The balanced chemical equation for the reaction between iron (Fe) and water (H₂O) to produce iron oxide (Fe₃O₄) and hydrogen gas (H₂) is:

3Fe + 4H₂O → Fe₃O₄ + 4H₂

Here's how to balance it:

1. Identify the reactants and products:

* Reactants: Fe (iron) and H₂O (water)

* Products: Fe₃O₄ (iron oxide) and H₂ (hydrogen)

2. Count the atoms of each element on both sides of the equation:

* Fe: 1 on the left, 3 on the right

* H: 2 on the left, 2 on the right

* O: 1 on the left, 4 on the right

3. Adjust the coefficients in front of the chemical formulas to balance the number of atoms:

* To balance Fe, place a 3 in front of Fe on the left side.

* To balance O, place a 4 in front of H₂O on the left side.

* To balance H, place a 4 in front of H₂ on the right side.

4. Verify that the equation is now balanced:

* Fe: 3 on both sides

* H: 8 on both sides

* O: 4 on both sides

Therefore, the balanced equation is 3Fe + 4H₂O → Fe₃O₄ + 4H₂