how many moles of chlorine gas react with 0.100 moles of Fe (metallic iron)?

It depends upon the chloride formed.

Fe + Cl2 ==> FeCl2 (iron II chloride)
2Fe + 3Cl2 ==> 2FeCl3 (iron III chloride).

In case 1, 0.1 mole Fe will react with 0.1 mole Cl2. (that's 0.1 mole Fe x (1 mole Cl2/1 mole Fe) = 0.1 x 1/1 = 0.1 mole Cl2).
In case 2, 0.1 mole Fe will react with 0.1 mole Fe x (3 moles Cl2/2 moles Fe) = 0.1 x (3/2) = ??

To determine the number of moles of chlorine gas that react with 0.100 moles of Fe (metallic iron), we need to balance the chemical equation for the reaction between chlorine gas (Cl2) and iron (Fe).

The balanced chemical equation is:

Fe + Cl2 → FeCl2

From the balanced equation, we can see that the stoichiometric ratio between Fe and Cl2 is 1:1. This means that for every 1 mole of Fe, we need 1 mole of Cl2 to react.

Since we have 0.100 moles of Fe, we will require the same number of moles of Cl2 to react. Therefore, the number of moles of chlorine gas that react is also 0.100 moles.