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A sample of a substance undergoes a first-order phase transition from a liquid to a solid state. The heat capacity of the substance is given by: Cp = a + bT + cT², where a, b, and c are constants, and T is the temperature. The enthalpy of fusion of the substance is ΔHf = 200 kJ/mol, and its melting point is 300 K. At a pressure of 1 atm, the substance begins to freeze at a temperature of 310 K, and the process is complete at a temperature of 300 K. Calculate the entropy change (ΔS) and the Gibbs free energy change (ΔG) for the freezing process.
- a)ΔS = 0.57 kJ/(mol.K), ΔG= -0.2 kJ/mol.
- b)ΔS = 0.67 kJ/(mol.K), ΔG= -0.1 kJ/mol.
- c)ΔS = 0.87 kJ/(mol.K), ΔG= -0.2 kJ/mol.
- d)ΔS = 0.67 kJ/(mol.K), ΔG= -0.2 kJ/mol.
Correct answer is option 'B'. Can you explain this answer?
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A sample of a substance undergoes a first-order phase transition from ...
In order to determine the specific heat capacity of the substance during the phase transition from liquid to solid, we need to know the values of the constants a, b, and c. Without this information, we cannot calculate the specific heat capacity accurately.
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A sample of a substance undergoes a first-order phase transition from ...
Concept:
Phase transition is a phenomenon where a substance undergoes a change in its physical state from one phase to another, under specific conditions of temperature, pressure, and/or composition. It is a common occurrence in nature and plays a significant role in thermodynamics.
Types of Phase Transitions: There are several types of phase transitions, including:
Phase transition is a phenomenon where a substance undergoes a change in its physical state from one phase to another, under specific conditions of temperature, pressure, and/or composition. It is a common occurrence in nature and plays a significant role in thermodynamics.
Types of Phase Transitions: There are several types of phase transitions, including:
- Solid-liquid transition (melting)
- Liquid-gas transition (vaporization)
- Solid-gas transition (sublimation)
- Liquid-liquid transition (miscibility/immiscibility)
- Solid-solid transition (polymorphism)
Explanation:
Heat capacity of substance: Cp = a + bT + cT² ,
Enthalpy of fusion: ΔHf = 200 kJ/mol, Melting point: 300 K, Pressure: 1 atm, Freezing temperature range: 310 K to 300 K.
WE assume that the process is a first-order phase transition.
The entropy change (ΔS) for the freezing process can be calculated using the following formula:
ΔS = ΔHf / Tm
where ΔHf is the enthalpy of fusion, and Tm is the melting point of the substance.
Substituting the given values, we get:
ΔS = 200 kJ/mol / 300 K, ΔS = 0.667 kJ/(mol.K)
Next, we can calculate the Gibbs free energy change (ΔG) using the formula:
ΔG = ΔH - TΔS
where ΔH is the enthalpy change of the freezing process.
To calculate ΔH, we need to first calculate the heat absorbed by the substance during the freezing process. This can be done by integrating the heat capacity equation over the freezing temperature range:
ΔH = ∫Cp dT
Since the process is a first-order phase transition, there is no change in volume, and the pressure is constant. Therefore, we can use the following equation to calculate ΔH:
ΔH = ΔHf = nΔHf
where n is the number of moles of the substance.
To calculate n, we can use the following formula:
n = m / M
where m is the mass of the substance, and M is the molar mass.
Let's assume that we have 1 mole of the substance, so n = 1.
The mass of the substance can be calculated using the density of the liquid and solid phases:
ρsolid = ρliquid = ρ
where ρ is the density of the substance.
The mass of the substance is then given by:
m = ρV
where V is the volume of the substance.
At the melting point, the substance has a volume of:
V = Vm = M/ρ = M/ρsolid = M/ρliquid
where Vm is the molar volume of the substance.
At the freezing point, the substance has a volume of:
Vf = Vm(1 - ΔV)
where ΔV is the change in volume during the freezing process. Since the substance undergoes a first-order phase transition, the change in volume is negligible. Therefore, we can assume that Vf ≈ Vm.
Now we can calculate the heat absorbed by the substance during the freezing process:
ΔH = ΔHf = nΔHf = 200 kJ/mol
Finally, we can calculate the Gibbs free energy change:
ΔG = ΔH - TΔS
ΔG= (200 - (300 X 0.667)) = (200-200.1) kJ/mol = -0.1 kJ/mol.
Heat capacity of substance: Cp = a + bT + cT² ,
Enthalpy of fusion: ΔHf = 200 kJ/mol, Melting point: 300 K, Pressure: 1 atm, Freezing temperature range: 310 K to 300 K.
WE assume that the process is a first-order phase transition.
The entropy change (ΔS) for the freezing process can be calculated using the following formula:
ΔS = ΔHf / Tm
where ΔHf is the enthalpy of fusion, and Tm is the melting point of the substance.
