To determine the correctly balanced equation for the formation of ammonia from hydrogen and nitrogen, we need to look at the reaction between hydrogen gas ([tex]$H_2$[/tex]) and nitrogen gas ([tex]$N_2$[/tex]).
The balanced chemical equation ensures that the number of atoms of each element is the same on both the reactant and product sides of the equation. Let's consider the chemical equation for the formation of ammonia:
[tex]\[ \text{Unbalanced Equation:} \quad H_2 + N_2 \rightarrow NH_3 \][/tex]
1. Count the atoms on both sides of the unbalanced equation:
[tex]\[ \text{Left side:} \quad H: 2, \quad N: 2 \][/tex]
[tex]\[ \text{Right side:} \quad H: 3, \quad N: 1 \][/tex]
2. Balance the nitrogen atoms:
Add a coefficient of 2 in front of [tex]$NH_3$[/tex] to balance the number of nitrogen atoms:
[tex]\[ H_2 + N_2 \rightarrow 2NH_3 \][/tex]
3. Count the atoms again after updating:
[tex]\[ \text{Left side:} \quad H: 2, \quad N: 2 \][/tex]
[tex]\[ \text{Right side:} \quad H: 6, \quad N: 2 \][/tex]
4. Balance the hydrogen atoms:
Add a coefficient of 3 in front of [tex]$H_2$[/tex]:
[tex]\[ 3H_2 + N_2 \rightarrow 2NH_3 \][/tex]
5. Recheck the atom count for full equation balance:
[tex]\[ \text{Left side:} \quad H: 6, \quad N: 2 \][/tex]
[tex]\[ \text{Right side:} \quad H: 6, \quad N: 2 \][/tex]
The balanced chemical equation that represents the formation of ammonia is:
[tex]\[ 3H_2 + N_2 \rightarrow 2NH_3 \][/tex]
Therefore, the correct option is C.
