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Explanation:

The kinetic energy (K.E.) of the Earth varies as it moves around the Sun in its elliptical orbit. Kinetic energy depends on the velocity of the Earth, which is higher when it is closer to the Sun (perihelion) and lower when it is farther (aphelion).

K.E. = (1/2)mv², where m is the mass of the Earth and v is its velocity.

As the Earth moves in its elliptical orbit:

The velocity increases ⇒ K.E. increases near perihelion.

The velocity decreases ⇒ K.E. decreases near aphelion.

This results in a periodic variation of K.E. over one complete orbit, 

Therefore, the correct answer is Option 3.

Explanation:

The cathode-ray tube experiment conducted by J.J. Thomson was a significant milestone in the study of atomic structure. 

• J.J. Thomson used the cathode-ray tube to study the properties of electrons.
• He was able to determine the charge-to-mass ratio of the electron (e/m).
• The experiment demonstrated that cathode rays are negatively charged particles (electrons).

In the cathode-ray tube experiment:

• Thomson applied an electric and magnetic field to the cathode rays.
• By measuring the deflection of the rays under these fields, he calculated the charge-to-mass ratio of the electron.

However, the experiment did not determine:

• The charge-to-mass ratio of a proton.
• The charge of an electron (determined later by Millikan's oil-drop experiment).
• The structure of the atom or the location of its mass in the nucleus (later established by Rutherford).

Therefore, the correct answer is Option 1.

Calculation:

Given:

Pressure (P) = 1.25 bar

Density (ρ) = 4.21 g dm^-3

Temperature (T) = 27°C = 27 + 273 = 300 K

Gas constant (R) = 0.083 dm³ bar mol^-1 K^-1

The formula for molar mass is:

M = (ρ × R × T) / P

Substituting the values:

M = (4.21 × 0.083 × 300) / 1.25

M = (104.853) / 1.25

M = 83.88 g mol^-1

Therefore, the correct answer is Option 2.

Concept:

To identify a base under the Arrhenius, Bronsted-Lowry, and Lewis theories, we consider the following:

• Arrhenius theory: A base is a substance that increases the concentration of OH^- ions in aqueous solution.
• Bronsted-Lowry theory: A base is a substance that can accept a proton (H⁺).
• Lewis theory: A base is a substance that can donate a pair of electrons.

Calculation:

• OH^- satisfies all three theories:
• Arrhenius: OH^- increases OH^- concentration in solution.
• Bronsted-Lowry: OH^- can accept a proton to form H₂O.
• Lewis: OH^- can donate a pair of electrons.
• O₂^- is a base under Bronsted-Lowry and Lewis theories but not Arrhenius, as it does not directly increase OH^- concentration.
• H₂O is neutral and does not satisfy the base criteria comprehensively under all three theories.
• NH₃ is a base under Bronsted-Lowry and Lewis theories but not Arrhenius.

Therefore, the substance that satisfies all three theories is OH^-.

Explanation:

When a block slides across a rough horizontal table, friction acts as a non-conservative force. The work done by friction primarily affects the energies of the system:

It reduces the kinetic energy of the block due to its opposing motion.

It increases the internal energy (heat energy) of the block and the surface due to frictional dissipation.

Friction does not change the potential energy since the motion occurs on a horizontal surface.

Thus, the work done by friction changes the kinetic and internal energies of the block but does not affect potential energy.

Therefore, the correct answer is Option 3.

CONCEPT:

Effect of Salts on the pH of Water

• When salts dissolve in water, they may hydrolyze to form acidic or basic solutions depending on the nature of their parent acid and base.
• Neutral salts are formed from a strong acid and a strong base and do not hydrolyze — hence, they do not alter the pH of water.
• Salts from:
• Strong acid + Strong base → Neutral (pH ≈ 7)
• Weak acid + Strong base → Basic solution (pH > 7)
• Strong acid + Weak base → Acidic solution (pH < 7)

EXPLANATION:

• NH₄Cl
• Formed from strong acid (HCl) + weak base (NH₃) → Acidic salt (pH < 7)
• KCN
• Formed from strong base (KOH) + weak acid (HCN) → Basic salt (pH > 7)
• KNO₃
• Formed from strong acid (HNO₃) + strong base (KOH) → Neutral salt
• Does not alter pH of water
• NaHCO₃
• Formed from weak acid (H₂CO₃) + strong base (NaOH) → Basic salt (pH > 7)

