Dipole moments are the result of the unequal distribution of electrons in a bond or in a molecule.  Electrons will move towards the more electronegative atoms, leading to a unequal distribution of charge refered to as a dipole moment.  The answer here if HF because the flourine will strongly overpower the H atom's ability to attract electrons and the molecule will have a very large seperation of charge with the F end being partially egative and the H end being partially positive. This dipole will be stronger than that of HCl becasue F is more electronegative than HCl.  

HCN has the largest difference in electronegativity, and the atoms are in a linear configuration. There is a strong dipole moment in the direction of nitrogen, without anything else canceling it out. Water has a dipole moment from each H, and the molecule is bent, so the dipoles partially cancel themselves out. SO₂ also has a bent configuration, so its dipoles partially cancel each other out as well. PCl₄ is tetrahedral, and all the dipoles cancel out.

Water is a polar molecule and oil a nonpolar molecule. Polar and nonpolar molecules do not readily mix. Like tends to dissolve like; polar solutes will dissolve in polar solvents, while nonpolar solutes will dissolve in nonpolar solvents.

Water has stronger attraction between molecules, but this does not play a role in solubility.

To determine the overall polarity of a molecule it is important to note any differences in electronegativity that occur between the molecule's constituent atoms, but it is also important to consider the overall shape of the molecule. BF₃ and CCl₄ may seem like tempting answers because these atoms contain very electronegative elements.  However in both molecules the shapes, BF₃ being trigonal planar and CCl₄ being tetrahedral, cause each dipole within the polar bonds to cancel eachother out making these molecules overall non-polar.  The answer is then H₂O because oxygen is bonded to two hydrogen molecules, and it also has two lone pairs casuing it to assume a bent conformation that is overall polar.  

Ionic bonds arise from a large difference in electronegativities between two atoms. This is most common between metal and non-metal compounds, since these are generally located on opposite sides of the periodic table.

Of the given compounds, only two contain ionic bonds. , , and are composed solely of non-metal atoms. Even though nitrate and phosphate ions are charged, they are still composed only of covalent bonds.

and are both ionic compounds. Barium and lithium are metals with very low electronegativities, while fluorine and oxygen are non-metals with very high electronegativities. By looking at the periodic table, however, we can see that the distance between lithium and fluorine is greater than the distance between oxygen and barium. This tells us that there will be a greater difference in electronegativity between lithium and fluorine, meaning that lithium fluoride will have the most ionic character.

The electronegativity values support this conclusion, showing that lithium fluoride has the greater difference.

Water is a polar solvent, which makes it an excellent solvent for dissolving polar substances. Pentane  is a nonpolar molecule, which means it will be insoluble in water.

The other compounds will all dissolve according to the below reactions.

Amphoteric compounds can act as both acids and bases. Water, H₂O, is the most commonly cited amphoteric compound. It can act as an acid to give H+ molecules, or act as a base to give OH– molecules.