Question

Why does boron trifluoride behave as a Lewis acid?

Answer 1

Lewis acid is a compound which has the tendency to accept electrons from a base. In general such compounds are electron deficient compounds.

Complete step by step answer:
The theory indicating the characteristics of acids and bases was given by G. N. Lewis. The theory is based on the ability of a substance for sharing electrons.
According to the theory the Lewis acids are the substances which accept electrons. The substances are chemical species which are electron deficient. The electrons deficiency arises due to incomplete octet in some cases and due to vacant higher orbitals in some cases.
Further it is worth mentioning that the Lewis base is an electron donar species. These substances have an excess of electrons in their valence shell. Due to this they are able to donate electrons so that the valence shell attains a half filled stability.
Now the compound given here is boron trifluoride. It is composed of one boron atom and three fluorine atoms. Boron is an element in the periodic table with atomic number $5$ and electronic configuration$\left[ {He} \right]2{s^2}2{p^1}$. The valence shell of boron atom is $2$ which have a total of $3$ electrons. The bonded element is fluorine which has an atomic number $9$ and electronic configuration$\left[ {He} \right]2{s^2}2{p^5}$. Thus the valence shell of fluorine is $2$ which have a total of $7$ electrons.
In order to complete the octet the fluorine atom needs only one electron. As boron has three electrons in total so it combines with three fluorine atoms. Thus the compound $B{F_3}$ is formed by forming three sigma bonds between boron and fluorine atoms.
But after the formation of $B{F_3}$ the central atom boron has a total of 6 valence electrons which is 2 less than octet. So it has the tendency to accept electrons from donar molecule which has excess electrons. Hence boron trifluoride behaves as a Lewis acid.

Note:
The boron trifluoride has empty p orbitals. But down the group in periodic table vacant p and d orbitals are available for electron acceptance and so this accounts for the acidity of their compounds.