Question

In the HCl molecule, the separation between the nuclei of the two atoms is about 1.27 Å. Find the approximate location of the center of mass (C.M) of the molecule, given that a chlorine atom is about 35.5 times as massive as a hydrogen atom, and nearly all the mass of an atom is concentrated in its nucleus.

Answer 1

The center of mass of the HCl molecule, given that chlorine is about 35.5 times as massive as hydrogen and the nuclei are separated by 1.27 Å, is approximately 1.26 Å, very close to the chlorine nucleus.

Step-by-step explanation:

To find the approximate location of the center of mass (C.M) of the HCl molecule, we use the concept of center of mass for a two-particle system. Given the separation distance between the hydrogen and chlorine nuclei is about 1.27 Å, and that the chlorine atom is approximately 35.5 times as massive as the hydrogen atom, we can set up a ratio.

The center of mass formula for a two-particle system is given by:

Center of Mass (C.M) = (m1 × x1 + m2 × x2) / (m1 + m2)

Let the location of hydrogen be x1 = 0 (taking it as a reference point), and the location of chlorine be x2 = 1.27 Å. Taking the mass of the hydrogen atom as 1 unit, the mass of the chlorine atom would be 35.5 units. Plugging into the formula:

C.M = (1 × 0 + 35.5 × 1.27) / (1 + 35.5)

After calculation:

C.M ≈ 1.26 Å

The center of mass is thus very close to the chlorine atom, reflecting its much greater mass in comparison to the hydrogen atom.