Phase Equilibria and Phase Rule MCQ Quiz - Objective Question with Answer for Phase Equilibria and Phase Rule - Download Free PDF

The Answer is  Degrees of freedom

Concept:-

• Degrees of Freedom (DOF): Degrees of freedom refer to the number of variables that can be independently varied without changing the number of phases in equilibrium. In the context of the phase rule, DOF indicates the system's flexibility to adjust certain parameters.
• Components: Components are the minimum number of independently variable chemical entities needed to describe the composition of each phase/system. Understanding components is crucial for applying the phase rule to different systems.
• Phase Equilibrium: Phase equilibrium involves the coexistence of different phases in a system under specific conditions. The phase rule helps analyze and predict the behavior of phases in equilibrium based on the given components and phases.
• Phase Diagrams: Phase diagrams visually represent the equilibrium conditions of a system, showing how different phases coexist at varying temperatures and pressures. The phase rule is often applied in the interpretation of phase diagrams.

Explanation:-

The phase rule equation, F = C - P + 2, represents the number of degrees of freedom (F) in a system at equilibrium. 

• F (Degrees of Freedom): This is the number of intensive variables (e.g., temperature, pressure, concentration) that can be independently varied without altering the number of phases in equilibrium.
• C (Number of Components): This is the minimum number of independently variable chemical entities needed to describe the composition of each phase/system.
• P (Number of Phases): This is the number of distinct, homogenous, and mechanically separable parts in the system that coexist under certain conditions.

Concept:

• Phase: A phase is a distinct form of matter with uniform physical and chemical properties, such as solid, liquid, gas, or plasma.
  • Example: Ice, water, and steam are three different phases of H₂O.
• Component: Components are the chemically distinct substances in a system, representing the minimum number of independent chemical species needed to define the system's composition.
  • Example: A saltwater solution has two components: salt (NaCl) and water (H₂O).
• Formula for component:
  • C=N-E
  • where:
    • N= number of constituents
    • E= number of equation

Key Difference:

• Phases are distinct physical forms (e.g., solid, liquid) within a system.
• Components are the basic chemical constituents involved in forming those phases.

Explanation:

\(MgCO_3(s)\leftrightharpoons MgO(s)+CO_2(g)\)

This reaction has 3 phases (2 solid and 1 gas).

For component:

• C = N-E   (N=3, two solids and one gas so 3 constituents)
• ​C = 3-1
• C = 2

Therefore, the correct option is 1.

CONCEPT:

Triple Point of Water

• The triple point of a substance is the unique set of conditions (temperature and pressure) at which all three phases—solid, liquid, and gas—can coexist in equilibrium.
• For water, the triple point is a well-known thermodynamic reference point that is used in the calibration of thermometers and the definition of the Kelvin scale.

EXPLANATION:

​

CONCLUSION:

So, the correct option is 2.

Concept:

The enthalpy of sublimation (ΔH_sub) can be determined using the Clausius-Clapeyron equation, which describes the relationship between the pressure, temperature, and the enthalpy change during a phase transition. For the sublimation process (solid to vapor), the Clausius-Clapeyron equation is given by:

• Slope of Solid-Vapor Curve: The given slope is \(\frac{dP}{dT} \)
• Volume Change of Vapor: The change in volume of vapor (( Delta V )) 
• Temperature: The given temperature (( T )) is 150 K.

Explanation:

• Step-by-Step Calculation:

• Substitute the given values into the Clausius-Clapeyron equation:

  • \( \frac{dP}{dT} = \frac{Δ H_{\text{sub}}}{T Δ V} \)

  • \(4.4 \text{ Pa K}^{-1} = \frac{Δ H_{\text{sub}}}{150 \text{ K} \times 47.8 \text{ m}^3} \)

• Rearrange to solve for (ΔH_sub):

  • \(Δ H_{\text{sub}} = 4.4 \text{ Pa K}^{-1} \times 150 \text{ K} \times 47.8 \text{ m}^3 \)

  • \(Δ H_{\text{sub}} = 31692 \text{ Pa m}^3 \)

• Convert the units from Pa m(³) to kJ (since 1 Pa m(³) = 1 J and 1000 J = 1 kJ):

  • \(Δ H_{\text{sub}} = 31692 \text{ J} = 31692 \times 10^{-3} \text {kJ} = 31.692 \text{ kJ mol}^{-1} \)

Conclusion:

The enthalpy of sublimation at 150 K is 31.6 kJ mol^-1.

