Which of the following are Lewis acids?

First, recall the definition of a Lewis acid. A Lewis acid is defined as a chemical species that accepts an electron pair. Conversely, a Lewis base donates an electron pair. With this definition in mind, let us examine each substance mentioned in the four options one by one.

We have $$\text{BCl}_3$$. Boron is a Group 13 element possessing only three valence electrons. In $$\text{BCl}_3$$, boron forms three covalent bonds, one with each chlorine atom. Counting the electrons around boron, we get $$3 \times 2 = 6$$ electrons, which is two short of the octet. Therefore the boron atom has an empty $$p$$-orbital that can accept a pair of electrons from an external donor. By the stated definition, $$\text{BCl}_3$$ behaves as a Lewis acid.

Next, consider $$\text{AlCl}_3$$. Aluminium, also in Group 13, mirrors boron’s electronic situation. In $$\text{AlCl}_3$$ the aluminium atom likewise possesses only six valence electrons in its bonding shell, leaving an empty orbital available for accepting an extra pair. Thus $$\text{AlCl}_3$$ is also a Lewis acid.

Now, look at $$\text{PH}_3$$. Phosphorus is in Group 15 and brings five valence electrons. In $$\text{PH}_3$$, three of those electrons form three $$\text{P-H}$$ sigma bonds, using up $$3 \times 2 = 6$$ electrons in shared pairs. That leaves one lone pair on phosphorus. Because this lone pair can be donated rather than accepted, $$\text{PH}_3$$ acts as a Lewis base, not a Lewis acid.

Finally, examine $$\text{CCl}_4$$. Carbon sits in the centre bonded to four chlorine atoms, giving it the full octet of $$8$$ valence electrons (four shared pairs). There is neither an empty orbital on carbon nor a deficiency of electrons, so $$\text{CCl}_4$$ neither seeks to accept nor readily donates an electron pair. Consequently, it is generally regarded as neither a Lewis acid nor a Lewis base under ordinary circumstances.

Summarising these observations:

$$\begin{aligned} \text{BCl}_3 &:;; \text{Lewis acid} \\ \text{AlCl}_3 &:;; \text{Lewis acid} \\ \text{PH}_3 &:;; \text{Lewis base (not acid)} \\ \text{CCl}_4 &:;; \text{neither acid nor base} \end{aligned}$$

The only option that lists exclusively Lewis acids is the one containing $$\text{BCl}_3$$ and $$\text{AlCl}_3$$, namely Option A.

Hence, the correct answer is Option A.