Substituting the given values, we get:
ΔS = 200 kJ/mol / 300 K, ΔS = 0.667 kJ/(mol.K)
Next, we can calculate the Gibbs free energy change (ΔG) using the formula:
ΔG = ΔH - TΔS
where ΔH is the enthalpy change of the freezing process.
To calculate ΔH, we need to first calculate the heat absorbed by the substance during the freezing process. This can be done by integrating the heat capacity equation over the freezing temperature range:
ΔH = ∫Cp dT
Since the process is a first-order phase transition, there is no change in volume, and the pressure is constant. Therefore, we can use the following equation to calculate ΔH:
ΔH = ΔHf = nΔHf
where n is the number of moles of the substance.
To calculate n, we can use the following formula:
n = m / M
where m is the mass of the substance, and M is the molar mass.
Let's assume that we have 1 mole of the substance, so n = 1.
The mass of the substance can be calculated using the density of the liquid and solid phases:
ρsolid = ρliquid = ρ
where ρ is the density of the substance.
The mass of the substance is then given by:
m = ρV
where V is the volume of the substance.
At the melting point, the substance has a volume of:
V = Vm = M/ρ = M/ρsolid = M/ρliquid
where Vm is the molar volume of the substance.
At the freezing point, the substance has a volume of:
Vf = Vm(1 - ΔV)
where ΔV is the change in volume during the freezing process. Since the substance undergoes a first-order phase transition, the change in volume is negligible. Therefore, we can assume that Vf ≈ Vm.
Now we can calculate the heat absorbed by the substance during the freezing process:
ΔH = ΔHf = nΔHf = 200 kJ/mol
Finally, we can calculate the Gibbs free energy change:
ΔG = ΔH - TΔS
ΔG= (200 - (300 X 0.667)) = (200-200.1) kJ/mol = -0.1 kJ/mol.
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A sample of a substance undergoes a first-order phase transition from a liquid to a solid state. The heat capacity of the substance is given by: Cp = a + bT + cT², where a, b, and c are constants, and T is the temperature. The enthalpy of fusion of the substance is ΔHf = 200 kJ/mol, and its melting point is 300 K. At a pressure of 1 atm, the substance begins to freeze at a temperature of 310 K, and the process is complete at a temperature of 300 K. Calculate the entropy change (ΔS) and the Gibbs free energy change (ΔG) for the freezing process.a)ΔS = 0.57 kJ/(mol.K), ΔG= -0.2 kJ/mol.b)ΔS = 0.67 kJ/(mol.K), ΔG= -0.1 kJ/mol.c)ΔS = 0.87 kJ/(mol.K), ΔG= -0.2 kJ/mol.d)ΔS = 0.67 kJ/(mol.K), ΔG= -0.2 kJ/mol.Correct answer is option 'B'. Can you explain this answer?
Question Description
A sample of a substance undergoes a first-order phase transition from a liquid to a solid state. The heat capacity of the substance is given by: Cp = a + bT + cT², where a, b, and c are constants, and T is the temperature. The enthalpy of fusion of the substance is ΔHf = 200 kJ/mol, and its melting point is 300 K. At a pressure of 1 atm, the substance begins to freeze at a temperature of 310 K, and the process is complete at a temperature of 300 K. Calculate the entropy change (ΔS) and the Gibbs free energy change (ΔG) for the freezing process.a)ΔS = 0.57 kJ/(mol.K), ΔG= -0.2 kJ/mol.b)ΔS = 0.67 kJ/(mol.K), ΔG= -0.1 kJ/mol.c)ΔS = 0.87 kJ/(mol.K), ΔG= -0.2 kJ/mol.d)ΔS = 0.67 kJ/(mol.K), ΔG= -0.2 kJ/mol.Correct answer is option 'B'. Can you explain this answer? for UGC NET 2024 is part of UGC NET preparation. The Question and answers have been prepared according to the UGC NET exam syllabus. Information about A sample of a substance undergoes a first-order phase transition from a liquid to a solid state. The heat capacity of the substance is given by: Cp = a + bT + cT², where a, b, and c are constants, and T is the temperature. The enthalpy of fusion of the substance is ΔHf = 200 kJ/mol, and its melting point is 300 K. At a pressure of 1 atm, the substance begins to freeze at a temperature of 310 K, and the process is complete at a temperature of 300 K. Calculate the entropy change (ΔS) and the Gibbs free energy change (ΔG) for the freezing process.a)ΔS = 0.57 kJ/(mol.K), ΔG= -0.2 kJ/mol.b)ΔS = 0.67 kJ/(mol.K), ΔG= -0.1 kJ/mol.c)ΔS = 0.87 kJ/(mol.K), ΔG= -0.2 kJ/mol.d)ΔS = 0.67 kJ/(mol.K), ΔG= -0.2 kJ/mol.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for UGC NET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sample of a substance undergoes a first-order phase transition from a liquid to a solid state. The heat capacity of the substance is given by: Cp = a + bT + cT², where a, b, and c are constants, and T is the temperature. The enthalpy of fusion of the substance is ΔHf = 200 kJ/mol, and its melting point is 300 K. At a pressure of 1 atm, the substance begins to freeze at a temperature of 310 K, and the process is complete at a temperature of 300 K. Calculate the entropy change (ΔS) and the Gibbs free energy change (ΔG) for the freezing process.a)ΔS = 0.57 kJ/(mol.K), ΔG= -0.2 kJ/mol.b)ΔS = 0.67 kJ/(mol.K), ΔG= -0.1 kJ/mol.c)ΔS = 0.87 kJ/(mol.K), ΔG= -0.2 kJ/mol.d)ΔS = 0.67 kJ/(mol.K), ΔG= -0.2 kJ/mol.Correct answer is option 'B'. Can you explain this answer?.
