To determine the formula mass of [tex]\((NH_4)_2SO_4\)[/tex], we need to sum the atomic masses of all the atoms in the compound. Here’s a step-by-step breakdown of the calculation:
1. Identify the atomic masses of the elements involved:
- Hydrogen (H): 1.01 amu
- Nitrogen (N): 14.01 amu
- Sulfur (S): 32.07 amu
- Oxygen (O): 16.00 amu
2. Determine the number of each type of atom within one formula unit of [tex]\((NH_4)_2SO_4\)[/tex]:
- There are 2 nitrogen (N) atoms.
- There are 8 hydrogen (H) atoms (since there are two [tex]\(\text{NH}_4^+\)[/tex] groups).
- There is 1 sulfur (S) atom.
- There are 4 oxygen (O) atoms.
3. Calculate the total mass contributed by each type of atom:
- For Nitrogen: [tex]\(2 \times 14.01 \text{ amu} = 28.02 \text{ amu}\)[/tex]
- For Hydrogen: [tex]\(8 \times 1.01 \text{ amu} = 8.08 \text{ amu}\)[/tex]
- For Sulfur: [tex]\(1 \times 32.07 \text{ amu} = 32.07 \text{ amu}\)[/tex]
- For Oxygen: [tex]\(4 \times 16.00 \text{ amu} = 64.00 \text{ amu}\)[/tex]
4. Sum the masses to find the formula mass of [tex]\((NH_4)_2SO_4\)[/tex]:
- Total formula mass = [tex]\(28.02 \text{ amu (N)} + 8.08 \text{ amu (H)} + 32.07 \text{ amu (S)} + 64.00 \text{ amu (O)}\)[/tex]
- Total formula mass = [tex]\(28.02 + 8.08 + 32.07 + 64.00\)[/tex]
- Total formula mass = 132.17 amu
Thus, the formula mass of [tex]\((NH_4)_2SO_4\)[/tex] is [tex]\(132.17 \text{ amu}\)[/tex]. Therefore, the correct option is [tex]\(132.17 \text{ amu}\)[/tex].
