CONCEPT:

Dipole Moment in Triatomic Molecules (XY₂)

• In a triatomic molecule XY₂, the dipole moment depends on the bond angle (θ) between the two Y atoms attached to the central X atom.
• Dipole moment is a vector quantity; for maximum dipole moment, the individual dipole vectors between X-Y bonds should not cancel each other out entirely.
• When the bond angle is 180°, the two dipole vectors are directly opposite and equal, leading to complete cancellation of dipole moments, resulting in a net dipole moment of zero.
• As the bond angle decreases from 180° to 90°, the dipole vectors start to align in a way that results in a net dipole moment, as the vectors no longer cancel each other fully.

EXPLANATION:

• θ = 90°: At this bond angle, the two dipole moments are closer to each other and do not fully cancel out. This arrangement produces a relatively high net dipole moment.
• θ = 120°: At this angle, the two dipole moments partially cancel each other but not completely. This configuration produces a moderate dipole moment.
• θ = 180°: At this linear angle, the dipole moments are opposite in direction and equal in magnitude, resulting in complete cancellation and a net dipole moment of zero.

MAXIMUM DIPOLE MOMENT:

• Among the given bond angles, θ = 90° gives the maximum dipole moment because the two dipole vectors have minimal cancellation, producing the highest possible net dipole moment for the molecule.

CONCLUSION:

The correct option is: Option 1 (θ = 90°)

CONCEPT:

Enthalpy Change for Temperature Variation

• The enthalpy change (ΔH) for a substance with variable heat capacity C_p can be calculated using the integral: 
• If C_p is given as a function of temperature, integrate over the given temperature range.
• For this problem, we are given C_p = 23 + 0.01T  and need to calculate ΔH from 300 K to 1000 K for 3 moles of silver.

CONCEPT:

Order of Reaction and Linear Plots

CONCLUSION:

The correct option is: Option 2) first - order kinetics

CONCEPT:

Concentration of a Solution (Molarity)

CONCLUSION:

The correct option is: Option 3 (0.005 M)

CONCEPT:

Isotherms on a Pressure-Volume P-V Diagram

• In thermodynamics, an isotherm represents a line on a Pressure-Volume P-V diagram where the temperature remains constant. Each curve on a P-V diagram shows how pressure and volume are related at a specific constant temperature.
• According to the Ideal Gas Law, PV = nRT , where:
  • P is the pressure of the gas,
  • V is the volume of the gas,
  • n is the number of moles of gas,
  • R is the ideal gas constant,
  • T is the temperature in Kelvin.
• For a given amount of gas n constant and a fixed temperature T constant, as the volume V changes, the pressure P changes in a way that keeps the product PV constant. This is the basis of an isothermal curve.
• Higher Temperature and Isotherms: As temperature increases, the product PV increases, which means that for the same pressure, the volume will be larger at higher temperatures. Thus, isotherms at higher temperatures are located further from the origin on a P-V diagram.

EXPLANATION:

• In the given P-V diagram, there are three isothermal curves labeled as T₁, T₂, and T₃.
• The position of these isotherms on the graph with T₁ being the top curve, followed by T₂ and then T₃ indicates the relative temperatures of each curve:
  • Since isotherms at higher temperatures are further away from the origin, the isotherm labeled T₁ represents the highest temperature.
  • The next isotherm, T₂, represents a lower temperature than T₁.
  • The lowest isotherm, T₃, represents the lowest temperature among the three.
• Therefore, the order of temperatures is:
  T₁ > T₂ > T₃

CONCLUSION:

The correct option is: Option 2 T₁ > T₂ > T₃

Concept:

To calculate the vapor pressure of a solution, we use Raoult's Law, which states:

Conclusion:

The vapor pressure of water at 293K when 30g of glucose is dissolved in 450g of water is approximately 17.80 mm Hg.

CONCEPT:

Calculating Oxidation Number

• The oxidation number of an atom in a compound can be calculated based on the known oxidation states of other atoms and the overall charge of the molecule.
• In this case, we use the oxidation states of hydrogen (H), nitrogen (N), and carbon (C) in the compound HNC.
• We assume the typical oxidation states: H = +1 and N = -3 (for simple compounds), and solve for C.

CALCULATION:

• For the compound HNC, the sum of the oxidation numbers must equal zero, as it is a neutral molecule.
• Let the oxidation number of C be  x .
• Applying the rule:
  • Oxidation number of H = +1
  • Oxidation number of N = -3
  • Equation: (+1) + (x) + (-3) = 0 
  • Simplifying: x - 2 = 0 → x = +2 

CONCLUSION:

• The correct option is: Option 1 (+2)

CONCEPT:

Second Order Reaction Kinetics

Concept:

Colligative properties are properties of solutions that depend on the number of solute particles but not on their nature. These properties include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure. Intensive properties are those that are independent of the amount of material present.

Explanation:

• Statement I: Except for osmotic pressure, all other colligative properties depend on the nature of the solvent.

  • This statement is incorrect because all colligative properties, including osmotic pressure, depend on the number of particles in the solution and not on the nature of the solvent.

• Statement II: Colligative properties are intensive properties.

  • This statement is correct because colligative properties do not depend on the quantity of the solvent or solute, but rather on the ratio of their quantities.

Conclusion:

Therefore, the correct option is: Statement I is INCORRECT, but Statement II is CORRECT

CONCEPT:

Oxidation Numbers in Different Compounds

• The oxidation number of an element in its elemental form is zero. For example, in S₈, each sulfur atom has an oxidation number of 0.
• In compounds, we calculate the oxidation number by assigning known oxidation states to other elements in the compound and solving for the unknown oxidation state of sulfur.
• In H₂S, the oxidation state of hydrogen is +1. In S₂F₂, fluorine has an oxidation state of -1.

• Let the oxidation number of each sulfur atom be x.
• The molecule has two sulfur atoms and two fluorine atoms. Since fluorine has an oxidation number of -1, we can set up the equation:

CONCLUSION:

• The correct option is: Option 1 (0, +1, -2)