Search Previous Year Questions

CONCEPT:

Faraday's Laws of Electrolysis

• Faraday's first law of electrolysis states that the amount of substance deposited at an electrode is directly proportional to the quantity of electricity passed through the electrolyte.
• The relationship can be expressed as:

m = (ItM)/(nF)

where m is the mass of the substance deposited, I is the current, t is the time, M is the molar mass of the substance, n is the number of electrons transferred per ion, and F is the Faraday constant.

EXPLANATION:

• For the electrolysis of aluminium chloride (AlCl₃), the reaction at the cathode is:

Al³⁺ + 3e^- → Al

• Given data:
• Current (I) = 2A
• Time (t) = 30 minutes = 30 × 60 = 1800 seconds
• Molar mass of Aluminium (M) = 27 g mol^-1
• Faraday constant (F) = 96500 C mol^-1
• In the reaction, the number of electrons (n) transferred per ion is 3.
• Using the formula:

m = (ItM)/(nF)

m = (2 × 1800 × 27)/(3 × 96500)

m = (97200)/(289500)

m = 0.336 g

Therefore, the amount of aluminium deposited at the cathode is 0.336 g.

CONCEPT:

Radioactive Decay

• Radioactive decay is a process by which the nucleus of an unstable atom loses energy by emitting radiation. The decay constant (λ) is a probability rate constant that quantifies the likelihood of decay of an atom per unit time.
• Key characteristics of radioactive decay:
• The decay constant (λ) is independent of temperature.
• The half-life (t_1/2) of a radioactive substance is the time required for half of the radioactive atoms to decay. The relationship between half-life and decay constant is given by:

t_1/2 = ln(2) / λ

EXPLANATION:

• Statement 1: Amount of radioactive substance remained after three half-lives is 1/8 of the original amount.
• This is true. After one half-life, half of the original amount remains. After three half-lives, (1/2)³ = 1/8 of the original amount remains.
• Statement 2: Decay constant does not depend upon temperature.
• This is true. The decay constant is a fundamental property of the radioactive substance and is not affected by temperature.
• Statement 3: Decay constant increases with increase in temperature.
• This is not true. The decay constant is independent of temperature.
• Statement 4: Half life is ln(2) times of 1/rate constant.
• This is true. The half-life (t_1/2) is given by t_1/2 = ln(2) / λ, where λ is the decay constant.

Therefore, the statement that is not true for radioactive decay is: Decay constant increases with increase in temperature.

CONCEPT:

Stereoisomers and Geometrical Isomerism

• Stereoisomers are compounds that have the same molecular formula and connectivity of atoms but differ in the spatial arrangement of atoms.
• Geometrical isomerism occurs in compounds with restricted rotation around a double bond or ring, resulting in cis-trans isomers.
• Each chiral center or double bond contributes to possible isomerism.

EXPLANATION:

It has 4 stereoisomers $\left[\begin{array}{ll} \mathrm{R} \text { cis } & \mathrm{R} \text { trans } \ \mathrm{Scis} & \mathrm{Strans} \end{array}\right]$

• Two factors contribute to stereoisomerism here:
• The double bond between the third and fourth carbon introduces cis and trans isomers.
• The chiral carbon (second carbon with -CH₃, -CH=CH-CH₃, -OH, and -H as substituents) introduces R and S configurations.
• Combining these, the molecule can exhibit the following configurations:
• Cis with R configuration
• Cis with S configuration
• Trans with R configuration
• Trans with S configuration
• Hence, the molecule has 4 possible stereoisomers.

Therefore, the total number of stereoisomers for the given molecule is 4.

EXPLANATION:​.

Electronegativity

• Electronegativity is a measure of the tendency of an atom to attract a bonding pair of electrons. The Pauling scale is the most commonly used scale for electronegativity.
• The electronegativity values (on the Pauling scale) for some elements are as follows:
• | | Li | Be | B | C | N | O | F | | --- | --- | --- | --- | --- | --- | --- | --- | | (E.N.) = On pauling scale | 1 | 1.5 | 2 | 2.5 | 3 | 3.5 | 4.0 |

For elements in the second period and third period:

• | | Na | Mg | Al | Si | P | S | Cl | | --- | --- | --- | --- | --- | --- | --- | --- | | (E.N.) = | 0.9 | 1.2 | 1.5 | 1.8 | 2.1 | 2.5 | 3.0
  |

Therefore, the electronegativity order that is incorrect is: Al < Mg < B < N

CONCEPT:

Electronic Configuration of Lanthanoids

• Lanthanoids are a series of 15 elements from lanthanum (La) to lutetium (Lu) in the periodic table, characterized by the filling of the 4f orbitals.
• The general electron configuration of lanthanoids is [Xe] 4fⁿ 5d^x 6s².
• The common oxidation states of lanthanoids include +2, +3, and sometimes +4.
• Key electron configurations:
• Europium (Eu): [Xe] 4f⁷ 6s²
• Gadolinium (Gd): [Xe] 4f⁷ 5d¹ 6s²
• Terbium (Tb): [Xe] 4f⁹ 6s²
• Samarium (Sm): [Xe] 4f⁶ 6s²

EXPLANATION:

• To determine which ions have a 4f⁷ configuration, we must consider the electron loss when forming the given ions:
• Europium (Eu):
• Eu²⁺: [Xe] 4f⁷ (Loses 2 electrons from 6s²)
• Eu³⁺: [Xe] 4f⁶ (Loses 2 electrons from 6s² and 1 electron from 4f⁷)
• Gadolinium (Gd):
• Gd³⁺: [Xe] 4f⁷ (Loses 2 electrons from 6s² and 1 electron from 5d¹)
• Terbium (Tb):
• Tb³⁺: [Xe] 4f⁸ (Loses 2 electrons from 6s² and 1 electron from 4f⁹)
• Samarium (Sm):
• Sm²⁺: [Xe] 4f⁶ (Loses 2 electrons from 6s²)

Therefore, the lanthanoid ions with a 4f⁷ configuration are Eu²⁺ and Gd³⁺.

