WEBVTT

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Here is the problem: Balance the chemical equation Cu plus HNO3 → Cu(NO3)2 plus NO plus H2O.

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Balance atoms of every element, then use the coefficients as mole ratios.

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Write an atom balance for each element. Give each species an unknown coefficient; atoms of every element must be equal on both sides.

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Solve the linear system with the smallest whole numbers. Exact elimination leaves one free coefficient; scaling by the least common denominator gives integers.

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Balanced equation.

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So the answer is 3Cu plus 8HNO3 → 3Cu(NO3)2 plus 2NO plus 4H2O.

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Coefficients in a balanced equation count particles (moles), not grams. Convert grams to moles, apply the mole ratio, then convert back to grams with the other species prime molar mass. Assumes the reaction goes to completion with the known species fully consumed (or formed).

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Cu: 3 equals 3, H: 8 equals 8, N: 8 equals 8, O: 24 equals 24, which checks out.