# Dielectric constant for water (fwd)

```Sender: venkat@poly.chem.vt.edu (Venkat Vasudevan)
Subject: WSN: Dielectric constant for water

Hi netters,
Seems like a trivial question but I am puzzled. I am using well known
data on dipole moment (1.86 Debye) and polarizability volume (1.47 Ang^^3) of
water to calculate its dielectric constant at 298 K.
I am using the well known Debye equation, namely,

(eps' -1)/(eps'+2) = Pm*rho/Mm          where

Pm = [Nav/(3*eps0)] * {alpha + mu**2/3kT}  is the molar polarizabilty.
rho is the density (g/cm3) and Mm is the molar mass in g/mol.

Here eps' -dielectric constant, eps0- vac.permitivity= 8.854 E-12  C^^2/(J M)
alpha is the polarizability, mu is the dipole moment and k is the Boltzman
constant (1.38E-23 J/K). The unit of debye in SI units is 1 D = 3.336E-30 C
Metre.

My problem arises with the second part of evaluating Pm.i.e., the permanent
dipole moment part.

For ex. when mu= 1.86 Debye= 1.86 x 3.336 E-30 C M. then

Pm (dipole) = [Nav/(3*eps0)] * mu**2/3kT = [6.023E23/3*8.854E-12]*
{3.850E-59/3*1.38E-23*298) = 7.076E-05 M^^3/mol.

To convert from M3 to Cm3, multiply by 1.0e6. This gives a total value of
Pm = 70.05 . If the polariability part was neglected (just argument sake)
then

(eps'-1)/(eps'+2) = 70.05 (cm3/mol)* 1.00 (g/cm3)/ 18.0 (g/mol)= 3.93.

This would give an eps' value to be negative which is ridiculous. Where is
the problem? I know it is somewhere in the conversion. But I checked a lot
of times and it seems right. Can anyone spot the mistake? Thanks in advance.
BTW, the dielectric constant for water is around 78.5 (eps').

Venkat

```