Taking into account the law of conservation of matter, the balanced reaction is:
2 Fe + 3 H₂SO₄ → Fe₂(SO₄)₃ + 3 H₂
First, you must know that the law of conservation of matter states that since no atom can be created or destroyed in a chemical reaction, the number of atoms that are present in the reagents has to be equal to the number of atoms present in the products.
Then, you must balance the chemical equation. This is, balancing a chemical equation is to equalize the number and class of reactant atoms, ions or molecules with the products, in order to comply with the law of conservation of mass.
For that, you must first look at the subscripts next to each atom to find the number of atoms in the equation. If the same atom appears in more than one molecule, you must add its amounts.
The coefficients located in front of each molecule indicate the amount of each molecule for the reaction. This coefficient can be modified to balance the equation, just as you should never alter the subscripts.
This is because the subscripts that are placed on chemical symbols or formulas indicate the number of atoms that make up the substance. If the coefficients are modified, the quantities of the substance change, but if the subscripts are modified, different substances are originated.
In this case, the balanced reaction is:
2 Fe + 3 H₂SO₄ → Fe₂(SO₄)₃ + 3 H₂
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