CONCEPT:

Phase Equilibria

dP/dT = ΔH/TΔV

• Phase equilibria describe the conditions under which different phases (solid, liquid, gas) coexist in equilibrium.
• The triple point is a unique temperature and pressure where all three phases coexist in equilibrium.
• The Clapeyron equation relates the slope of a phase boundary to the enthalpy and entropy changes during a phase transition:
• The critical point is the end of the liquid-vapor equilibrium line, where distinct liquid and gas phases cease to exist.
• Below the eutectic temperature, a system typically exists in a multi-phase region (e.g., solid-solid or solid-liquid mixture).

EXPLANATION:

• Option 1: Correct. At the triple point, all three phases (solid, liquid, gas) coexist in thermodynamic equilibrium.
• Option 2: Incorrect. Below the eutectic temperature, the system exists as a mixture of phases, not as a single-phase region.
• Option 3: Correct. The Clapeyron equation quantitatively describes the phase boundary between any two phases in terms of thermodynamic parameters.
• Option 4: Correct. The critical point represents the temperature and pressure above which the liquid and vapor phases become indistinguishable.

Correct Options: 1, 3 and 4.

Concept:

• Phase of a system is defined as the physical state that can be separated from other part of system mechanically.
• Components are distinct constituents that are independently variable.
• In a system, minimum number of independently variable factors that can be used to define the system gives degree of freedom (F). The factors can be pressure, temperature , or composition/concentration.

Degree of Freedom(F) = C- P+ 2

C is the number of components of system

and P is the number of phase

Explanation:

For given system, number of components, C = 2

number of phase, P = 3

Degree of freedom, F should be

\(F= C-P+2 \)

\(F=2-3+2 \)

\(F=1 \)

Conclusion:

Hence, the degree of freedom of a two component system with its  3 phases in simultaneous equilibrium is 1

Concept:

According to Gibb's Phase rule,

\(F=C-P+2\)

Where,

F is the the number of degrees of freedom, C is the number of chemically independent constituents of the system, and P is the number of phases.

Explanation:

We know that, \(F=C-P+2 \)

\(P=C+2-F \)

Given,

For one component system, \(C=1\)

Now we get, \(P=1+2-F=3-F\) 

For P to be maximum, F should be equal to zero.

Hence, \(P=3-F=3-0=3\)

Conclusion: -

The maximum number of phases that can be simultaneously in equilibrium for a one component system is 3. So the option 3 is correct.

Concept: 

The Clausius–Clapeyron relation characterizes a discontinuous phase transition between two phases of matter of a single constituent. On a pressure-temperature (P–T) diagram, the line separating the two phases is known as the coexistence curve. The Clausius–Clapeyron relation gives the slope of the tangents to this curve. The Clausius–Clapeyron relation can be used to find the relationship between pressure and temperature along the phase.

Explanation: 

The given phase diagram is as follows: 

We know that the melting point is the temperature at which liquid changes into solid or vice-versa.

As the diagram depicts by the dotted line between solid and liquid as the pressure increases the melting point is decreasing. 

Thus, based on the given diagram the statement: 'Melting point increases with pressure ', is wrong.

Hence, the correct option is (1).

Conclusion:-

So, the INCORRECT statement is Melting point increases with pressure

Concept:

• A phase diagram is a representation of states of a substance according to varied temperature and pressure.
• Generally, Temperature is kept on the X-axis and Pressure is kept on the y axis.
• When we cross the curves of the phase diagram, we go from one phase to another phase.
• Phase diagrams basically demonstrate the effect of temperature and pressure on the state of matter.
• At the boundary of the phase curve, the matter exists in equilibrium between two-state.
• At the triple point denoted by Tc, matter exists in all three states, solid, liquid and gas.

Explanation:

• The phase diagram of carbon dioxide is given below:
  • ​
• Extrapolating the graph, we see that:

• From the graph, we see that below Tc, it does not exist in a liquid state so, ​below Tc, it does not exist in the liquid state is a true statement.
• From the graph, we see that if we increase the temperature above the triple point, it exists in a liquid state when pressure is increased.
• So, above Tc, it does not exist in the liquid state is a false statement.
• At the critical temperature, all three phases exist, so at Tc, it can exist in all three phases is a correct statement.
• From the graph we see that if we increase the pressure after T1, solid-state does exist, so, the statement above T1, it does not exist in solid-state is a false statement.

Therefore, 1 and 2 are the correct option.

Explanation:-

• If the temperature is constant at 200 K  and We increase the pressure from 1 atm to 50 atm CO₂ gas will remain solid it will not liquify in any condition therefore, Statement 1 is Incorrect.

Important Points

• The liquefication of a gas depends upon its critical temperature.
• If the force of attraction between the particles is high then its intermolecular spaces will be less resulting easy liquefication process.
• The liquefication process for gases is completed in two steps - cooling and compression.

