Step 1: Understanding the Concept:
Lewis acidity depends on both inductive effect and back-donation of lone pairs.
Step 2: Detailed Explanation:
BF\(_3\) is the weakest Lewis acid because F donates its lone pairs strongly to B (p\(\pi\)-p\(\pi\) back-bonding), reducing electron deficiency. As we go down the group, back-bonding decreases, so Lewis acidity increases. Order: BI\(_3\)>BBr\(_3\)>BCl\(_3\)>BF\(_3\).
Step 3: Final Answer:
\(\mathrm{BI}_3>\mathrm{BBr}_3>\mathrm{BCl}_3>\mathrm{BF}_3\)