According to the balanced equation above, how many moles of hi would be necessary to produce 2.5 mol of i2, starting with 4.0 mol of kmno4 and 3.0 mol of h2so4?

Answer is 5.0 mol.

Explanation;

The balanced reaction between KMnO₄ and HI is

2KMnO₄ + 10HI + 3H₂SO₄ → 2MnSO₄ + K₂SO₄ + 5I₂ + 8H₂O

The stoichiometric ratio between HI and I₂ is 2 :1.

Hence, moles of HI needed = moles of 5I₂ produced x 2

= 2.5 mol x 2

= 5.0 mol

2h2o2--> 2h2o + o2

this reaction is of the spontaneous decomposition of hydrogen peroxide down into water and oxygen.

add 2 molecules of hydrogen peroxide and 2 molecules of water. since oxygen is naturally diatomic, the total number of atoms of each element is now the same on both sides of the equation so it is balanced.

this may not be entirely correct but let me know.