If I have 6HCl, why can't I change the subscripts and write 3H2Cl2?
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This is because in 1 hydrochloric acid molecule, you have one atom of hydrogen and one atom of chlorine. If you change this to H2Cl2, you are saying that you have 2 atoms of hydrogen and two atoms of chlorine in a single molecule of hydrochloric acid. This changes the properties of the substance and the substance altogether.
For example, there is a difference between C2H2, i.e. acetylene and CH4, i.e. methane. They both are different substances.
Similarly, when you write 6HCl, you say that you have 6 molecules of HCl and when you write 3H2Cl2, you say that you have 3 molecules of H2Cl2 which is a different substance.
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