A water molecule has a net dipole moment of 6.2*10^-30 C-m because oxygen is mor

Question

A water molecule has a net dipole moment of 6.2*10^-30 C-m because oxygen is more electronegative than hydrogen. Assuming the geometrical structure of the water molecule given below, what is the dipole moment of each O-H bond? What is teh excess positive charge on each H atom? If a water molcule is in a uniform electric field of 100 N/C, what is the maximum torque it can feel? What is the maximum energy difference between any two orientations?

A water molecule has a net dipole moment of 6.2*10^-30 C-m because oxygen is more electronegative than hydrogen. Assuming the geometrical structure of the water molecule given below, what is the dipole moment of each O-H bond? What is the excess positive charge on each H atom? If a water molecule is in a uniform electric field of 100 N/C, what is the maximum torque it can feel? What is the maximum energy difference between any two orientations?

Explanation / Answer

1)

from the geometry of H2O molecule

Net Dipole moment oh H2O = 2*dipole moment of each O-H bond*cos(104.5/2 degree)

so,

dipole moment of each O-H bond = Net Dipole moment oh H2O / (2*cos(104.5/2 degree) )

==> dipole moment of each O-H bond = 6.2*10^-30/(2*cos(104.5/2 degree)) = 5.1*10^-30 C-m

2)

we have , charge of dipole = q = 2*excess charge on each H atom

so,

Dipole moment = p = q*d

q = p/d = 6.2*10^-30/(96*10^-12) = 6.45*10^-20 C

so,

excess charge on each H atom = 6.45*10^-20/2 = 3.225*10^-20 C

3)

torque = P*E*sin(theta)

so,

max. torque when theta=90 ... it means sin(theta) = 1

max. Torque = P*E = 6.2*10^-30*100 = 6.2*10^-28 N-m

4)

Energy difference = -P*E*cos(theta)

so,

max. when theta=0 ... it means cos(theta) = 1

so,

Max. Energy difference = -P*E = -6.2*10^-28 J

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