Question

Why is ${\mathrm{F}}_2$ a nonpolar molecule, but $\mathrm{HF}$ is a polar molecule?

Short answer

${\mathrm{F}}_2$is nonpolar but $\mathrm{HF}$ is polar because of electronegativity difference.

Step-by-step solution

Given information

We are to find why $\mathrm{HF}$is polar whereas ${\mathrm{F}}_2$ is nonpolar.

Simplify

An electronegativity difference must be present between the atoms for the connection to be polar.
Because both atoms in the $\mathrm{H}-\mathrm{H}$ bond have the same electronegativity, we wouldn't anticipate there to be a difference such that the electrons of one atom pull the electron density towards itself.
On the other hand, we can see that hydrogen is on the left side of the periodic table, while fluorine is on the right, and since electronegativity increases from left to right in the periodic table, we would expect this bond to be polar, with the fluorine atom pulling the electron density towards itself.

electronegativity of $\mathrm{F}=3.98$ and $\mathrm{H}=2.2$

Therefore ${\mathrm{F}}_2$is nonpolar but $\mathrm{HF}$ is polar.