1) mathrm(Fe) stackrel(1)(arrow) mathrm(Fe) mathrm(Br)_(3) stackrel(2)(arrow) mathrm(Fe)(mathrm(OH))_(3) stackrel(3)(arrow) mathrm(Fe)_(2) mathrm(O)_(3) stackrel(4)(arrow) mathrm(FeO) stackrel(5)(arrow) mathrm(Fe) stackrel(6)(arrow) mathrm(Fe)_(2) mathrm(Br)_(2)

The given sequence of reactions represents the transformation of iron (Fe) through various compounds. Let's break down each step:<br /><br />1. \( \mathrm{Fe} \rightarrow \mathrm{FeBr}_{3} \): Iron reacts with bromine (Br2) to form iron(III) bromide (FeBr3).<br /><br />2. \( \mathrm{FeBr}_{3} \rightarrow \mathrm{Fe}(\mathrm{OH})_{3} \): Iron(III) bromide reacts with water (H2O) to form iron(III) hydroxide (Fe(OH)3).<br /><br />3. \( \mathrm{Fe}(\mathrm{OH})_{3} \rightarrow \mathrm{Fe}_{2} \mathrm{O}_{3} \): Iron(III) hydroxide decomposes upon heating to form iron(III) oxide (Fe2O3).<br /><br />4. \( \mathrm{Fe}_{2} \mathrm{O}_{3} \rightarrow \mathrm{FeO} \): Iron(III) oxide reacts with carbon monoxide (CO) to form iron(II) oxide (FeO).<br /><br />5. \( \mathrm{FeO} \rightarrow \mathrm{Fe} \): Iron(II) oxide reacts with carbon dioxide (CO2) to form iron (Fe).<br /><br />6. \( \mathrm{Fe} \rightarrow \mathrm{Fe}_{2} \mathrm{Br}_{2} \): Iron reacts with bromine (Br2) to form iron(II) bromide (Fe2Br2).<br /><br />Therefore, the correct answer is: \( \mathrm{Fe}_{2} \mathrm{Br}_{2} \).