Therefore, the correct answer is KNO₃

CONCEPT:

Molarity and Stoichiometry

• Molarity (M) is defined as moles of solute per liter of solution:

M = (moles of solute) / (volume of solution in L)

• To find moles of NaOH formed, we must:
• Calculate the moles of Na₂O.
• Use the balanced chemical equation to determine moles of NaOH formed.
• Balanced equation:

Na₂O(s) + H₂O(l) → 2NaOH(aq)

• 1 mole of Na₂O gives 2 moles of NaOH

EXPLANATION:

• Given:
• Mass of Na₂O = 1.55 g
• Molar mass of Na₂O = 2×23 + 16 = 62 g/mol
• Moles of Na₂O:

= 1.55 g / 62 g/mol = 0.025 mol

• From the balanced equation:

1 mol Na₂O → 2 mol NaOH

0.025 mol Na₂O → 0.050 mol NaOH

• Volume of solution = 100 mL = 0.100 L
• Molarity of NaOH:

= 0.050 mol / 0.100 L = 0.500 M

Therefore, the molarity of the NaOH solution is 0.500 M.

CONCEPT:

pH and OH^- Concentration

• The pH of a solution is a measure of its hydrogen ion (H⁺) concentration, given by:

pH = -log[H⁺]

• The relationship between pH and pOH in an aqueous solution is:

pH + pOH = 14

• The hydroxide ion (OH^-) concentration can be calculated using the equation:

[OH^-] = 10^-pOH

EXPLANATION:

• In the given problem:
• The pH of the vinegar solution is 4.0.
• Using the relationship pH + pOH = 14:
• pOH = 14 - pH
• pOH = 14 - 4.0
• pOH = 10
• Using the formula [OH^-] = 10^-pOH:
• [OH^-] = 10^-10

Therefore, the amount of OH^- ion present in the solution is 1 × 10^-10 M.

CONCEPT:

Stoichiometry of Chemical Reactions

• Stoichiometry is the calculation of reactants and products in chemical reactions based on the law of conservation of mass.
• To balance a chemical equation, the number of atoms of each element on the reactants side must equal the number of atoms of the same element on the products side.

EXPLANATION:

• The given unbalanced reaction is:

Fe₂O₃ + CO → Fe + CO₂

• To balance the equation:
• Iron (Fe) atoms: There are 2 Fe atoms in Fe₂O₃, so 2 Fe atoms must appear in the product.
• Oxygen (O) atoms: Fe₂O₃ contains 3 O atoms, which combine with CO to produce CO₂. Balancing requires 3 CO molecules to produce 3 CO₂ molecules.
• The balanced equation is:

Fe₂O₃ + 3CO → 2Fe + 3CO₂

• From the balanced equation:
• 1 mole of Fe₂O₃ reacts with 3 moles of CO to produce 2 moles of Fe.
• For 1 mole of Fe to be formed, half the amount of reactants is required: 1 mole of Fe₂O₃ reacts with 1.5 moles of CO.

Thus, for 1 mole of Fe to be formed, 1.5 moles of CO are needed.

Therefore, the correct answer is 1.5 moles of CO.

CONCEPT:

Henry's Law

• Henry's Law states that the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid.
• The mathematical expression for Henry's Law is:

S = k_H × P

• S = Solubility of the gas (in Molarity, M)
• k_H = Henry's Law constant (M/bar)
• P = Pressure of the gas (in bar)
• From this expression, if the pressure changes, the solubility changes proportionally.

EXPLANATION:

• Given data:
• Solubility of N₂ at 1 bar = 6.9 × 10^-4 M
• Pressure of N₂ = 1 bar
• From Henry's Law:

k_H = S / P = (6.9 × 10^-4 M) / (1 bar) = 6.9 × 10^-4 M/bar

• When the pressure changes to 0.8 bar:

S = k_H × P = (6.9 × 10^-4 M/bar) × (0.8 bar)

S = 5.5 × 10^-4 M

Therefore, the solubility of nitrogen in water at 0.8 bar is 5.5 × 10^-4 M, which corresponds to option 4.