Question

In the HCl molecule, the separation between the nuclei of the two atoms is about 1.27 Å (1 Å = 10-10 m). Find the approximate location of the CM 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

It is given that the separation between the nuclei of the H and Cl atoms is 1.27× 10 −10  m and Cl atom is 35.5 times as massive as H atom.

The following figure shows molecule of HCl with centre of mass at a distance x from Cl atom.

Let the mass of H atom be m, mass of Cl atom be 35.5m and distance of centre of mass from H atom be ( 1.27−x )× 10 −10  m.

Let us assume that, the centre of mass of the molecule is at origin. Then centre of mass is given as,

C.M.= ∑ ( m⋅x ) ∑ m

Substitute the values.

0= m( 1.27−x )+35.5x m+35.5m m( 1.27−x )+35.5x=0 x=−0.037× 10 −10  m

The negative sign shows that the centre of mass would lie at the left of the molecule.

Thus, the distance of centre of mass from H atom is,

( 1.27−x )× 10 −10 =( ( 1.27−0.037 )× 10 −10  m )( 1 A o 10 −10 m ) ≈1.24 A o

Therefore, the centre of mass of HCl molecule lies 1.24 A o from the H end.