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Question: Even though we technically CAN use (moles base)/(moles acid) in the Henderson-Hasselbalch equation, is it the same as using molarity?
Answer: In the Henderson-Hasselbach equation, you SHOULD put in the molarity, but since the total volume is the same for both the base and the acid (they are sitting in the same solution, so they have the same total volume of solution), the volumes will cancel. For example say the total volume is 10 L, [(moles base)/(10)]/[moles acid)/(10)] = (moles base)/(moles acid). If this makes you uncomfortable, or you are afraid you may not divide by the volume when you have to (for instance at the stoichiometric point), then by all means calculate the molarity and plug that in to the Henderson-Hasselbach equation.
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