a) The balanced equation for the reaction would be as follows:
[tex]2 Al(OH)_3 + 3 H_2SO_4 ---> Al_2(SO_4)_3 + 6 H_2O[/tex]
b) The mole ratio of aluminum hydroxide to sulfuric acid is 2:3. This means that every 1 mole of the aluminum hydroxide would require 1.5 moles of sulfuric acid.
0.5 mole aluminum hydroxide would require:
0.5 x 3/2 = 0.75 moles of sulfuric acid.
But only 0.500 moles of sulfuric acid is present. Thus, the limiting reagent is sulfuric acid.
c) With 0.5 moles sulfuric acid, the mole of aluminum hydroxide required would be:
0.5 x 2/3 = 0.33
Excess moles of aluminum hydroxide = 0.5 - 0.33
= 0.17 moles
d) The mole ratio of sulfuric acid to aluminum sulfate produced is 3:1. With 0.5 moles sulfuric acid, the mole of aluminum sulfate produced would be:
0.5 x 1/3 = 0.17 moles
But the percentage yield is 77%
77/100 x 0.17 = 0.13 moles
Thus, the moles of aluminum sulfate that would be obtained with a percentage yield of 77% would be 0.13 moles.
More on stoichiometric calculations can be found here: https://brainly.com/question/8062886