Fundamental Principles of Chemical Thermodynamics
Importance of the Zeroth Law of Thermodynamics
(a) Importance of Zeroth Law of Thermodynamics: The Zeroth Law of Thermodynamics states that if two systems are separately in thermal equilibrium with a third system, then they are in thermal equilibrium with each other.
Why Heat Capacity Cp is Greater Than Cv
(b) Why is Cp greater than Cv? At constant volume, no work is done by the gas, so all the heat supplied increases its internal energy. At constant pressure, the gas expands and does external work in addition to increasing its internal energy. Therefore, more heat is required at constant pressure than at constant volume.
Significance of the Compressibility Factor
(d) What is the significance of the compressibility factor?
Answer: The compressibility factor (Z) is defined as:
Z = PV / nRT
It measures the deviation of a real gas from ideal gas behavior. For an ideal gas, Z = 1.
- If Z > 1, repulsive forces dominate.
- If Z < 1, attractive forces dominate.
Thus, the compressibility factor helps in predicting and analyzing the behavior of real gases under different conditions of temperature and pressure.
The Clausius-Clapeyron Equation
(E) What is the Clausius-Clapeyron equation?
Ans: The Clausius–Clapeyron equation relates the vapor pressure of a liquid to its temperature and the latent heat of vaporization. It is used to calculate the variation of vapor pressure with temperature and to determine the latent heat of vaporization.
Concept of Mean Heat Capacity
Demonstrate the concept of mean heat capacity.
Ans: The mean heat capacity of a substance over a temperature range is the average heat capacity between two temperatures. CM = Q / (t2 – t1)
Criteria for Chemical Reaction Equilibrium
Criteria for Chemical Reaction Equilibrium: A chemical reaction is in equilibrium when there is no net change in composition and the forward and reverse reaction rates are equal. Thermodynamically, the criterion for equilibrium at constant temperature and pressure is: ΔG = 0
Phase Rule and Duhem’s Theorem
Q. What is the phase rule? Illustrate the significance of the degree of freedom and Duhem’s theorem.
Ans: The phase rule gives the relationship between the number of phases, components, and degrees of freedom of a system at equilibrium: F = C – P + 2.
Degree of Freedom (F)
The number of independent intensive variables required to completely specify the state of a system at equilibrium. It indicates whether a system is invariant (F = 0), univariant (F = 1), or bivariant (F = 2).
Duhem’s Theorem
For a homogeneous system in equilibrium, fixing two independent intensive variables completely determines all other intensive properties of the system. This theorem simplifies the thermodynamic description of equilibrium systems.
Physical Significance of Chemical Potential
Q. What is the physical significance of Chemical Potential?
Chemical potential is the partial molar Gibbs free energy of a component and represents the change in Gibbs free energy when one mole of the component is added to the system at constant temperature and pressure. It acts as the driving force for mass transfer and determines phase and chemical equilibrium.
Activity and Activity Coefficient
What do you mean by Activity and Activity Coefficient?
Activity: The effective concentration of a component in a solution, representing its actual thermodynamic behavior, is called activity.
Activity Coefficient: The ratio of activity to mole fraction is called the activity coefficient. It measures the deviation of a real solution from ideal behavior. For an ideal solution, the activity coefficient is unity.
Standard State of Fugacity for a Gas
What is the standard state of fugacity for a Gas?
The fugacity of a gas is defined as the pure ideal gas at unit pressure (1 bar) and the same temperature as the system.
Four Cycles of a Carnot Engine
Four Cycles of a Carnot Engine
Ans: The Carnot engine operates reversibly between a high-temperature reservoir (TH) and a low-temperature reservoir (TC) through four processes:
- Isothermal Expansion (1 → 2): The gas expands at constant temperature TH. Heat QH is absorbed from the hot reservoir. The gas does work on the surroundings.
- Adiabatic Expansion (2 → 3): The gas expands without heat exchange (Q = 0). Temperature decreases from TH to TC.
- Isothermal Compression (3 → 4): The gas is compressed at constant temperature TC. Heat QC is rejected to the cold reservoir.
- Adiabatic Compression (4 → 1): The gas is compressed without heat exchange (Q = 0). Temperature rises from TC back to TH, restoring the initial state.
Partial Molar Properties and Their Uses
(a) Partial Molar Properties: Definition, Significance, and Uses
The partial molar property of a component is defined as the change in an extensive property of a solution when one mole of that component is added, keeping temperature, pressure, and the amounts of all other components constant.
