The Valence Shell Electron Pair Repulsion Vsepr Theory

: Linear geometry (AX E )
: Square planar (AX E )
: Trigonal pyramidal (AX E )
These geometries follow VSEPR theory.

The bond angles in molecules are determined by the repulsion between electron pairs around the central atom, according to the VSEPR (Valence Shell Electron Pair Repulsion) theory.
I.
: The central atom is oxygen (O).
It has 6 valence electrons.
In , it forms two bonds with hydrogen atoms and has two lone pairs of electrons.
The electron pair geometry is tetrahedral (4 electron pairs), and the molecular geometry is bent.
The bond angle is approximately 104.
5°.
The two lone pairs cause greater repulsion, reducing the bond angle from the ideal tetrahedral angle of 109.
5°.
II.
: The central atom is nitrogen (N).
It has 5 valence electrons.
In , it forms three bonds with hydrogen atoms and has one lone pair of electrons.
The electron pair geometry is tetrahedral (4 electron pairs), and the molecular geometry is trigonal pyramidal.
The bond angle is approximately 107°.
The single lone pair causes repulsion, reducing the bond angle from 109.
5°.
The repulsion is less than in due to only one lone pair.
III.
: The central atom is carbon (C).
It has 4 valence electrons.
In , it forms four bonds with hydrogen atoms and has no lone pairs of electrons.
The electron pair geometry is tetrahedral (4 electron pairs), and the molecular geometry is also tetrahedral.
The bond angle is 109.
5°.
There are no lone pairs to cause additional repulsion.
IV.
: The central atom is sulfur (S).
It has 6 valence electrons.
In , it forms two double bonds with oxygen atoms and has one lone pair of electrons.
The electron pair geometry is trigonal planar (3 electron pairs), and the molecular geometry is bent.
The ideal bond angle for trigonal planar is 120°.
The presence of a lone pair causes repulsion, reducing the bond angle to approximately 119°.
The double bonds also contribute to greater electron density and thus more repulsion than single bonds, which can affect the bond angle.
However, the dominant factor here is the trigonal planar electron pair geometry and the effect of the lone pair.
Comparing the approximate bond angles: ( )> ( )> ( )> ( ) The correct order of bond angles is IV>III>II>I.

- Molecule A ( ): T-shaped, as it follows the structure of a tri-atomic molecule with three bonding pairs and two lone pairs.
- Molecule B ( ): T-shaped due to the presence of three bonding pairs and two lone pairs on the central atom.
- Molecule C ( ): Angular shape, due to two bonding pairs and two lone pairs on oxygen.
- Molecule D ( ): See-saw shape, with four bonding pairs and one lone pair on sulfur.

Step 1: Understanding the problem.
The question asks for the total number of angular nodes of orbitals associated with the third shell .
The angular nodes are associated with the azimuthal quantum number . Step 2: Finding the value of .
For , the possible values of are:
for the -orbital
for the -orbital
for the -orbital
Step 3: Counting the angular nodes.
The number of angular nodes for an orbital is equal to . So:
-orbitals ( ) have 0 angular nodes.
-orbitals ( ) have 1 angular node.
-orbitals ( ) have 2 angular nodes.
\ Step 4: Total number of angular nodes.
The total number of angular nodes is the sum of the angular nodes for each orbital type:
0 for the -orbitals, 1 for the -orbitals, and 2 for the -orbitals.
Total angular nodes = .
Step 5: Conclusion.
Thus, the correct answer is option (1).

Step 1: Kinetic Energy of an Ideal Gas The kinetic energy for an ideal gas is given by: where: - is the number of moles, - is the universal gas constant, - is the temperature in Kelvin. Step 2: Computing for Given 4 g of : Temperature conversion: Step 3: Computing for Given 6.4 g of : Temperature conversion: Step 4: Ratio of Kinetic Energy Since : Conclusion Thus, the correct answer is:

The root mean square (rms) velocity of gas molecules is given by , where R is the ideal gas constant, T is the absolute temperature (in Kelvin), and M is the molar mass of the gas (in kg/mol).
Let be the temperature of SO and be the temperature of O .
Let be the molar mass of SO and be the molar mass of O .
Given .
Squaring both sides and cancelling : Temperature of O : .
Molar masses: Sulfur (S) atomic mass g/mol.
Oxygen (O) atomic mass g/mol.
Molar mass of SO ( ) = g/mol.
Molar mass of O ( ) = g/mol.
The ratio of molar masses .
(Note: units g/mol cancel out, same as kg/mol for ratio).
Now calculate : So, the temperature of SO should be 600 K.
This matches option (3).

Step 1: Analyze Statement-I
Stronger intermolecular forces favor liquid or solid state, not gaseous state. Hence, statement-I is incorrect.
Step 2: Analyze Statement-II
More than 10 elements exist as gases at room temperature (e.g., all noble gases, N , O , H , etc.). Statement-II is incorrect.
Step 3: Conclusion
Both statements are incorrect.

This is the Van der Waals equation, which accounts for real gas behavior by modifying the ideal gas law. Here: - accounts for intermolecular forces (attraction), - accounts for the volume occupied by gas molecules. The correct form of the equation is (V - b) = RT, where is the pressure, is the volume, and is the temperature.

Using the ideal gas law :
- Option (1): At constant and , , so . This is a hyperbolic relationship, but over a small range, it approximates a straight line with a negative slope. Correct.
- Option (2): A positive slope contradicts . Incorrect.
- Option (3): At constant and , . Thus, P vs. has a negative slope, but this is less commonly emphasized compared to P vs. V.
- Option (4): At constant and , , so V vs. has a negative slope, not positive. Incorrect.
Option (1) is the most standard correct statement for ideal gases in this context.

Step 1: Analyze each statement Statement I: Glass is considered an extremely viscous liquid rather than a true solid. Statement II: Surface tension decreases with an increase in temperature due to weakening of cohesive forces. Statement III: For an ideal gas, compressibility factor , not zero. Step 2: Conclusion
Only statements I and II are correct.

The root mean square (rms) velocity of gas molecules is given by , where R is the ideal gas constant, T is the absolute temperature (in Kelvin), and M is the molar mass of the gas (in kg/mol).
Let be the temperature of SO and be the temperature of O .
Let be the molar mass of SO and be the molar mass of O .
Given .
Squaring both sides and cancelling : Temperature of O : .
Molar masses: Sulfur (S) atomic mass g/mol.
Oxygen (O) atomic mass g/mol.
Molar mass of SO ( ) = g/mol.
Molar mass of O ( ) = g/mol.
The ratio of molar masses .
(Note: units g/mol cancel out, same as kg/mol for ratio).
Now calculate : So, the temperature of SO should be 600 K.
This matches option (3).

Step 1: Kinetic Energy of an Ideal Gas The kinetic energy for an ideal gas is given by: where: - is the number of moles, - is the universal gas constant, - is the temperature in Kelvin. Step 2: Computing for Given 4 g of : Temperature conversion: Step 3: Computing for Given 6.4 g of : Temperature conversion: Step 4: Ratio of Kinetic Energy Since : Conclusion Thus, the correct answer is: