To determine if the chemical equation [tex]\(4 NH_3 \rightarrow 2 N_2 + 6 H_2\)[/tex] is balanced, and if the coefficients are in the lowest whole number form, we can follow these steps:
1. Check if the equation is balanced:
- Count the atoms of each element on the left side:
- There are 4 molecules of [tex]\(NH_3\)[/tex].
- Each [tex]\(NH_3\)[/tex] molecule contains 1 Nitrogen (N) atom and 3 Hydrogen (H) atoms.
- Therefore, on the left side:
- Nitrogen (N): [tex]\(4 \times 1 = 4\)[/tex] atoms
- Hydrogen (H): [tex]\(4 \times 3 = 12\)[/tex] atoms
- Count the atoms of each element on the right side:
- There are 2 molecules of [tex]\(N_2\)[/tex].
- Each [tex]\(N_2\)[/tex] molecule contains 2 Nitrogen (N) atoms.
- Therefore, on the right side:
- Nitrogen (N): [tex]\(2 \times 2 = 4\)[/tex] atoms
- There are 6 molecules of [tex]\(H_2\)[/tex].
- Each [tex]\(H_2\)[/tex] molecule contains 2 Hydrogen (H) atoms.
- Therefore, on the right side:
- Hydrogen (H): [tex]\(6 \times 2 = 12\)[/tex] atoms
- Compare the counts on both sides:
- Nitrogen: 4 atoms on both sides.
- Hydrogen: 12 atoms on both sides.
- Since the number of atoms of each element is the same on both sides, the equation is balanced.
2. Check if the coefficients are in the lowest whole number ratio:
- The coefficients in the given equation are 4:2:6.
- Find the greatest common divisor (GCD) of these coefficients: The GCD of 4, 2, and 6 is 2.
- Divide each coefficient by the GCD (2) to obtain the lowest whole number ratio:
- [tex]\( \frac{4}{2} = 2 \)[/tex]
- [tex]\( \frac{2}{2} = 1 \)[/tex]
- [tex]\( \frac{6}{2} = 3 \)[/tex]
- This gives new coefficients of 2:1:3.
Since the coefficients could be reduced to 2,1, and 3, the correct answer is:
B. No, because the coefficients could be reduced to 2, 1, and 3.
