States Of Matter

C * = Most probable speed
= Average speed =
C = Root square speed corrected as root means square speed, i.e
and as we know

NOTE
As no option correspond to root square speed, it is understood as misprint. It should be root mean square speed.

Compressibility factor

(For one mole of real gas)

van der Waal equation



At low pressure







So,

At high pressure and low temperature, gaseous atoms or molecules get closer to each other and van der Waal forces operates. So molecules or atoms start attracting each other. Hence a gas deviate the most from its ideal behaviour. While in ideal behaviour we consider that gases do not attract each, i.e., there is no intermolecular forces of attraction.

hydrogen bond is dipole-dipole intraction

at very high pressure
so, is negligible


compremibilityfactor

Answer (a)

Answer (b) At very low temperature, real gases show ideal behaviour

air escaped from vessel, air remain
is vessel , P, V constant

For

Step 1: Understanding the Question:
The question asks for the relationship between the interaction energy of London dispersion forces and the distance `r` between the particles.
Step 2: Key Formula or Approach:
This is a direct question based on the theory of intermolecular forces. We need to recall the distance dependence of the potential energy for different types of van der Waals forces.
Step 3: Detailed Explanation:
Intermolecular forces are categorized into several types. The London dispersion force is a type of van der Waals force that arises from temporary, fluctuating dipoles in nonpolar molecules.
The potential energy (U) of interaction between molecules depends on the distance `r` between them.
- For ion-dipole interaction, U 1/r .
- For dipole-dipole interaction (Keesom forces), U 1/r for rotating dipoles and U 1/r for stationary dipoles.
- For dipole-induced dipole interaction (Debye forces), U 1/r .
- For London dispersion forces (induced dipole-induced dipole), the interaction energy is also proportional to 1/r .
Therefore, the interaction energy U is proportional to , which can be written as .
The question states the energy is proportional to r . Comparing this with our finding, we get x = -6.
Step 4: Final Answer:
The value of x is -6. This corresponds to option (D).

Step 1: Understanding the Concept:
Boyle's Law states that for a fixed mass of an ideal gas at a constant temperature, the pressure of the gas is inversely proportional to its volume.
This means the product of pressure and volume remains constant.
Step 2: Key Formula or Approach:
From the ideal gas equation:

At constant temperature ( ) and constant amount of gas ( ), the term is a constant.
Therefore, .
Step 3: Detailed Explanation:
Since is a constant, its value does not change regardless of the pressure applied to the gas.
If we plot on the y-axis and on the x-axis, the graph will be a straight line with a slope of zero.
This results in a horizontal line parallel to the pressure axis.
The other graphs represent different relationships:
- Graph A shows directly proportional to , which is incorrect.
- Graph B shows inversely proportional to , which is incorrect.
- Graph C shows a hyperbolic relationship, which usually describes vs , not vs .
Step 4: Final Answer:
The correct plot is a horizontal line, as shown in option (D).

Step 1: Understanding the Question:
The question asks for the units of the van der Waals constant 'a' based on the van der Waals equation.
Step 2: Key Formula or Approach:
The principle of dimensional homogeneity states that quantities can be added or subtracted only if they have the same physical dimensions. In the van der Waals equation, the term is added to the pressure . Therefore, the units of must be the same as the units of pressure .
Step 3: Detailed Explanation:
Let's rearrange the equation to solve for the units of 'a'.
We are given the units in one of the options as atm, dm (since dm = L, a common unit for volume), and mol. Let's use these units.

Unit of Pressure (P) = atm
Unit of Volume (V) = dm
Unit of moles (n) = mol
Now, substitute these into the equation for the units of 'a'.
Step 4: Final Answer:
The unit of the parameter 'a' is atm dm mol , which matches option (B).

Step 1: Understanding the Question:
Two flasks containing nitrogen gas at different conditions are connected. We need to find the final equilibrium pressure after the valve is opened. Since the flasks are not thermally insulated, we assume the system is isolated, so the total internal energy is conserved.
Step 2: Calculate Initial Moles in Each Flask:
Molar mass of N = 28.0 g/mol.
- Flask I: mol. T = 300 K, V = 1 L.
- Flask II: mol. T = 60 K, V = 2 L.
Step 3: Determine the Final State:
When the valve is opened, the gases mix.
- Total moles, mol.
- Total volume, m .
To find the final temperature, , we use the conservation of internal energy. For an ideal diatomic gas like N , .


Setting :

K.
Step 4: Calculate Final Pressure:
Using the Ideal Gas Law, .
Step 5: Convert to bar and find x:
1 bar = 10 Pa.
We are given bar.
The value of x as an integer is 84.

Step 1: Ideal gas law is . Acetylene is (Molar mass ).
Step 2: .
Step 3: .
Step 4: .
Step 5: . Rounding to the nearest integer, .

Step 1: Volume is constant ( ). Use Gay-Lussac's Law: .
Step 2: Convert initial temperature to Kelvin: K.
Step 3: Substitute values: .
Step 4: K.
Step 5: Convert back to Celsius: .

Concept:

Sublimation is the direct conversion of a solid into vapour without passing through the liquid phase.
Boiling occurs when vapour pressure of a liquid equals external atmospheric pressure.
Step 1: Verification of Statement I. Certain solids like camphor, ammonium chloride, and naphthalene undergo sublimation. This property is used to purify such substances.
Step 2: Verification of Statement II. When external pressure is reduced, the vapour pressure equals atmospheric pressure at a lower temperature. Conclusion: Both Statement I and Statement II are correct.

Step 1: Sublimation.
Sublimation is indeed a purification process used to separate substances that change directly from solid to gas without going through the liquid phase. This is a common process for certain solids like iodine and dry ice.
Step 2: Boiling point and pressure.
The boiling point of a substance is influenced by the atmospheric pressure. If the pressure is lowered, the boiling point decreases. This is because less energy is required for the substance to vaporize.
Step 3: Conclusion.
Both statements are correct, so the correct answer is (1).