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I believe Professor Lavelle mentioned that, if we wanted, we could include and write out the potassium as K+ on both sides of the equation. Nitrous acid stays as one molecule when in water, but potassium nitrite, as a salt, dissociates in water to form NO2- and K+. That NO2- is included in the HNO2 of the nitrous acid on the reactants side of the equation, but Lavelle chose not to include K+ in the equation because it does not play any part during this reaction as a whole. If you were to rewrite the equation including the potassium, it would look like the following.
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