is the more dense compound more polar?

Not necessarily. Density and polarity are independent properties of a compound. Density refers to the mass per unit volume of a substance, while polarity refers to the distribution of electrical charge within a molecule. A compound can have a high density but be nonpolar, or a low density but be highly polar. Density is determined by the arrangement and packing of molecules, while polarity is determined by differences in electronegativity and overall molecular structure.