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the polarity of a molecule has to do with the distribution of charges or the 'electronegativity' differences between different bonded atoms in a molecule.

 

A molecule like water has unequal sharing of electrons, which creates a 'dipole moment' from the partial charges associated with each atom. This 'inbalance' of charge affects the physical properties of the molecule.

 

A solution made with a polar solvent is known as a polar solution. So, water would be a good example of this.

 

In general a good rule of thumb to remember is 'like dissolves like'. Meaning that polar solvents tend to dissolve polar solutes. Which is why oil (which is nonpolar) is immiscible in water. However a nonpolar molecule, like ethanol, would be a good solvent for grease stains.

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