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To be more specific, lets take a look at the Lewis Structure of two such examples:

The first one is SiCl${_3}$F. The red arrow represents an ionic bond while the blue is a polar covalent bond.

Now, the polar bonds on the Cl atoms that are separated horizontally cross out. Looking vertically, however, the ionic bond is stronger than the polar bond, so does that mean the molecule over-all is a polar molecule? I say this because my textbook says it is a tetrahedral polar.

The next one is SiF${_2}$Cl${_2}$. Same here; the ionic bonds and polar bonds should cancel out and the molecule would be a non-polar molecule overall, but my textbook says it is a polar molecule for some reason. enter image description here

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    $\begingroup$ There's no ionic bond in here. Difference in standard electronegativities is not enough to tell, even misleading here. $\endgroup$ – Mithoron Dec 5 '16 at 1:14
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    $\begingroup$ Beyond what @Mithoron said, remember that these molecules won't be planar -- they're tetrahedral. So, e.g., the 'horizontal' $\ce{Si\!-\!Cl}$ bonds don't cancel each other out -- they'll still have a residual contribution to the overall polarity of the molecule. $\endgroup$ – hBy2Py Dec 5 '16 at 1:38
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1) The silicon to fluoride bond is polar covalent. Even though an electronegativity difference of more than 2.0 generally indicates an ionic bond, the cutoff rises as the average electronegativity of the two combining species rises.

For example, in sodium bromide, the electronegativity difference is only 1.9, but the average electronegativity between sodium (0.9) and bromine (2.5) is 1.7 which is on the low side meaning that the cutoff will can be lower than 1.9.

In the silicon-fluorine bond, the electronegativity difference is 2.2 which would indicate an ionic bond, but since the average electronegativity between silicon and fluorine is (1.8+4.0)/2 or 2.9, which is on the high side, the threshold for electronegativity difference to form an ionic bond is higher.

For a molecule to be polar, it has to have polar covalent bonds, but not every molecule with polar covalent bonds is polar. It won't be polar if the molecule is symmetrical across the x, y and z axis cutting through the central atom. So the first example is polar because it is not symmetrical.

The second molecule is polar because it is also not symmetrical, since it it not square-planar, but rather tetrahedral.

enter image description here

(image source)

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