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Would there ever be a case, or is it even possible to have multiple correct answers for the stoichiometric coefficients when balancing a chemical equation? Could there ever be two different "sets" of coefficients that abide to conservation of mass, or is there always one specific way to balance an equation?
There will always be multiples of the stoichiometric coefficients that you could come up with, or might end up with if you made a calculation error somewhere along the way, but the goal of balancing the equation is to get the lowest possible whole number coefficients. Because we are looking for the lowest possible whole numbers I believe there is always only one correct answer.
Since the goal in balancing equations is to find the lowest stoichiometric coefficients, there is only one right answer. Although different multiples of the coefficients could result in equal numbers of atoms on both sides, there is only one arrangement of coefficients that is the lowest.
Yes, you would be able to divide (you can look at it as multiplying by 1/2, too). But you would have to make sure that all the stoichiometric coefficients in the equation can be divided by the same number and still be a whole number. If you are able to divide all the coefficients by the same number and still get all whole numbers for the coefficients, then that is the correct balanced equation.
Though, the stoichiometric coefficients in chemical equations are meant to represent values in moles, these reactions are happening between individual atoms in equal proportions as the coefficients represent. Because the coefficients are simply representative of the ratios between atoms in chemical reactions, TECHNICALLY any multiple of these ratios would still be a valid balanced equation. However, it is more reasonable to represent these equations in the lowest possible factors for simplicity purposes.
You may think that there are multiple correct answers for stoichiometric coefficients, but usually the stoichiometric coefficients should all be simplified to their lowest possible values. So, if you think there are multiple correct answers try dividing each coefficient by one number and if all the coefficients end up as positive integers then that is most likely the correct answer. For example, if all your coefficients are even numbers, try dividing by 2.
Technically while the stoichiometric coefficients follow the same ratio, whatever number they are multiplied by will remain a correct answer, but generally this would not be helpful, and the smallest ratio is preferred. Try to simplify it down as much as you can while remaining with whole numbers.
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