To find the formula mass of the compound [tex]\((NH_4)_2SO_4\)[/tex], let's follow these steps:
1. Identify the atomic masses of each element in the compound:
- Hydrogen (H) has an atomic mass of approximately [tex]\(1.01 \, \text{amu}\)[/tex].
- Nitrogen (N) has an atomic mass of approximately [tex]\(14.01 \, \text{amu}\)[/tex].
- Sulfur (S) has an atomic mass of approximately [tex]\(32.07 \, \text{amu}\)[/tex].
- Oxygen (O) has an atomic mass of approximately [tex]\(16.00 \, \text{amu}\)[/tex].
2. Count the number of each type of atom in the compound [tex]\((NH_4)_2SO_4\)[/tex]:
- There are 2 nitrogen atoms (N).
- There are 2 groups of [tex]\(NH_4\)[/tex], each containing 4 hydrogen atoms, so there are [tex]\(2 \times 4 = 8\)[/tex] hydrogen atoms (H).
- There is 1 sulfur atom (S).
- There are 4 oxygen atoms (O).
3. Calculate the total mass contributed by each element:
- The total mass of nitrogen: [tex]\(2 \times 14.01 = 28.02\)[/tex]
- The total mass of hydrogen: [tex]\(8 \times 1.01 = 8.08\)[/tex]
- The total mass of sulfur: [tex]\(1 \times 32.07 = 32.07\)[/tex]
- The total mass of oxygen: [tex]\(4 \times 16.00 = 64.00\)[/tex]
4. Sum the masses to find the formula mass:
[tex]\[
\text{Formula mass} = 28.02 + 8.08 + 32.07 + 64.00 = 132.17 \, \text{amu}
\][/tex]
Thus, the formula mass of [tex]\((NH_4)_2SO_4\)[/tex] is [tex]\(132.17 \, \text{amu}\)[/tex].
Among the given options, the correct answer is:
[tex]\[
\boxed{132.17 \, \text{amu}}
\][/tex]
