Average Effective Dipole moment

In summary, we are given the water relative permitivity of 81 and an electric field of E=x[V/m] (x unit vector) inside the water. We are asked to find the vector P(dipole polarization per unit volume). Assuming a density of 1000[kg/m3] and 3.34 × 1025 molecules per kg of water, we can calculate an average effective dipole moment of each water molecule when E= x[V/m]. This dipole moment is induced by the applied electric field, which causes the molecules to align preferentially along the field. We can also calculate the displacement angle (the angle between the x-axis and the angle of each dipole inside the water) using trigonometry
  • #1
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Homework Statement



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)?

Then

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.




Homework Equations


X = eps - 1 and P=eps0*X*E
P=Nv(p) or P=1/ΔVƩ(p)

The Attempt at a Solution


X=81-1 = 80
And so P=eps080x
From that I would plug into the other equation correct, but i am not sure what to do once i have that plugged in for P and what to plug into for the rest
 
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  • #2
So I found out the average dipole moment by doing

80eph0/(Density of water)(# molecules of water) and got 2.119e-38 [C*m]

Now it ask for the displacement angle (the angle between the x-axis and the angle of the each dipole inside the water) when the E field is 1.0x. Since the E field is in the x direction only would the displacement angle be zero since the E field runs along the x axis
 
  • #3
I need to be able to prove this if this is true and i don't really have any formula for finding a displacement angle. I assume it has something to do with using trig but I am not 100%

P=ε080 x
Average dipole moment is 2.119e-38 [C*m]
E = 1.0 x

And I am assuming the values are correct.
 

1. What is an average effective dipole moment?

An average effective dipole moment is a measure of the polarity of a molecule, which is determined by the distribution and magnitude of the charges within the molecule. It is a vector quantity that takes into account both the magnitude and direction of the dipole moment.

2. How is the average effective dipole moment calculated?

The average effective dipole moment is calculated by multiplying the distance between the charges in a molecule by the magnitude of the charges and the cosine of the angle between them. This calculation takes into account the distribution of charges within the molecule and provides a single value to represent the overall polarity of the molecule.

3. What factors affect the average effective dipole moment?

The average effective dipole moment is affected by the electronegativity of the atoms in a molecule, the shape and symmetry of the molecule, and the distance between the charges. Asymmetric molecules with large differences in electronegativity between atoms tend to have larger dipole moments.

4. What is the importance of the average effective dipole moment in chemistry?

The average effective dipole moment is important in understanding the physical and chemical properties of molecules. It affects the molecule's polarity, solubility, and reactivity. For example, molecules with larger dipole moments tend to have stronger intermolecular forces and therefore higher boiling points.

5. How is the average effective dipole moment experimentally determined?

The average effective dipole moment can be experimentally determined using techniques such as infrared spectroscopy and dielectric measurements. Infrared spectroscopy measures the vibrational modes of a molecule, which can provide information about the distribution of charges. Dielectric measurements measure the molecule's response to an external electric field, which can indicate the polarity of the molecule.

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