Bihar Board Chemistry VVI Questions 2025

Bihar Board Class 12th Chemistry Important Questions 2025

What is Compressibility Factor? Explain the Factors which affects Z-value

Compressibility Factor and Factors affects Z-value

Compressibility factor is a measure of deviation of a gas from ideal gas behavior when pressure and temperature changes. It is also called Z-factor and helps to understand how gases behave under different conditions. It is a dimensionless quantity that relates the actual behavior of a real gas to that of an ideal gas.

Compressibility factor is the ratio of the actual volume (V) to the ideal volume (V_ideal) of a gas .
Mathematically, it can be written as-
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CUET UG 2024 Chemistry Question Paper and Answer Key

NTA conducted the CUET 2024 Chemistry paper on May 15, 2024 in pen and paper format from 10 am to 11 am. Students can download the CUET 2024 Chemistry question paper PDF and Answer Key here. CUET UG 2024 Chemistry Question Paper and Answer Key

Coupling Constant or Spin-Spin Coupling Constant(J)

Coupling constant is the strength of the spin-spin splitting interaction and the distance between centers of two adjacent peaks or lines in a multiplet. It is also called spin-spin coupling constant (J).

In the above diagram, one is quartered (A) and other is triplet (B). Quartered means three more protons are present in the neighboring proton and triplet means two more protons are present in the neighboring proton. Quartered or triplet are a multiplet in which more than one peaks are present so the coupling constant is the distance 'J' between the two adjacent peaks in a multiplet.
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Spin-Spin Interaction or Coupling of NMR Signals

The splitting of nmr signal into 2nI + 1 peaks due to interaction of adjacent nuclear spins under high resolution is called spin-spin interaction. Though signal splits but the area under the curve remains the same. Unlike chemical shift (δ), it is independent of magnetic field. The relative peak intensities are given by coefficients of terms in the expansion of (r + 1)ⁿ:
(r + 1)¹: r + 1 i.e. 1 : 1
(r + 1)²: r² + 2r + 1 i.e. 1 : 2 : 1
(r + 1)³: r³ + 3r² + 3r + 1 i.e. 1 : 3 : 3 : 1
(r + 1)⁴: r⁴ + 4r³ + 6r² + 4r + 1 i.e. 1 : 4 : 6 : 4 : 1
(r + 1)⁵: r⁵ + 5r⁴ + 10r³ + 10r² + 5r + 1 i.e. 1 : 5 : 10 : 10 : 5 : 1
It is not operative beyond three bonds and so, splitting occurs due to neighbouring H atoms and no splitting is caused by protons of the same environment or equivalent protons.
Let us consider ethanol-
CH₃—CH₂—OH
Number of peaks for CH₂ = 2nI+1 = 2 X 3 X ½ + 1 = 4
Number of peaks for CH₃ = 2nI+1 = 2 X 2 X ½ + 1 = 3
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Classical Theory of Raman Effect: Molecular Polarizability

The basic concept of classical theory of the Raman effect depends on the polarizability of a molecule and the applied Electric field.

When a molecule is placed in a static electric field, a distortion takes place in it because of the attraction of positively charged nuclei towards negative pole of the field and of electron towards positive pole. This separation of charge centers causes an induced electric dipole moment in the molecule and the molecule becomes polarized. The magnitude of induced dipole (𝜇) depends both on magnitude of the applied field (E) and on the case with which the molecule can be distorted. Thus,
𝜇 = 𝛼E
where α is the polarizability of the molecule.
In case of hydrogen molecule, the polarizibility is anisotropic i.e. the electron that form the bond are more easily displaced by the field along the bond axis than along the one across this direction.
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Radial and Angular Distribution Curves

In the atomic orbital, there is probability of finding an electron in a particular volume element at a given distance and direction from the nucleus. This gives two types of probability of finding electrons, the radial probability distribution function i.e. probability of finding an electron at a given radial distance from the nucleus without considering the direction from the nucleus (i.e. how far away from the nucleus the orbital extends and the number of nodes the orbital has).
The radial distribution functions depend on both n and l. This means that the number of nodes an orbital has and how far that orbital extends from the nucleus depends on the principle quantum number or energy level of the orbital (the 1 in 1s, the 2 in 2s, the 3 in 3s, etc.) and the type of orbital (s vs. p vs. d).
The number of Radial nodes can be clculated by the given formula-
Number of Radial nodes = n - l - 1 = n - (l + 1)
Where n = principal quantum number, l = Azimuthal quantum number
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Quantum Theory of Raman Effect