EXPLANATION:

Trends in the Periodic Table

• Ionic Radii: The size of the ionic radii decreases as the positive charge of the ion increases.
• Order: Al³⁺ < Mg²⁺ < Na⁺ < F^-
• Ionisation Enthalpy: The energy required to remove an electron from an atom in its gaseous state. It generally increases across a period from left to right.
• Order: B < C < O < N
• Metallic Character: The degree to which an element exhibits metallic properties, which decreases across a period and increases down a group.
• Order: B < Al < Mg < K
• Electronegativity: The tendency of an atom to attract electrons in a chemical bond. It generally increases across a period from left to right.
• Order: Si < P < S < Cl

The correct matching is  A-IV, B-I, C-II, D-III

CONCEPT:

Vitamins and their Chemical Names

• Vitamins are essential nutrients required by the body to function properly. Each vitamin has a specific chemical name.
• Ascorbic acid is the chemical name for Vitamin C.

EXPLANATION:

• Adipic acid: This is not a vitamin, but a dicarboxylic acid commonly used in the production of nylon.
• Aspartic acid: This is not a vitamin, but an amino acid involved in the synthesis of proteins.
• Ascorbic acid: This is Vitamin C, an essential nutrient for the repair of tissues and the enzymatic production of certain neurotransmitters.
• Saccharic acid: This is not a vitamin, but an oxidized derivative of glucose.

Therefore, the acid that is a vitamin is ascorbic acid (Vitamin C).

The correct answer is: (3) Ascorbic acid

CONCEPT:

First Law of Thermodynamics

• The first law of thermodynamics states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (q) plus the work done on the system (w):
• ΔU = q + w
• In a thermally insulated (adiabatic) system, there is no heat exchange with the surroundings, so:
• q = 0
• When work is done on the system (for example, by mechanically stirring the liquid), the work done (w) is positive, which increases the internal energy (ΔU) of the system.

EXPLANATION:

• Since the vessel is thermally insulated, there is no heat exchange with the surroundings:
• q = 0
• The work is done on the liquid by mechanically stirring it, so:
• w > 0
• According to the first law of thermodynamics:
• ΔU = q + w
• Since q = 0, we have ΔU = w
• When w > 0, ΔU > 0

Therefore, the correct option for the thermodynamic parameters is  ΔU > 0, q = 0, w > 0​

CONCEPT:

Bohr's Model of the Atom

• In Bohr's model, the radius of the ( n )th orbit of an atom is given by:
• $r_n = \frac{n^2 a_0}{Z}$
• where:
• ( rn ) = radius of the ( n )th orbit
• ( a0 ) = Bohr radius (radius of the first stationary state of the hydrogen atom)
• ( n ) = principal quantum number
• ( Z ) = atomic number of the element
• For the first excited state, ( n = 2 ).

APPLICATION TO HELIUM ION (He⁺):

• For the Helium ion (He⁺), the atomic number ( Z ) is 2.
• For the first excited state, ( n = 2 ).
• Substituting these values into the formula for the radius:
• $r = \frac{n^2 a_0}{Z} \ = \frac{(2)^2 a_0}{2} \ = \frac{4 a_0}{2} \ = 2 a_0$

Therefore, the radius of the first excited state of the Helium ion is r = 2a0

CONCEPT:

SN₁ and SN₂ Reactions

• SN₁ Mechanism: This is a two-step mechanism where the rate-determining step involves the formation of a carbocation intermediate. It is favored by:
• Stable carbocations (tertiary > secondary > primary).
• Polar protic solvents.
• SN₂ Mechanism: This is a single-step mechanism involving a backside attack by the nucleophile. It is favored by:
• Less steric hindrance (methyl > primary > secondary; tertiary is unfavorable).
• Polar aprotic solvents.

EXPLANATION:

CH3 – O – CH2 – Cl will undergo SN1 mechanism because \(\mathrm{CH}{3}-\mathrm{O}-\stackrel{+}{\mathrm{C}} \mathrm{H}{2}\)  is highly stable. 

• Statement I: CH₃–O–CH₂–Cl undergoes the SN₁ mechanism even though it is a primary halide because the intermediate carbocation (CH₃–O–CH₂⁺) formed is stabilized by resonance with the oxygen atom.
• Statement II: CH₃–C(CH₃)₂–CH₂–Cl (neopentyl chloride) does not undergo the SN₂ mechanism easily due to significant steric hindrance around the reactive center, which obstructs the nucleophilic backside attack.
• Both statements are correct based on the mechanisms and the structural properties of the molecules.

Therefore, both Statement I and Statement II are correct.