new feature. If we consider each newly formed compound as a new
component the significance of the different areas, lines, and points can be
easily understood. A schematic phase diagram of the ferric chloride-water
system.

The correct option for the number of eutectics in the phase diagram of Fe₂Cl₃ - water system is 5.

CONCEPT:

Phase Rule and Reduced Phase Rule

• Gibbs' Phase Rule states the relationship between the number of phases (P), components (C), and degrees of freedom (F) in a thermodynamic system. The general form of the phase rule is given by:
• F = C - P + 2 where:
  • F = Degrees of freedom (number of independent variables like temperature, pressure, or composition that can be changed without changing the number of phases in equilibrium)
  • C = Number of components
  • P = Number of phases

EXPLANATION:

For a two-component system (binary system), we have C = 2 . Applying this to the Gibbs' Phase Rule, we get:

F = C - P + 2

F = 2 - P + 2

F = 4 - P

Thus, for a two-component system, the reduced phase rule equation simplifies to:

F = 4 - P

The correct option is 2) F = 4 - P.

Concept:

The temperature dependence of the vapor pressures of solid and liquid phases of a substance are often given by empirical relationships where the logarithm of the vapor pressure is linear with respect to the inverse of the temperature. At the triple point, the vapor pressures of all three phases (solid, liquid, and gas) are equal.

• Triple Point: The temperature at which a substance can coexist in solid, liquid, and gas phases in equilibrium.

• Vapor Pressure Equations: Given the equations for solid and liquid phases:

Explanation:

• At the triple point, the vapor pressures of solid and liquid phases are equal. Therefore, we equate the given expressions:

Conclusion:

The temperature of the triple point of A is 200 K. Therefore, the correct answer is option 1.

- Correct Answer Explanation:
- The process involves cooling a substance at a constant pressure from a point labeled 'X'. Without the specific phase diagram, we can infer from the correct answer that point 'X' must be in the gas phase region, above the boiling point of the substance at the given pressure.
- As the substance is cooled to 30undefinedC at constant pressure, it first condenses from gas to liquid once it crosses the boiling point at that pressure. This transition is the gas to liquid phase change.
- Continuing to cool, when the substance reaches its freezing point at the given pressure, it transitions from liquid to solid. This is the liquid to solid phase change.
- The entire process involves moving through three phases: starting as a gas, condensing to a liquid, and then freezing into a solid. Hence, the process correctly described is "Changes from gas to liquid to solid".

- Overview of Incorrect Options:
- Option 1: Changes from gas to liquid
- This option only accounts for the initial phase change (gas to liquid) and ignores the subsequent cooling that leads to the liquid to solid transition.
- Option 3: Remains as liquid
- This option incorrectly suggests that the substance, once cooled to 30undefinedC, stays in the liquid phase throughout, not accounting for the solidification phase at or below the freezing point.
- Option 4: Remains as solid
- This option is incorrect as it suggests the substance was in the solid phase to begin with and remains so, which contradicts the given process of cooling from a point 'X' that suggests starting from a gas phase and going through phase changes.
- Without the visual phase diagram, the explanation relies on understanding that substances can transition through different phases (solid, liquid, gas) depending on temperature and pressure conditions, and the given scenario describes cooling a substance through two phase transitions: gas to liquid, then liquid to solid, at constant pressure.

According to Le-Chatelier's principle, the increase of pressure on a chemical equilibrium shift in that direction in which the number of gaseous molecules decreases and vice-versa thus in this reaction, increase in pressure favours the backward reaction.