To balance the chemical equation [tex]\( NH_3 + O_2 \rightarrow NO + H_2O \)[/tex], we will follow a systematic approach to ensure that the number of atoms of each element is the same on both the reactant and product sides of the equation.
1. Balance Nitrogen (N) atoms:
- On the left side, we have nitrogen coming from [tex]\( NH_3 \)[/tex] (only 1 nitrogen atom per molecule of [tex]\( NH_3 \)[/tex]).
- On the right side, nitrogen comes from [tex]\( NO \)[/tex] (only 1 nitrogen atom per molecule of [tex]\( NO \)[/tex]).
- Since both sides have 1 nitrogen atom, nitrogen is already balanced.
2. Balance Hydrogen (H) atoms:
- On the left side, hydrogen comes from [tex]\( NH_3 \)[/tex]. Since there are 3 hydrogen atoms in [tex]\( NH_3 \)[/tex], we have 3 hydrogen atoms on the left.
- On the right side, hydrogen comes from [tex]\( H_2O \)[/tex]. Each [tex]\( H_2O \)[/tex] molecule contains 2 hydrogen atoms.
- To balance hydrogen, we need to equalize the number of hydrogen atoms on both sides. We need 6 hydrogen atoms on both sides, so we use 2 [tex]\( NH_3 \)[/tex] molecules (which give us [tex]\(2 \times 3 = 6\)[/tex] hydrogen atoms) and 3 [tex]\( H_2O \)[/tex] molecules (which give us [tex]\(3 \times 2 = 6\)[/tex] hydrogen atoms).
- The equation becomes: [tex]\( 2 NH_3 + O_2 \rightarrow 2 NO + 3 H_2O \)[/tex].
3. Balance Oxygen (O) atoms:
- On the left side, oxygen comes from [tex]\( O_2 \)[/tex].
- On the right side, oxygen comes from both [tex]\( NO \)[/tex] and [tex]\( H_2O \)[/tex]. We have 2 statements, each [tex]\( NO \)[/tex] molecule containing 1 oxygen atom and 3 [tex]\( H_2O \)[/tex] molecules containing 3 oxygen atoms.
- We have a total of [tex]\(2 \times 1 + 3 \times 1 = 5\)[/tex] oxygen atoms on the right side. To balance the oxygen atoms, we need 5 oxygen atoms on the left, which would require [tex]\( \frac{5}{2} \)[/tex] molecules of [tex]\( O_2 \)[/tex].
To avoid fractional coefficients, we multiply the whole equation by 2 to make all coefficients whole numbers.
4. Multiply the entire equation by 2:
- The equation now becomes [tex]\( 4 NH_3 + 5 O_2 \rightarrow 4 NO + 6 H_2O \)[/tex].
Thus, the correct balanced equation is:
[tex]\[ 4 NH_3 + 5 O_2 \rightarrow 4 NO + 6 H_2O \][/tex]
The correct answer is:
C. [tex]\( 4 NH_3 + 5 O_2 \rightarrow 4 NO + 6 H_2O \)[/tex]
