In coordination chemistry, it is common to use “non-coordinating” anions as counterions for cationic complexes. These anions are essentially inert, and do not interfere in the study of the coordination complexes. A very common example is hexafluorophosphate, PF6–. Why do you think that PF6– is used more often than BF4–? Ignore any solubility concerns.

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 !