A sample of a substance undergoes a first-order phase transition from a liquid to a solid state. The heat capacity of the substance is given by: Cp = a + bT + cT², where a, b, and c are constants, and T is the temperature. The enthalpy of fusion of the substance is ΔHf = 200 kJ/mol, and its melting point is 300 K. At a pressure of 1 atm, the substance begins to freeze at a temperature of 310 K, and the process is complete at a temperature of 300 K. Calculate the entropy change (ΔS) and the Gibbs free energy change (ΔG) for the freezing process.a)ΔS = 0.57 kJ/(mol.K), ΔG= -0.2 kJ/mol.b)ΔS = 0.67 kJ/(mol.K), ΔG= -0.1 kJ/mol.c)ΔS = 0.87 kJ/(mol.K), ΔG= -0.2 kJ/mol.d)ΔS = 0.67 kJ/(mol.K), ΔG= -0.2 kJ/mol.Correct answer is option 'B'. Can you explain this answer? for UGC NET 2024 is part of UGC NET preparation. The Question and answers have been prepared according to the UGC NET exam syllabus. Information about A sample of a substance undergoes a first-order phase transition from a liquid to a solid state. The heat capacity of the substance is given by: Cp = a + bT + cT², where a, b, and c are constants, and T is the temperature. The enthalpy of fusion of the substance is ΔHf = 200 kJ/mol, and its melting point is 300 K. At a pressure of 1 atm, the substance begins to freeze at a temperature of 310 K, and the process is complete at a temperature of 300 K. Calculate the entropy change (ΔS) and the Gibbs free energy change (ΔG) for the freezing process.a)ΔS = 0.57 kJ/(mol.K), ΔG= -0.2 kJ/mol.b)ΔS = 0.67 kJ/(mol.K), ΔG= -0.1 kJ/mol.c)ΔS = 0.87 kJ/(mol.K), ΔG= -0.2 kJ/mol.d)ΔS = 0.67 kJ/(mol.K), ΔG= -0.2 kJ/mol.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for UGC NET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sample of a substance undergoes a first-order phase transition from a liquid to a solid state. The heat capacity of the substance is given by: Cp = a + bT + cT², where a, b, and c are constants, and T is the temperature. The enthalpy of fusion of the substance is ΔHf = 200 kJ/mol, and its melting point is 300 K. At a pressure of 1 atm, the substance begins to freeze at a temperature of 310 K, and the process is complete at a temperature of 300 K. Calculate the entropy change (ΔS) and the Gibbs free energy change (ΔG) for the freezing process.a)ΔS = 0.57 kJ/(mol.K), ΔG= -0.2 kJ/mol.b)ΔS = 0.67 kJ/(mol.K), ΔG= -0.1 kJ/mol.c)ΔS = 0.87 kJ/(mol.K), ΔG= -0.2 kJ/mol.d)ΔS = 0.67 kJ/(mol.K), ΔG= -0.2 kJ/mol.Correct answer is option 'B'. Can you explain this answer?.
Solutions for A sample of a substance undergoes a first-order phase transition from a liquid to a solid state. The heat capacity of the substance is given by: Cp = a + bT + cT², where a, b, and c are constants, and T is the temperature. The enthalpy of fusion of the substance is ΔHf = 200 kJ/mol, and its melting point is 300 K. At a pressure of 1 atm, the substance begins to freeze at a temperature of 310 K, and the process is complete at a temperature of 300 K. Calculate the entropy change (ΔS) and the Gibbs free energy change (ΔG) for the freezing process.a)ΔS = 0.57 kJ/(mol.K), ΔG= -0.2 kJ/mol.b)ΔS = 0.67 kJ/(mol.K), ΔG= -0.1 kJ/mol.c)ΔS = 0.87 kJ/(mol.K), ΔG= -0.2 kJ/mol.d)ΔS = 0.67 kJ/(mol.K), ΔG= -0.2 kJ/mol.Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for UGC NET.
