Physical Chemistry

Step 1: Start with van der Waals constants.
For a real gas, At the critical point: Step 2: Express (the volume correction factor) in terms of , , and .
From the expression: Substitute into the expression: Step 3: Conclusion.
The volume correction factor .

To determine the bond order, we use the molecular orbital theory, where the bond order is given by: We calculate the bond order for each species:
- N : Bond order = 3 (from molecular orbital theory).
- F : Bond order = 1 (since the bonding electrons fill the orbitals and anti-bonding orbitals reduce the bond order).
- NO : Bond order = 3 (because of the removal of one electron).
- O : Bond order = 2 (adding one extra electron).
- N : Bond order = 2 (loss of one electron reduces the bond order).
- CO: Bond order = 3.
- O : Bond order = 2.
- O : Bond order = 1.
The species with a bond order of 3 are: N , NO , CO.
Final Answer:

The rotational frequency of a molecule is related to its moment of inertia. The moment of inertia of a molecule is given by: where is the reduced mass and is the bond length.
For isotopic substitution, the reduced mass changes, affecting the rotational frequency. The reduced mass for a molecule with two atoms is: For , we have: The ratio of the rotational frequencies for and will be inversely proportional to the square root of the reduced masses: Since the mass of oxygen increases from 16 to 18, the frequency will decrease. The change in the frequency can be calculated using the ratio of the reduced masses. The first absorption for occurs at 3.84 cm , so: Using the known masses, the frequency for is approximately . Final Answer:

Step 1: VSEPR theory.
VSEPR (Valence Shell Electron Pair Repulsion) theory helps in determining the molecular geometry by considering the repulsion between electron pairs around the central atom.
Step 2: Geometries of the species.
- PCl has 5 bonds and 0 lone pairs on the central phosphorus atom, leading to a trigonal bipyramidal geometry.
- SF has 4 bonds and 1 lone pair, giving it a trigonal bipyramidal geometry with a see-saw shape.
- ClF has 3 bonds and 2 lone pairs on the central chlorine atom, resulting in a T-shaped geometry, not trigonal bipyramidal.
- I is a single atom and cannot have a trigonal bipyramidal geometry.
- Sb(Ph) has 5 bonds and no lone pairs on the central antimony atom, which gives a trigonal bipyramidal geometry.
- BrF has 5 bonds and 0 lone pairs on the central bromine atom, which also has a square pyramidal geometry, not trigonal bipyramidal.
Step 3: Conclusion.
The correct species with trigonal bipyramidal geometry are PCl and SF , so option (A) is correct.
Final Answer:

Step 1: Understanding the dipole moment.
The dipole moment of a molecule is influenced by the electronegativity difference between atoms, the molecular shape, and the presence of any polar bonds. A greater electronegativity difference between atoms, particularly in the case of the halogens and oxygen, leads to a greater dipole moment.
Step 2: Analyzing the compounds.
- Fluoromethane has the highest dipole moment because fluorine is the most electronegative element, creating a strong dipole.
- Chloromethane has a slightly lower dipole moment than fluoromethane because chlorine is less electronegative than fluorine.
- Methanol has a significant dipole moment due to the highly polar O-H bond, but the dipole moment is less than that of fluoromethane and chloromethane because the C-H bonds are not polar enough to add much to the dipole moment.
- Dimethylether has the smallest dipole moment because the two C-O bonds cancel each other out, and it has no highly electronegative atoms like fluorine or chlorine.
Step 3: Conclusion.
The correct order of the dipole moments is: chloromethane>fluoromethane>methanol>dimethylether. Final Answer:

Step 1: Understanding asymmetric top molecules.
Asymmetric top molecules are those in which the three moments of inertia are all different. These molecules lack a plane of symmetry and have no special symmetry in their rotational properties.
Step 2: Analyzing the options.
- (D) CH OH, H O, and H CO are examples of asymmetric top molecules because they all have different moments of inertia.
- The other options contain molecules that either have a plane of symmetry or do not satisfy the condition of having three different moments of inertia.
Step 3: Conclusion.
The correct set of asymmetric top molecules is option (D).
Final Answer:

Step 1: Understanding ion-dipole interactions.
Ion-dipole interactions occur between an ion and a polar molecule (such as water). The strength of this interaction depends on the charge of the ion and the dipole moment of the polar molecule, and it generally decreases with the distance between them.
Step 2: Dependence on distance.
The ion-dipole interaction is inversely proportional to the square of the distance between the ion and the dipole molecule, meaning it follows the relation , where is the distance between the ion and the dipole.
Step 3: Conclusion.
The correct relationship for ion-dipole interactions with distance is .
Final Answer: