Questions: Change the coefficient(s) to correctly balance the unbalanced equation. 3 NO2(g) + H2 O(l) → HNO3(aq) + 2 NO(g)

Solution Steps

First, identify the elements present in the chemical equation: nitrogen (N), oxygen (O), and hydrogen (H). The goal is to ensure that the number of atoms of each element is the same on both sides of the equation.

Count the number of atoms for each element on both sides of the equation:

• Reactants:

  • \( \text{N: } 3 \times 1 = 3 \)
  • \( \text{O: } 3 \times 2 + 1 = 7 \)
  • \( \text{H: } 2 \times 1 = 2 \)

• Products:

  • \( \text{N: } 1 + 2 = 3 \)
  • \( \text{O: } 3 + 2 = 5 \)
  • \( \text{H: } 1 \)

To balance the hydrogen atoms, adjust the coefficient of \(\mathrm{HNO}_{3}\) to 2:

\[ 3 \mathrm{NO}_{2}(g) + \mathrm{H}_{2} \mathrm{O}(l) \rightarrow 2 \mathrm{HNO}_{3}(aq) + 2 \mathrm{NO}(g) \]

Now recount the atoms:

• Reactants:

  • \( \text{N: } 3 \)
  • \( \text{O: } 7 \)
  • \( \text{H: } 2 \)

• Products:

  • \( \text{N: } 2 + 2 = 4 \)
  • \( \text{O: } 2 \times 3 + 2 = 8 \)
  • \( \text{H: } 2 \times 1 = 2 \)

To balance the nitrogen atoms, adjust the coefficient of \(\mathrm{NO}_{2}\) to 4:

\[ 4 \mathrm{NO}_{2}(g) + \mathrm{H}_{2} \mathrm{O}(l) \rightarrow 2 \mathrm{HNO}_{3}(aq) + 2 \mathrm{NO}(g) \]

Recount the atoms:

• Reactants:

  • \( \text{N: } 4 \)
  • \( \text{O: } 4 \times 2 + 1 = 9 \)
  • \( \text{H: } 2 \)

• Products:

  • \( \text{N: } 2 + 2 = 4 \)
  • \( \text{O: } 2 \times 3 + 2 = 8 \)
  • \( \text{H: } 2 \)

To balance the oxygen atoms, adjust the coefficient of \(\mathrm{H}_{2}\mathrm{O}\) to 2:

\[ 4 \mathrm{NO}_{2}(g) + 2 \mathrm{H}_{2} \mathrm{O}(l) \rightarrow 2 \mathrm{HNO}_{3}(aq) + 2 \mathrm{NO}(g) \]

Recount the atoms:

• Reactants:

  • \( \text{N: } 4 \)
  • \( \text{O: } 4 \times 2 + 2 = 10 \)
  • \( \text{H: } 2 \times 2 = 4 \)

• Products:

  • \( \text{N: } 2 + 2 = 4 \)
  • \( \text{O: } 2 \times 3 + 2 = 8 \)
  • \( \text{H: } 2 \times 1 = 2 \)

Final Answer