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Here you can find the meaning of A sample of a substance undergoes a first-order phase transition from a liquid to a solid state. The heat capacity of the substance is given by: Cp = a + bT + cT², where a, b, and c are constants, and T is the temperature. The enthalpy of fusion of the substance is ΔHf = 200 kJ/mol, and its melting point is 300 K. At a pressure of 1 atm, the substance begins to freeze at a temperature of 310 K, and the process is complete at a temperature of 300 K. Calculate the entropy change (ΔS) and the Gibbs free energy change (ΔG) for the freezing process.a)ΔS = 0.57 kJ/(mol.K), ΔG= -0.2 kJ/mol.b)ΔS = 0.67 kJ/(mol.K), ΔG= -0.1 kJ/mol.c)ΔS = 0.87 kJ/(mol.K), ΔG= -0.2 kJ/mol.d)ΔS = 0.67 kJ/(mol.K), ΔG= -0.2 kJ/mol.Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A sample of a substance undergoes a first-order phase transition from a liquid to a solid state. The heat capacity of the substance is given by: Cp = a + bT + cT², where a, b, and c are constants, and T is the temperature. The enthalpy of fusion of the substance is ΔHf = 200 kJ/mol, and its melting point is 300 K. At a pressure of 1 atm, the substance begins to freeze at a temperature of 310 K, and the process is complete at a temperature of 300 K. Calculate the entropy change (ΔS) and the Gibbs free energy change (ΔG) for the freezing process.a)ΔS = 0.57 kJ/(mol.K), ΔG= -0.2 kJ/mol.b)ΔS = 0.67 kJ/(mol.K), ΔG= -0.1 kJ/mol.c)ΔS = 0.87 kJ/(mol.K), ΔG= -0.2 kJ/mol.d)ΔS = 0.67 kJ/(mol.K), ΔG= -0.2 kJ/mol.Correct answer is option 'B'. Can you explain this answer?, a detailed solution for A sample of a substance undergoes a first-order phase transition from a liquid to a solid state. The heat capacity of the substance is given by: Cp = a + bT + cT², where a, b, and c are constants, and T is the temperature. The enthalpy of fusion of the substance is ΔHf = 200 kJ/mol, and its melting point is 300 K. At a pressure of 1 atm, the substance begins to freeze at a temperature of 310 K, and the process is complete at a temperature of 300 K. Calculate the entropy change (ΔS) and the Gibbs free energy change (ΔG) for the freezing process.a)ΔS = 0.57 kJ/(mol.K), ΔG= -0.2 kJ/mol.b)ΔS = 0.67 kJ/(mol.K), ΔG= -0.1 kJ/mol.c)ΔS = 0.87 kJ/(mol.K), ΔG= -0.2 kJ/mol.d)ΔS = 0.67 kJ/(mol.K), ΔG= -0.2 kJ/mol.Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of A sample of a substance undergoes a first-order phase transition from a liquid to a solid state. The heat capacity of the substance is given by: Cp = a + bT + cT², where a, b, and c are constants, and T is the temperature. The enthalpy of fusion of the substance is ΔHf = 200 kJ/mol, and its melting point is 300 K. At a pressure of 1 atm, the substance begins to freeze at a temperature of 310 K, and the process is complete at a temperature of 300 K. Calculate the entropy change (ΔS) and the Gibbs free energy change (ΔG) for the freezing process.a)ΔS = 0.57 kJ/(mol.K), ΔG= -0.2 kJ/mol.b)ΔS = 0.67 kJ/(mol.K), ΔG= -0.1 kJ/mol.c)ΔS = 0.87 kJ/(mol.K), ΔG= -0.2 kJ/mol.d)ΔS = 0.67 kJ/(mol.K), ΔG= -0.2 kJ/mol.Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A sample of a substance undergoes a first-order phase transition from a liquid to a solid state. The heat capacity of the substance is given by: Cp = a + bT + cT², where a, b, and c are constants, and T is the temperature. The enthalpy of fusion of the substance is ΔHf = 200 kJ/mol, and its melting point is 300 K. At a pressure of 1 atm, the substance begins to freeze at a temperature of 310 K, and the process is complete at a temperature of 300 K. Calculate the entropy change (ΔS) and the Gibbs free energy change (ΔG) for the freezing process.a)ΔS = 0.57 kJ/(mol.K), ΔG= -0.2 kJ/mol.b)ΔS = 0.67 kJ/(mol.K), ΔG= -0.1 kJ/mol.c)ΔS = 0.87 kJ/(mol.K), ΔG= -0.2 kJ/mol.d)ΔS = 0.67 kJ/(mol.K), ΔG= -0.2 kJ/mol.Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice UGC NET tests.
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