Certainly! Let's calculate the formula mass or molecular mass of manganese(II) sulfate monohydrate, which is represented as [tex]\( MnSO_4 \cdot 2 H_2O \)[/tex].
Here's a detailed step-by-step solution:
1. Identify the atomic masses of each element:
- Manganese (Mn): 54.938 amu
- Sulfur (S): 32.06 amu
- Oxygen (O): 16.00 amu
- Hydrogen (H): 1.008 amu
2. Identify the number of each atom in the compound:
- MnSO₄ contains 1 Mn, 1 S, and 4 O atoms.
- [tex]\(2 H_2O\)[/tex] means we have 2 molecules of water, contributing 4 H atoms and 2 O atoms (since each water molecule [tex]\(H_2O\)[/tex] contains 2 H and 1 O).
3. Calculate the total number of each type of atom in the entire compound:
- Manganese: 1 Mn
- Sulfur: 1 S
- Oxygen: 4 O from MnSO₄ + 2 O from 2 H₂O = 6 O
- Hydrogen: 4 H from 2 H₂O
4. Multiply the number of atoms by their respective atomic masses:
- [tex]\( \text{Mass of Mn} = 1 \times 54.938 \)[/tex]
- [tex]\( \text{Mass of S} = 1 \times 32.06 \)[/tex]
- [tex]\( \text{Mass of O} = 6 \times 16.00 \)[/tex]
- [tex]\( \text{Mass of H} = 4 \times 1.008 \)[/tex]
5. Calculate the contributions from each element:
- Manganese: [tex]\( 54.938 \)[/tex] amu
- Sulfur: [tex]\( 32.06 \)[/tex] amu
- Oxygen: [tex]\( 6 \times 16.00 = 96.00 \)[/tex] amu
- Hydrogen: [tex]\( 4 \times 1.008 = 4.032 \)[/tex] amu
6. Sum all the contributions to obtain the total molecular mass:
- Total molecular mass = [tex]\( 54.938 + 32.06 + 96.00 + 4.032 = 187.03 \)[/tex] amu
Therefore, the formula mass or molecular mass of [tex]\( MnSO_4 \cdot 2 H_2O \)[/tex] is [tex]\( 187.03 \)[/tex] amu.
