# Average effective dipole moment?

In summary, the conversation discusses determining the average effective dipole moment of water molecules when an electric field is applied. It mentions the density and number of molecules in water, as well as the dielectric constant and polarization per unit volume. The concept of effective dipole moment is explained, as well as its relation to the real dipole moment per molecule. Guidance is requested for the second part of the original question.

Hi ,
I crashes myself with this problem about diploe.
Please can I have some suggestions.

Assume that the density of water is 1000 [kg/m3]
and that there are 3.34 × 1025 molecules per kg of water. (One mole of water weighs 18.0[g] since atomic weight of water is 18.0. A mole contains a number of molecules that is equal to Avogadro number (6.02 × 10^23)).

Determine an average effective dipole moment of each water molecule when E= x [V/m].(x is unit vector)

Note: each molecule of water has dipole moment. The average dipole moment,
however, is zero since these dipole moments are randomly oriented. The average effectivedipole moment px is induced by the applied electric filed because the molecules are preferentially oreinted along the field.

they also talk about average effective dipole moment, I don't know what they mean by that!

thank you
B

You also need the dielectric constant of water. Then you can work out the polarization per unit volume.

You are correct in fact it was the preceding problem.

the question was :
water relative permitivity is about 81. If the electric field E=x[V/m] (x unit vector) is inside the water, what is the vector P(dipole polarization per unit volume)?

I found P=7.08x10^(-10)x

I don't know if I am right.
Then can you please give me some guidance for the second part(original post)?

Thank you

The dipole per unit volume should be in units of charge*length/length^3 = charge/length^2

The relevant eqns are:

Er=1+X
where Er is relative permittivity, X is susceptibility. Both are dimensionless.

X=<P>/E eps0

where E is applied field, eps0 is perm. of free-space.

Average effective dipole moment is presumably just the dipole per unit volume / Number of molecules per unit vol. i.e., the dipole per molecule.

It's an 'effective' dipole, because, as the question says- for zero field, the ave. net dipole per unit volume is zero- but it doesn't follow that the dipole per molecule is zero (even though the 'effective' dipole per molecule is zero).

That's because though each molecule has a dipole in zero ext. field, the molecules are all pointing in random orientations- so the addition of all those dipole vectors comes to zero (per unit volume).

So, the effective dipole is not the same as the real dipole moment per molecule.

Thank you very much christianjb

## What is an average effective dipole moment?

An average effective dipole moment is a measure of the overall polarity of a molecule. It takes into account the individual dipole moments of the bonds within the molecule, as well as their orientations.

## How is the average effective dipole moment calculated?

The average effective dipole moment is calculated by summing the individual dipole moments of all the bonds in the molecule, taking into account their orientations, and dividing by the total number of bonds. This results in a vector quantity, with both magnitude and direction.

## What are the units of average effective dipole moment?

The units of average effective dipole moment are typically measured in Debye (D), which is equivalent to 3.336 x 10^-30 Coulomb-meter (Cm).

## How does the average effective dipole moment affect a molecule's properties?

A molecule with a larger average effective dipole moment will have a stronger overall polarity, which can affect its solubility, reactivity, and intermolecular forces. This can also impact the molecule's physical properties, such as melting and boiling points.

## Can the average effective dipole moment change?

Yes, the average effective dipole moment of a molecule can change depending on its conformation or when it undergoes a chemical reaction. Additionally, the environment in which the molecule is placed can also affect its average effective dipole moment.