Hydrogen gas can be produced from a reaction of steam with iron metal according to the equation below:3Fe (s) + 4H2O (g) ⟶4 H2 (g) + Fe3O4 (s)What mass of steam  is needed to produce 86.2 g of hydrogen?  Express your answer in the correct number of significant figures.

To solve this problem, we need to use stoichiometry, which is a method in chemistry that uses relationships between reactants and/or products in a chemical reaction to determine desired quantitative data.

Here are the steps:

1. First, we need to find the molar mass of hydrogen (H2) and water (H2O). The molar mass of H2 is approximately 2.02 g/mol and the molar mass of H2O is approximately 18.02 g/mol.

2. Next, we need to find out how many moles of H2 are in 86.2 g. We do this by dividing the mass of H2 by its molar mass. So, 86.2 g ÷ 2.02 g/mol = 42.7 mol of H2.

3. Now, we look at the balanced chemical equation. It tells us that 4 moles of H2O are needed to produce 4 moles of H2. This means the ratio of H2O to H2 is 1:1. So, we need 42.7 mol of H2O to produce 42.7 mol of H2.

4. Finally, we find the mass of H2O needed by multiplying the number of moles by its molar mass. So, 42.7 mol x 18.02 g/mol = 769.7 g of H2O.

Therefore, 770 g of steam (to three significant figures) is needed to produce 86.2 g of hydrogen.