Question

What is the Intermolecular distance in HCl if EN in H and Cl is 2.1 and 3 and Intermolecular distance between H2 and Cl2 is 1.98 and 0.74

Answer 1

The calculated intramolecular bond length of HCl is 1.279 Å.

Answer 2

The question asks for the "Intermolecular distance in HCl". However, the provided information—electronegativity values of H and Cl, and distances associated with $H_2$ and $Cl_2$ (0.74 Å and 1.98 Å)—are characteristic of intramolecular bond lengths of these molecules, not intermolecular distances. Intermolecular distances are typically much larger and relate to van der Waals forces or crystal structures. Given the context of JEE/NEET level questions, it is highly probable that the term "Intermolecular distance" is a misnomer for "intramolecular bond length".

We will proceed to calculate the intramolecular bond length of HCl using the given data.

Step 1: Determine Covalent Radii The bond length in a homonuclear diatomic molecule (like $H_2$ or $Cl_2$) is approximately twice the covalent radius of the atom.

• For $H_2$: The bond length is given as 0.74 Å. $2 \times r_H = 0.74 \text{ Å}$ $r_H = \frac{0.74}{2} \text{ Å} = 0.37 \text{ Å}$
• For $Cl_2$: The bond length is given as 1.98 Å. $2 \times r_{Cl} = 1.98 \text{ Å}$ $r_{Cl} = \frac{1.98}{2} \text{ Å} = 0.99 \text{ Å}$ These inferred covalent radii (0.37 Å for H and 0.99 Å for Cl) are consistent with standard literature values.

Step 2: Calculate Electronegativity Difference The electronegativity values for Hydrogen (H) and Chlorine (Cl) are given as 2.1 and 3.0, respectively. The difference in electronegativity ($\Delta EN$) is crucial for determining the polarity of the bond and its length. $\Delta EN = |EN_{Cl} - EN_H|$ $\Delta EN = |3.0 - 2.1|$ $\Delta EN = 0.9$

Step 3: Estimate Bond Length using Pauling's Formula Pauling's formula is used to estimate the bond length ($d_{AB}$) of a polar covalent bond between atoms A and B. It considers the sum of their covalent radii and a correction factor based on the electronegativity difference: $d_{AB} = r_A + r_B - C \cdot |\Delta EN|$ Where:

• $r_A$ and $r_B$ are the covalent radii of atoms A and B.
• $\Delta EN$ is the absolute difference in electronegativity between A and B.
• $C$ is an empirical constant, commonly taken as 0.09 Å.

Applying this formula to HCl: $d_{HCl} = r_H + r_{Cl} - 0.09 \cdot |\Delta EN|$ Substituting the values: $d_{HCl} = 0.37 \text{ Å} + 0.99 \text{ Å} - 0.09 \cdot |0.9|$ $d_{HCl} = 1.36 \text{ Å} - 0.09 \cdot 0.9$ $d_{HCl} = 1.36 \text{ Å} - 0.081 \text{ Å}$ $d_{HCl} = 1.279 \text{ Å}$

The calculated bond length of HCl is approximately 1.279 Å. This value is very close to the experimentally determined bond length of HCl (1.274 Å).

Note: A simpler approximation would be to just sum the covalent radii ($0.37 + 0.99 = 1.36$ Å), which is also the average of the given $H_2$ and $Cl_2$ bond lengths. However, Pauling's formula is more accurate as it accounts for the polarity of the bond.