Question

What is the maximum torque on a molecule of HCl (dipole moment p = 3.60

Answer 1

A dipole is two equal & opposite charges, q, separated by a small distance "L".
The magniyude of the Dipole Moment is
p = qL

It is a vector defined as pointing along "L" from - to +
When placed in an E-field the charges will have equal & opposite forces on them, causing the Dipole to rotate and allign with the E-field.

The equal & opposite forces on the Dipole create a torque "T" which can easily be shown to have the magnitude;

T = pESin@

where the torque can be measured about any axis and where @ is the angle between the p & E vectors.
From inspection, maximum torque occurs when @ = 90 deg and Sin(90)=1

T(max) = pE = (3.6x10^-30)(3.1x10^4) = 11.16 x 10^-26 N-m

2)The law of motion for rotational dynamics is;
Net Torque = (Moment of Inertia) x (angular acceleration)
T = I(aa)
From above, when p & E are at 90deg the torque is pE, so use this for left side;
pE = I(aa)
E = I(aa)/p
= (2.7x10^-47)(2.93x10^21)/(3.6x10^-30)
= 2.2 x 10^4 N/C