To determine the correct equation that represents the formation of ammonia ([tex]\(NH_3\)[/tex]) from hydrogen ([tex]\(H_2\)[/tex]) and nitrogen ([tex]\(N_2\)[/tex]), we need to ensure the chemical equation is balanced. Here's the step-by-step process:
1. List the atoms involved in the reactants and products:
- Reactants: Hydrogen ([tex]\(H_2\)[/tex]) and Nitrogen ([tex]\(N_2\)[/tex])
- Product: Ammonia ([tex]\(NH_3\)[/tex])
2. Write the general form of the chemical reaction:
[tex]\[ x H_2 + y N_2 \rightarrow z NH_3 \][/tex]
3. Identify the atoms on each side:
- Hydrogen appears as [tex]\(H_2\)[/tex] on the reactant side.
- Nitrogen appears as [tex]\(N_2\)[/tex] on the reactant side.
- Ammonia ([tex]\(NH_3\)[/tex]) contains one nitrogen atom and three hydrogen atoms on the product side.
4. Balance the equation for each type of atom:
- Nitrogen: On the product side, [tex]\(z\)[/tex] molecules of [tex]\(NH_3\)[/tex] result in [tex]\(z\)[/tex] nitrogen atoms.
Therefore, [tex]\(y \cdot 2\)[/tex] (since each [tex]\(N_2\)[/tex] molecule has 2 nitrogen atoms) must equal [tex]\(z\)[/tex].
- Hydrogen: On the product side, [tex]\(z\)[/tex] molecules of [tex]\(NH_3\)[/tex] result in [tex]\(3z\)[/tex] hydrogen atoms.
Therefore, [tex]\(x \cdot 2\)[/tex] (since each [tex]\(H_2\)[/tex] molecule has 2 hydrogen atoms) must equal [tex]\(3z\)[/tex].
5. Set up the balance equations:
- For Nitrogen: [tex]\(2y = z\)[/tex]
- For Hydrogen: [tex]\(2x = 3z\)[/tex]
6. Solve for the simplest integer values:
- Start with [tex]\(y = 1\)[/tex]: then [tex]\(z = 2\)[/tex]
- Plugging [tex]\(z = 2\)[/tex] into the hydrogen equation: [tex]\(2x = 3 \cdot 2\)[/tex] => [tex]\(2x = 6\)[/tex] => [tex]\(x = 3\)[/tex]
7. Substitute the values into the general form:
[tex]\[ 3 H_2 + 1 N_2 \rightarrow 2 NH_3 \][/tex]
8. Check the balance:
- Reactants: 3 molecules of [tex]\(H_2\)[/tex] provide [tex]\(6\)[/tex] H atoms and 1 molecule of [tex]\(N_2\)[/tex] provides [tex]\(2\)[/tex] N atoms.
- Products: 2 molecules of [tex]\(NH_3\)[/tex] provide [tex]\(6\)[/tex] H atoms and [tex]\(2\)[/tex] N atoms.
- Both sides have the same number of each type of atom, hence the balanced equation is correct.
Thus, the correct equation representing the chemical reaction forming ammonia is:
[tex]\[ \boxed{3 H_2 + N_2 \rightarrow 2 NH_3} \][/tex]
Therefore, the correct option is [tex]\( \boxed{D} \)[/tex].
