Question

3Cl2 +6KOH->KClO3 +5KCl =3H2O

write a conversion factor that could be used to convert between moles od potassium hydroxide and moles of potassium chlorate
You have a typo.
3Cl2 +6KOH->KClO3 +5KCl + 3H2O
z mols KOH x (1 mol KClO3/5 mols KOH) = ? mols KClO3

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