Why boron trihydride is weaker lewis acid than boron tribromide and boron tri-iodide?

There is no back-bonding in case of boron trihydride so it is a stronger lewis acid than boron trichloride ( even though chlorine atom is more electronegative than hydrogen atom).

Then why boron trihydride is weaker lewis acid than boron tribromide and boron tri-iodide?

• Backbonding is ineffective in case of tribromides and triiodides since their 4p and 5p orbitals dont really overlap well with the 2p of boron. Morever they are electronegative and can make the boron more positive, and increase the tendency to accept a pair of electrons. – Pritt says Reinstate Monica May 17 '17 at 6:39

Predicting the acidic strengths of $$\ce{BX_3}$$ using back-bonding is one plausible theory. This article1 hints us to use bond-strength data to predict the same:

The weaker Lewis acid strength of $$\ce{BF3}$$ compared to $$\ce{BCl3}$$ with respect to bases such as $$\ce{NMe3}$$ is explained in terms of the ligand close-packing (LCP) model. The halogen ligands remain close-packed during the formation of the complex leading to an increase in the $$\pu{B−Hal}$$ bond length. Because a $$\ce{B−F}$$ bond is stronger than a $$\ce{B−Cl}$$ bond, more energy is required to stretch a $$\ce{B−F}$$ bond than a $$\ce{B−Cl}$$ bond. Hence $$\ce{BF3}$$ is a weaker acid than $$\ce{BCl3}$$.

Pulling up the bond strength data, I get:

$$\begin{array}{c|c} \mathbf{Bond} & \mathbf{Strength (KJ/mole) } \\\hline \text{B-H} & \text{389}\\ \text{B-F} & \text{613} \\ \text{B-Cl} & \text{456}\\ \text{B-Br} & \text{377}\\ \text{B-I} & \text{?}\end{array}$$

Building up on these two pieces of information, it can be said that since $$\ce{B-H}$$ bond is stronger than $$\ce{B-Br}$$ and $$\ce{B-I}$$ (see below), $$\ce{BH3}$$ is a weaker acid than $$\ce{BBr3}$$ and $$\ce{BI3}$$.

I'm afraid I couldn't find the data for $$\ce{B-I}$$ bond, but since we can compare the bond-strengths of boron trifluorides on the basis of back-bonding theory, we can be sure that the strength of $$\ce{B-I}$$ bond will be $$\lt \pu{377 kJ mol^-1}$$.

References

1. Ligand Close-Packing and the Lewis Acidity of BF3 and BCl3 Bryan D. Rowsell, Ronald J. Gillespie, and George L. Heard Inorganic Chemistry 1999 38 (21), 4659-4662 DOI: 10.1021/ic990713m