What is the coefficient for Fe when the following equations is cor Fe_(3)O_(4)+Alarrow Al_(2)O_(3)+Fe

To balance the chemical equation \(Fe_{3}O_{4} + Al \rightarrow Al_{2}O_{3} + Fe\), we need to ensure that the number of atoms of each element is the same on both sides of the equation.<br /><br />Let's start by writing down the number of atoms for each element in the unbalanced equation:<br /><br />- \(Fe_{3}O_{4}\): 3 Fe, 4 O<br />- \(Al\): 1 Al<br />- \(Al_{2}O_{3}\): 2 Al, 3 O<br />- \(Fe\): 1 Fe<br /><br />Now, let's balance the equation step by step:<br /><br />1. Balance the Fe atoms:<br /> - There are 3 Fe atoms on the left side and 1 Fe atom on the right side.<br /> - To balance the Fe atoms, we need to put a coefficient of 3 in front of Fe on the right side:<br /> \[<br /> Fe_{3}O_{4} + Al \rightarrow Al_{2}O_{3} + 3Fe<br /> \]<br /><br />2. Balance the Al atoms:<br /> - There is 1 Al atom on the left side and 2 Al atoms on the right side.<br /> - To balance the Al atoms, we need to put a coefficient of 2 in front of Al on the left side:<br /> \[<br /> Fe_{3}O_{4} + 2Al \rightarrow Al_{2}O_{3} + 3Fe<br /> \]<br /><br />3. Balance the O atoms:<br /> - There are 4 O atoms on the left side and 3 O atoms on the right side.<br /> - The O atoms are already balanced in this equation.<br /><br />So, the balanced chemical equation is:<br />\[<br />Fe_{3}O_{4} + 2Al \rightarrow Al_{2}O_{3} + 3Fe<br />\]<br /><br />The coefficient for Fe in the balanced equation is 3.