To determine the formula mass of [tex]\((NH_4)_2SO_4\)[/tex], let's break down the molecule into its constituent atoms and sum their contributions based on their atomic masses.
1. Identify the number of each type of atom in the molecule:
- [tex]\((NH_4)_2SO_4\)[/tex] consists of:
- 2 ammonium ions [tex]\((NH_4)^+\)[/tex]
- 1 sulfate ion [tex]\((SO_4)^{2-}\)[/tex]
2. Count the number of atoms for each element:
- Hydrogen (H): Each ammonium ion [tex]\((NH_4)^+\)[/tex] contains 4 hydrogen atoms. Since there are 2 ammonium ions, the total number of hydrogen atoms is:
[tex]\[
2 \times 4 = 8 \text{ hydrogen atoms}
\][/tex]
- Nitrogen (N): Each ammonium ion [tex]\((NH_4)^+\)[/tex] contains 1 nitrogen atom. Since there are 2 ammonium ions, the total number of nitrogen atoms is:
[tex]\[
2 \times 1 = 2 \text{ nitrogen atoms}
\][/tex]
- Sulfur (S): The sulfate ion [tex]\((SO_4)^{2-}\)[/tex] contains 1 sulfur atom.
- Oxygen (O): The sulfate ion [tex]\((SO_4)^{2-}\)[/tex] contains 4 oxygen atoms.
3. Find the atomic masses:
- Hydrogen (H): 1.01 amu
- Nitrogen (N): 14.01 amu
- Sulfur (S): 32.07 amu
- Oxygen (O): 16.00 amu
4. Calculate the total contribution to the formula mass from each type of atom:
- Hydrogen (H):
[tex]\[
8 \times 1.01 \text{ amu} = 8.08 \text{ amu}
\][/tex]
- Nitrogen (N):
[tex]\[
2 \times 14.01 \text{ amu} = 28.02 \text{ amu}
\][/tex]
- Sulfur (S):
[tex]\[
1 \times 32.07 \text{ amu} = 32.07 \text{ amu}
\][/tex]
- Oxygen (O):
[tex]\[
4 \times 16.00 \text{ amu} = 64.00 \text{ amu}
\][/tex]
5. Sum the contributions to find the formula mass:
[tex]\[
8.08 \text{ amu} + 28.02 \text{ amu} + 32.07 \text{ amu} + 64.00 \text{ amu} = 132.17 \text{ amu}
\][/tex]
Therefore, the formula mass of [tex]\((NH_4)_2SO_4\)[/tex] is [tex]\(132.17\)[/tex] amu. The correct answer is:
[tex]\[
132.17 \text{ amu}
\][/tex]
