CHE PHYSICAL CHEMISTRY 2 EXAM
Thermodynamics Kinetics Quantum Chemistry and Electrochemistry
Questions and Answers Verified Solutions 2026 2027
1. What thermodynamic state function represents the heat exchanged during a constant
pressure process?
A. Internal energy (U)
B. Helmholtz free energy (A)
C. Enthalpy (H)
D. Entropy (S)
Rationale: Enthalpy is defined as H = U + PV. Under constant pressure, the differential change dH equals
the reversible heat transferred (q_p).
2. According to the Second Law of Thermodynamics, what condition must be satisfied
for a spontaneous process in an isolated system?
A. Delta S_total > 0
B. Delta H_system < 0
C. Delta G_system > 0
D. Delta S_system = 0
Rationale: For an isolated system, no heat flows across the boundary, so entropy must increase (Delta S
> 0) for any real spontaneous process.
3. What mathematical relation governs the temperature dependence of the equilibrium
constant K for a chemical reaction?
A. Nernst Equation
B. van 't Hoff Equation
C. Arrhenius Equation
D. Gibbs-Helmholtz Equation
Rationale: The van 't Hoff equation, d(ln K)/dT = Delta H° / (R T^2), describes how equilibrium constants
shift with temperature changes.
, 4. In quantum mechanics, what requirement must a wave function satisfy to represent a
physically acceptable quantum state?
A. It must be infinite at coordinate boundaries
B. It must be single-valued, continuous, and square-integrable
C. It must be strictly real-valued without imaginary components
D. It must equal zero everywhere except at energy nodes
Rationale: Square-integrability ensures the total probability integrates to 1, while continuity and single-
valuedness keep probability density well-behaved.
5. What zero-point energy is associated with a 1D harmonic oscillator of fundamental
frequency v?
A. E = 0
B. E = h v
C. E = (1/2) h v
D. E = (3/2) h v
Rationale: The energy levels of a harmonic oscillator are E_n = (n + 1/2) h v. Setting n = 0 gives the
ground-state zero-point energy (1/2) h v.
6. What happens to the energy level spacing of a particle in a 1D box when the box length
L is doubled?
A. Energy levels double in magnitude
B. Energy levels decrease by a factor of 4
C. Energy levels increase by a factor of 4
D. Energy level spacing remains unchanged
Rationale: Energy levels for a particle in a box are E_n = (n^2 h^2) / (8 m L^2). Since energy is inversely
proportional to L^2, doubling L reduces energy levels to 1/4.
7. Which quantum operator corresponds to total energy in the time-independent
Schrödinger equation?
A. Momentum operator
B. Hamiltonian operator
C. Angular momentum operator
D. Position operator
Thermodynamics Kinetics Quantum Chemistry and Electrochemistry
Questions and Answers Verified Solutions 2026 2027
1. What thermodynamic state function represents the heat exchanged during a constant
pressure process?
A. Internal energy (U)
B. Helmholtz free energy (A)
C. Enthalpy (H)
D. Entropy (S)
Rationale: Enthalpy is defined as H = U + PV. Under constant pressure, the differential change dH equals
the reversible heat transferred (q_p).
2. According to the Second Law of Thermodynamics, what condition must be satisfied
for a spontaneous process in an isolated system?
A. Delta S_total > 0
B. Delta H_system < 0
C. Delta G_system > 0
D. Delta S_system = 0
Rationale: For an isolated system, no heat flows across the boundary, so entropy must increase (Delta S
> 0) for any real spontaneous process.
3. What mathematical relation governs the temperature dependence of the equilibrium
constant K for a chemical reaction?
A. Nernst Equation
B. van 't Hoff Equation
C. Arrhenius Equation
D. Gibbs-Helmholtz Equation
Rationale: The van 't Hoff equation, d(ln K)/dT = Delta H° / (R T^2), describes how equilibrium constants
shift with temperature changes.
, 4. In quantum mechanics, what requirement must a wave function satisfy to represent a
physically acceptable quantum state?
A. It must be infinite at coordinate boundaries
B. It must be single-valued, continuous, and square-integrable
C. It must be strictly real-valued without imaginary components
D. It must equal zero everywhere except at energy nodes
Rationale: Square-integrability ensures the total probability integrates to 1, while continuity and single-
valuedness keep probability density well-behaved.
5. What zero-point energy is associated with a 1D harmonic oscillator of fundamental
frequency v?
A. E = 0
B. E = h v
C. E = (1/2) h v
D. E = (3/2) h v
Rationale: The energy levels of a harmonic oscillator are E_n = (n + 1/2) h v. Setting n = 0 gives the
ground-state zero-point energy (1/2) h v.
6. What happens to the energy level spacing of a particle in a 1D box when the box length
L is doubled?
A. Energy levels double in magnitude
B. Energy levels decrease by a factor of 4
C. Energy levels increase by a factor of 4
D. Energy level spacing remains unchanged
Rationale: Energy levels for a particle in a box are E_n = (n^2 h^2) / (8 m L^2). Since energy is inversely
proportional to L^2, doubling L reduces energy levels to 1/4.
7. Which quantum operator corresponds to total energy in the time-independent
Schrödinger equation?
A. Momentum operator
B. Hamiltonian operator
C. Angular momentum operator
D. Position operator
