Assume that 50.0mL of 1.0MNaCl(aq) and 50.0mL of 1.0MAgNO3(aq) were combined. According to the balanced equation, if 50.0mL of 2.0MNaCl(aq) and 50.0mL of 1.0MAgNO3(aq) were combined, the amount of precipitate formed would

2fe + 3h2so4 -> fe2(so4)3 + 3h2

it is necessary to balance equations in order to get the proper amount of reactants as well as products in order not to make a miscalculation.

you cannot change the subscripts as that would change the substance itself. for instance, diatomic elements such as h2 only have the subscript two when a gas. another example would be so4, if you were to change the subscript, the element would no longer be sulfate.

we change the coefficients instead as that only changes the number of molecules rather than the substance itself.

hope this !