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Picture of molecules

The dielectric constant of a more polar molecule should be higher than a molecule which is less polar(polarity can be measured by dipole moment), so methanol should have higher dipole moment than water as $CH_3$ increase electron density around $O$ more than $H$ (Inductive effect), so methanol should also have higher dielectric constant than water.
Similarly dipole moment or dielectric constant of ethanol > methanol, and dipole moment or dielectric constant of dimethyl ether > ethanol. In reality the opposite of what I said happens. Why?
I read this Comparing the dipole moment of water and ethanol but, the answer given still doesn't answer the question why? He says it's because $H$ is more electropositive than $C$ but that contradicts inductive effect.

Saif
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  • Why do you mention the dielectric constant ($\epsilon$) at all? As soon as you bring up $\epsilon$ the discussion must also address intermolecular interactions. For water this makes a large difference. Limit your discussion to gas phase molecular dipole moments. Then you compare an intramolecular property. – Buck Thorn Jan 30 '24 at 07:31
  • @BuckThorn I want to compare dielectric constants of these molecules. I don't understand how intermolecular interactions can influence value of dielectric constant, as my understanding of a dielectric is a substance with net charge 0, and the molecules have a positively charged part and a negatively charged part. The molecules can be jumbled up in many orientations. But when I apply an electric field onto the substance, all the molecules will experience the field's electric force and experiences torque until the molecule moves inline with the field. So now every molecule is in 1 orientation. – Saif Jan 31 '24 at 07:43
  • So now the dielectric substance is polarized. The resultant electric field will now be different as the molecules's electric field will interfere against the external applied electric field.
    dielectric constant = (Applied electric field) / (Net electric field) So if dipole of molecule is more, the electric field created by molecules which opposes the external applied electric field will increase and net electric field decreases so dielectric constant is more (by using the formula). So dielectric constant is only proportional to dipole moment?     – Saif Jan 31 '24 at 07:50
  • Even if the molecule doesn't have a positively charged part and a negatively charged part, that is dipole moment = 0. It can still act like a dielectric, as the electric field can pull on the electrons instead and polarize the molecule. – Saif Jan 31 '24 at 07:56
  • What I meant with my comment is that you might want to limit the comparison to molecular properties, ideally obtained in the gas phase. As soon as you bring up a macroscopic property such as the dielectric constant for water and alcohols you have to take into account the structure of the liquid and intermolecular interactions such as hydrogen bonding. That doesn't mean you throw away everything you've learned. It means that things get more complicated. Perhaps someone will answer and provide an explanation. – Buck Thorn Jan 31 '24 at 16:24
  • yes i want to know how it gets more complicated. Intermolecular interactions or liquid structure shouldn't play a part I think because all that is happening is that the molecules are becoming in line with the electric field, that is the molecules stop rotating at a point where they experience no force from the field. But maybe the liquid structure or intermolecular forces can stop it from rotating? but then the substance will have dieelectric constant = 1, as there is no opposing electric field from the molecules which doesn't happen here with these molecules. – Saif Feb 01 '24 at 05:05

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