The Kinetic Theory Of Gases

Step 1: Hydrogen makes up about 75% of the baryonic mass of the universe. However, Earth's troposphere is dominated by (78%) and (21%). Statement A is true.
Step 2: Hydrogen is indeed the lightest element (atomic mass ). Statement R is true.
Step 3: Because it is so light, Hydrogen molecules have high thermal velocities that exceed Earth's escape velocity. Consequently, most primordial hydrogen escaped into space, which is why it's rare in our atmosphere. Thus, R explains A.

Step 1: Understanding the Concept:
Methane behaves as an ideal gas, so we can use the ideal gas equation to find the number of moles present in the given volume at a specific pressure and temperature.
The total mass of the gas is the product of the number of moles and the molar mass of methane.
Step 2: Key Formula or Approach:
1. Ideal Gas Law: .
2. Mass: .
Step 3: Detailed Explanation:
1. Convert Units:
Volume .
Since , .
Molar mass of ( ) = .

2. Calculate Moles ( ):



3. Calculate Mass ( ):


Rounding to the nearest integer, .
Step 4: Final Answer:
The value of is 26.

As temperature increases, solubility first decreases then increases, hence first increases, then decreases. At moderate temperature, the value of follows the order:

Step 1: Understanding the Concept:
Molar heat capacity ( ) depends on the degrees of freedom available to the substance in its current phase (solid, liquid, or gas) and its molecular complexity.
Step 2: Detailed Explanation:
1. Helium (g): Helium is a monatomic gas. Its molar heat capacity at constant pressure ( ) is approximately .
2. Copper (s): According to the Dulong-Petit Law, the molar heat capacity of most solid elements is approximately .
3. Bromine (l): Bromine is a liquid at room temperature and is diatomic ( ). Liquids generally have much higher molar heat capacities than solids or gases because they possess many vibrational, translational, and rotational modes, along with strong intermolecular interactions. For Bromine (l), .

Comparing the values: .
Therefore, the order is Bromine(l) >Copper(s) >Helium(g).
Step 3: Final Answer:
The correct order of molar heat capacities is Bromine(l) >Copper(s) >Helium(g).

Step 1: Understanding the Concept:
Heat capacity at constant pressure ( ) and constant volume ( ) are related by Mayer's formula for an ideal gas: . Additionally, the First Law of Thermodynamics ( ) governs the energy distribution during these processes.

Step 2: Key Formula or Approach:
1. Mayer's Relation: . Since is a positive constant, . 2. Constant Volume Process: .

Step 3: Detailed Explanation:
1. Statement I analysis: According to Mayer's relation, is always greater than because at constant pressure, heat is used for both increasing internal energy and doing expansion work. Thus, Statement I is false. 2. Statement II analysis: In an isochoric (constant volume) process, work done is zero. Therefore, . All heat added increases the internal kinetic energy (chaotic motion) of the molecules, leading to a temperature rise. Thus, Statement II is true.

Step 4: Final Answer:
Statement I is false, but Statement II is true.

Step 1: Understanding the Concept:
Osmotic pressure depends on the total concentration of dissolved particles (osmolarity). A semi-permeable membrane allows solvent (water) to pass but blocks solute particles (ions). Hypotonic solutions have lower particle concentration compared to another.

Step 2: Key Formula or Approach:
1. Van't Hoff factor = total ions produced upon dissociation.
2. Osmotic concentration = .

Step 3: Detailed Explanation:
Side 'x' ( ): Dissociates into . Thus, .
Conc .
Side 'y' ( ): Dissociates into . Thus, .
Conc .
- (A) False: Ions don't pass membrane; Prussian blue reaction cannot happen.
- (B) False: Definition of semi-permeable membrane is that solutes cannot pass.
- (C) True: Side 'y' has lower osmolarity ( ), so it is hypotonic.
- (D) False: To stop or reverse osmosis, a specific minimum pressure (osmotic pressure difference) must be applied, not "any value".

Step 4: Final Answer:
Statement (C) is correct.

Step 1: Determine electronic configuration of each ion.
All complexes are low spin octahedral.
Step 2: Count unpaired electrons in low spin case.
Step 3: Arrange in decreasing order.

Final Answer: