For $C u (s) + N O_{3} (a q) + H^{+} (a q) \to C u^{2 +} (a q) + N O_{2} (g) + x H_{2} O (l)$ , when the equation is balanced what is the coefficient of $H^{+}$ ?

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Solution

The correct option is D 4
The unbalanced chemical equation is
$C u (s) + N O_{3}^{-} (a q) + H^{+} (a q) \to C u^{2 +} (a q) + N O_{2} (g) + H_{2} O (l)$
All atoms except H and O are balanced. Assign oxidation numbers.
$C u (s) 0 + N + 5 O_{3}^{-} (a q) + H^{+} (a q) \to C u^{2 +} + 2 (a q) + N + 4 O_{2} (g) + H_{2} O (l)$
The oxidation number of Cu increases from 0 to +2. Total increase in the oxidation number is 2. The oxidation number of N decreases from +5 to +4. Total decrease in the oxidation number is 1. Balance increase in oxidation number with decrease in oxidation number by using appropriate coefficients.
$C u (s) + 2 N O_{3}^{-} (a q) + H^{+} (a q) \to C u^{2 +} (a q) + 2 N O_{2} (g) + H_{2} O (l)$
Balance O atoms by adding one water molecule on products side.
$C u (s) + 2 N O_{3}^{-} (a q) + H^{+} (a q) \to C u^{2 +} (a q) + 2 N O_{2} (g) + 2 H_{2} O (l)$
Balance H atoms by adding 3 protons to reactant side.
$C u (s) + 2 N O_{3}^{-} (a q) + 4 H^{+} (a q) \to C u^{2 +} (a q) + 2 N O_{2} (g) + 2 H_{2} O (l)$
This is balanced chemical equation. The coefficient of $H^{+}$ ions is 4.

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