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:
  • \( \text{fraction of α-phase} = \frac{X_{\beta} - X_{\text{total}}}{X_{\beta} - X_{\alpha}} \)
  where \(X_{\beta} \) and \(X_{\alpha} \)are the compositions of nitrobenzene in the β-phase and α-phase, respectively, and \(X_{\text{total}}\) is the overall composition of nitrobenzene in the mixture.

EXPLANATION:

• From the phase diagram, at 300 K:
  • \(X_{\alpha} \) (nitrobenzene composition in α-phase) ≈ 0.3
  • \(X_{\beta} \) (nitrobenzene composition in β-phase) ≈ 0.8
  • \(X_{\text{total}} \) (overall nitrobenzene composition in the mixture) = 0.4
• Now, applying the lever rule:
  • \( \text{fraction of α-phase} = \frac{0.8 - 0.4}{0.8 - 0.3} = \frac{0.4}{0.5} = 0.8 \)
• 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 = \( 0.6 \times 0.8 = 0.48 \) 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 of a system is defined as the physical state that can be separated from other part of system mechanically.
• Components are distinct constituents that are independently variable.
• In a system, minimum number of independently variable factors that can be used to define the system gives degree of freedom (F). The factors can be pressure, temperature , or composition/concentration.

Degree of Freedom(F) = C- P+ 2

C is the number of components of system

and P is the number of phase

Explanation:

For given system, number of components, C = 2

number of phase, P = 3

Degree of freedom, F should be

\(F= C-P+2 \)

\(F=2-3+2 \)

\(F=1 \)

Conclusion:

Hence, the degree of freedom of a two component system with its  3 phases in simultaneous equilibrium is 1

The correct answer is Solidifies directly

Concept:-

• Phase Diagram: A phase diagram is a graphical representation of pressure-temperature conditions under which various phases of a substance are in equilibrium. It delineates the relative areas of stability for gas, liquid, and solid phases, and shows the points of phase transitions, such as melting (solid to liquid), boiling (liquid to gas), sublimation (solid to gas), deposition/desublimation (gas to solid), etc.
• Triple Point: The triple point of a substance is a particular condition (specific pressure and temperature) at which all three phases - solid, liquid, and gas - coexist in equilibrium. Every substance has a unique triple point. For example, the triple point of water is exactly 273.16 Kelvin (0.01 Celsius) and 611.657 pascals of pressure.
• Deposition/Desublimation: This is the phase transition from the gas phase directly to the solid phase without passing through an intermediate liquid phase. It normally occurs at conditions of low temperature and pressure, such as under conditions less than the triple point in a phase diagram.
• Sublimation: It is the direct transition of a substance from the solid to the gaseous state, bypassing the liquid state. Dry ice, or solid carbon dioxide, is a common example of a substance that undergoes sublimation at room temperature and pressure.​​​​​

Explanation:-

• Substances can exist in three states: solid, liquid, and gas. These are determined by the intensity of molecular interactions and the thermal energy of the molecules, both of which are influenced by external conditions such as temperature and pressure.
• A phase diagram is used to represent the states of matter of a substance under different temperature and pressure conditions. This diagram highlights the equilibrium boundaries between the different states of matter.
• One important feature of a phase diagram is the triple point, which is the specific set of conditions (at a particular temperature and pressure) where all three states of matter (solid, liquid, and gas) are in equilibrium - meaning they co-exist without changing into each other.
• Now, when the pressure conditions are less than the triple point pressure, interesting things happen. Under this condition, the liquid state of the substance does not exist. This means there's no equilibrium boundary between the gas and liquid phases, which therefore makes the gas unable to transition into a liquid even if we cool it down.
• Instead, when we cool the gas under this pressure condition, it transforms directly into a solid. This process is known as desublimation or deposition, which is the transition from the gaseous state directly to the solid state, skipping the liquid state.

conclusion:-

So ,the vapour of a pure substance, when cooled under a pressure less than its triple-piont pressure Solidifies directly

Concept:

According to Gibb's Phase rule,

\(F=C-P+2\)

Where,

F is the the number of degrees of freedom, C is the number of chemically independent constituents of the system, and P is the number of phases.

Explanation:

We know that, \(F=C-P+2 \)

\(P=C+2-F \)

Given,

For one component system, \(C=1\)

Now we get, \(P=1+2-F=3-F\) 

For P to be maximum, F should be equal to zero.

Hence, \(P=3-F=3-0=3\)

Conclusion: -

The maximum number of phases that can be simultaneously in equilibrium for a one component system is 3. So the option 3 is correct.