Quantum theory of the Raman effect explains the phenomenon by considering the interaction between incident photons and vibrational modes of molecules of the system.
It imagines perfectly elastic collisions taking place between the light photons with energy h𝜈 and molecules of mass m in energy state E_p moving with a velocity v. After collision, if E_q is the energy state of the molecule and v' is its velocity then-
E_p + ½ mv² + h𝜈 = E_q + ½ mv'² + h𝜈'
where, v and v' are the velocities of photon before and after collision respectively.
It can be easily proved that the velocity of the molecule practically remain unchanged.
we have-
E_p + h𝜈 = E_q + h𝜈'
or, v' = v + [E_p − E_q]/h
or, v' = v + Δv
From this equation, we have three cases-
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Thermodynamic Derivation of Gibb's Phase Rule

Let a heterogeneous system of two phases a and b containing three components 1,2 and 3 in equilibrium. The chemical potential (µ) of these three components in two phases can be written as-
µ₁(a), µ₂(a), µ₃(a), µ₁(b), µ₂(b), µ₃(b)
If we consider the closed system in equilibrium at a fixed temperature and pressure, the Gibb's Duhem equation we have-
Σµ dn = 0
Let a small amount δn₁ is transformed under equilibrium conditions from a to b phase, then-
µ₁(a).dn₁ + µ₁(b).dn₁ = 0
or,   µ₁(a) = µ₁(b)
Similarly,   µ₂(a) = µ₂(b)
and   µ₃(a) = µ₃(b)
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Thermodynamic Derivation of Nernst's Distribution Law

The thermodynamic derivation of the distribution law is based upon the principle that if there are two phases in equilibrium (i.e. two immiscible solvents containing the same solute dissolved in them), the chemical potential(μ) of a substance present in them must be same in both the phases.
From thermodynamics, we know that the chemical potential (μ) of a substance is a solution given by-
μ = μ^o + RT lna
Where μ^o is the standard chemical potential and 'a' is the activity of the solute in the solution.
Thus for the solute in liquid A, we have-
μ_A = μ^o_A + RT lna_A
Similarly for the solute in liquid B we have-
μ_B = μ^o_B + RT lna_B
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Wien Effect

Conductance Under High Potential Gradient

The increase in conductance of an electrolyte at high potential gradients is known as Wien effect. Wien measured the conductance using high voltages of the order of 20,000 volts cm^-1. At such higher voltages the moving ion will be almost free from the effect of the oppositely charged ionic atmosphere. The ion will be moving so fast that there will no time for the ionic atmosphere to be built up. Under these circumstances, the asymmetry and electrophoretic effects may be negligible or even absent. The conductance, therefore, increases and approaches a certain limiting value. This observation had been experimentally verified by Wien much before the development of the theory of strong electrolytes.
The Wien effect is greater when the interionic forces due to ionic atmosphere are large and this exists for concentrated solutions of high- valence ions. The weak acids and bases are dissociated only to a small extent and the Wien effect is several times greater than the expected value. The deviation increases with voltage. The powerful electrical fields produce a temporary dissociation into ions of the molecules of weak acid or base. This phenomenon is called the dissociation field effect.
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Debye- Falkenhagen Effect

Conductance Under High A.C. Frequencies

Debye- Falkenhagen examined the conductance behaviour of strong eletrolytic solution by applying alternating current (AC) of different frequncies. They observed that the conductivity of an electrolytic solution increases when voltage of a very high frequency is applied. This is known as Debye–Falkenhagen effect.
They predicted that if the frequency of alternating current is high so that the time of oscillation is less than the relaxation time of the ionic atmosphere, the asymmetry effect will be almost absent. That is, the ionic atmosphere around the central ion will remain symmetric. In such a situation, the retarding effect due to asymmetry will be entirely absent and the conductance may be higher. The conductance of the solution, therefore, should vary with the frequency of the alternating current used.
Higher the frequency, higher the conductance, this effect also termed dispersion conductance has been experimentally verified.
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Debye- Huckel Onsager Theory

In case of weak electrolytes the increase in equivalent conductance with dilution can be easily explained on the basis of Arrhenius theory, according to which the conductance increases due to increase in dissociation of weak electrolyte with dilution. But this explanation cannot be applied in case of strong electrolytes like NaCl as they are almost completely dissociated into constituent ions (Na⁺ and Cl⁻) even at moderate concentration.
Peter Debye and Huckel in 1923 initially derived an equation to describe how the equivalent conductance of electrolytic solution changes on dilution. Later this equation was further improved by Onsager and now this equation is known as Debye Huckel Onsager equation.
Debye-Huckel-Onsager Theory is based on the following Assumptions-
1. Strong electrolytes are completely dissociate into their constituent ions in solution.
2. Due to Coulornbic forces between the charges of the ions, they do not behave like molecules in their transport and thermodynamic properties.
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