Significance
- Describes the contribution of each component to the total property of a mixture.
- Helps in understanding non-ideal solution behavior.
- Essential for defining chemical potential.
Uses in Thermodynamic Calculations
- Calculation of mixture properties such as volume, enthalpy, entropy, and Gibbs free energy.
- Determination of chemical potential.
- Analysis of phase and chemical equilibria.
- Design and calculation of separation processes.
Effect of Temperature on the Equilibrium Constant
What is the effect of temperature on the equilibrium constant?
Answer: The equilibrium constant (K) depends only on temperature.
- For an endothermic reaction, increasing the temperature increases the value of the equilibrium constant because the equilibrium shifts towards the products.
- For an exothermic reaction, increasing the temperature decreases the value of the equilibrium constant because the equilibrium shifts towards the reactants.
Equilibrium constant Kc: The ratio of the product of equilibrium concentrations of products to that of reactants, each raised to their stoichiometric coefficients.
Definition of Thermodynamics
2(a) What is meant by thermodynamics?
Thermodynamics is the branch of science that deals with the relationships between heat, work, energy, and the properties of matter in equilibrium.
Closed System vs. Isolated System
2(b) Difference between Closed System and Isolated System
A closed system is a system in which mass cannot cross the system boundary, but energy can be transferred in the form of heat or work. For example, a gas enclosed in a sealed piston-cylinder arrangement is a closed system. An isolated system, on the other hand, is a system in which neither mass nor energy can cross the boundary. Therefore, there is no exchange of matter, heat, or work with the surroundings. An ideal thermos flask is considered an example of an isolated system. Thus, a closed system allows energy transfer but not mass transfer, whereas an isolated system allows neither mass nor energy transfer.
Concept of Partial Molar Quantity
2(c) What is the concept of Partial Molar Quantity?
The partial molar property of a component is the change in an extensive property of a solution when one mole of that component is added, keeping temperature, pressure, and moles of other components constant.
Specific Heat Capacity Explained
4(g) What is specific heat capacity?
Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by 1 K (or 1°C). C = Q / (m Δt)
Difference Between Bubble Point and Dew Point
4(f) Differentiate between Bubble Point and Dew Point
The bubble point is the temperature or pressure at which the first bubble of vapor is formed when a liquid mixture is heated or its pressure is reduced. At this point, the liquid starts to boil and the system is predominantly in the liquid phase. In contrast, the dew point is the temperature or pressure at which the first drop of liquid is formed when a vapor mixture is cooled or its pressure is increased. At this point, condensation begins and the system is predominantly in the vapor phase. Thus, the bubble point marks the beginning of vaporization, whereas the dew point marks the beginning of condensation.
Entropy and the Criterion for Spontaneity
5(b) Entropy change when partition is removed: When the partition between two compartments containing the same gas is removed in an insulated vessel, free expansion occurs.
5(c) How do you define entropy? Why is entropy considered a criterion for the direction of spontaneous processes?
Entropy is a thermodynamic property that measures the degree of randomness or energy dispersal in a system.
Criterion for Spontaneity
According to the second law, for a spontaneous process:
- If ΔSuniverse > 0: The process is spontaneous.
- If ΔSuniverse = 0: The system is in equilibrium.
- If ΔSuniverse < 0: The process is non-spontaneous.
Virial and Van der Waals Equations of State
Virial Equation of State: The Virial Equation of State is an empirical equation used to describe the behavior of real gases by correcting the ideal gas equation. It is expressed as: PV / RT = 1 + B/V + C/V2 + D/V3 + …
Van der Waals Equation of State: The Van der Waals equation is a modified form of the ideal gas equation that accounts for intermolecular forces and the molecular volume of real gases.
The Gibbs-Duhem Equation
Gibbs-Duhem Equation: The Gibbs-Duhem equation expresses the relationship between the chemical potentials of the components in a thermodynamic system. It shows that the chemical potentials of the components cannot change independently when temperature and pressure are constant.
Equilibrium Constant: The equilibrium constant is the ratio of the product of equilibrium concentrations of products to that of reactants, each raised to their stoichiometric coefficients. For the reaction aA + bB ↔ cC + dD, the constant is: K = [C]c[D]d / [A]a[B]b
Principle of Corresponding States
Principle of Corresponding States (or Corresponding Factors): The principle of corresponding states states that all gases, when compared at the same reduced temperature and reduced pressure, have approximately the same compressibility factor and exhibit similar behavior regardless of their chemical nature.