Which reagent is the limiting reactant when 0.400 mol Al(OH)3 and 0.400 mol H2SO4 are allowed to react

H₂SO₄  will be the limiting reagent.

Explanation:

The balanced reaction is:

2 Al(OH)₃ + 3 H₂SO₄ → Al₂(SO₄)₃ + 6 H₂O

The limiting reagent is one that is consumed first in its entirety, determining the amount of product in the reaction. When the limiting reagent is finished, the chemical reaction will stop.

To determine the limiting reagent, it is possible to use the reaction stoichiometry of the reaction (that is, the relationship between the amount of reagents and products in a chemical reaction).

You can use a simple rule of three as follows: if by stoichiometry 2 moles of Al(OH)₃ reacts with 3 moles of H₂SO₄, how much moles of H₂SO₄ will be needed if 0.4 moles of Al(OH)₃ react?

moles of H₂SO₄= 0.6 moles

But 0.6 moles of H₂SO₄ are not available, 0.40 moles are available. Since you have less moles than you need to react with 0.4 moles of Al(OH)₃, H₂SO₄  will be the limiting reagent.