Sure! Let's balance the equation for the formation of ammonia (NH_3) from nitrogen (N_2) and hydrogen (H_2) step-by-step:
Unbalanced Equation:
[tex]\[ \text{N}_2(g) + \text{H}_2(g) \rightarrow \text{NH}_3(g) \][/tex]
1. Count the atoms of each element on both sides of the reaction:
- On the left side (reactants):
- Nitrogen (N): 2 atoms from [tex]\(\text{N}_2\)[/tex]
- Hydrogen (H): 2 atoms from [tex]\(\text{H}_2\)[/tex]
- On the right side (products):
- Nitrogen (N): 1 atom in [tex]\(\text{NH}_3\)[/tex]
- Hydrogen (H): 3 atoms in [tex]\(\text{NH}_3\)[/tex]
2. Balance the nitrogen atoms first:
- On the left side, we have 2 nitrogen atoms in one molecule of [tex]\(\text{N}_2\)[/tex].
- On the right side, each molecule of [tex]\(\text{NH}_3\)[/tex] has 1 nitrogen atom. To balance the nitrogen atoms, we need 2 molecules of [tex]\(\text{NH}_3\)[/tex]:
[tex]\[ \text{N}_2(g) + \text{H}_2(g) \rightarrow 2\text{NH}_3(g) \][/tex]
3. Re-count the atoms after modifying the equation:
- Left side:
- Nitrogen (N): 2 atoms
- Hydrogen (H): 2 atoms from [tex]\(\text{H}_2\)[/tex]
- Right side:
- Nitrogen (N): 2 atoms (from 2x [tex]\(\text{NH}_3\)[/tex])
- Hydrogen (H): 6 atoms (from 2x [tex]\(\text{NH}_3\)[/tex])
4. Balance the hydrogen atoms now:
- On the left side, we currently have 2 hydrogen atoms (1 molecule of [tex]\(\text{H}_2\)[/tex]).
- On the right side, we need a total of 6 hydrogen atoms (from 2 molecules of [tex]\(\text{NH}_3\)[/tex]).
- Therefore, we need 3 molecules of [tex]\(\text{H}_2\)[/tex] to provide those 6 hydrogen atoms:
[tex]\[ \text{N}_2(g) + 3\text{H}_2(g) \rightarrow 2\text{NH}_3(g) \][/tex]
5. Final check for balance:
- Left side:
- Nitrogen (N): 2 atoms from [tex]\(\text{N}_2\)[/tex]
- Hydrogen (H): 6 atoms from 3 molecules of [tex]\(\text{H}_2\)[/tex]
- Right side:
- Nitrogen (N): 2 atoms from 2 molecules of [tex]\(\text{NH}_3\)[/tex]
- Hydrogen (H): 6 atoms from 2 molecules of [tex]\(\text{NH}_3\)[/tex]
Both sides have 2 nitrogen atoms and 6 hydrogen atoms. Therefore, the equation is balanced.
Balanced Equation:
[tex]\[ \text{N}_2(g) + 3\text{H}_2(g) \rightarrow 2\text{NH}_3(g) \][/tex]
So, the balanced chemical equation is:
[tex]\[ \text{N}_2(g) + 3\text{H}_2(g) \rightarrow 2\text{NH}_3(g) \][/tex]
