Calculate the molar mass of magnesium sulfate heptahydrate, mgso4·7h2o.
The Correct Answer and Explanation is :
To calculate the molar mass of magnesium sulfate heptahydrate (MgSO₄·7H₂O), we need to sum up the atomic masses of all the elements in the formula, including those of magnesium sulfate (MgSO₄) and the seven water molecules (7H₂O).
Step 1: Atomic Masses
Here are the atomic masses of the elements involved:
- Magnesium (Mg) = 24.305 g/mol
- Sulfur (S) = 32.065 g/mol
- Oxygen (O) = 16.00 g/mol
- Hydrogen (H) = 1.008 g/mol
Step 2: Break down the formula
The formula for magnesium sulfate heptahydrate is MgSO₄·7H₂O, which consists of:
- One magnesium atom (Mg)
- One sulfur atom (S)
- Four oxygen atoms in the sulfate part (SO₄)
- Seven water molecules (7H₂O), where each water molecule consists of two hydrogen atoms and one oxygen atom.
Step 3: Molar Mass of MgSO₄
Now, we can calculate the molar mass of MgSO₄:
- Mg = 1 × 24.305 = 24.305 g/mol
- S = 1 × 32.065 = 32.065 g/mol
- O (from SO₄) = 4 × 16.00 = 64.00 g/mol
So, the molar mass of MgSO₄ is:
[
24.305 + 32.065 + 64.00 = 120.37 \, \text{g/mol}
]
Step 4: Molar Mass of 7H₂O
Next, calculate the molar mass of 7 water molecules (7H₂O):
- H = 2 × 1.008 = 2.016 g/mol (per water molecule)
- O = 1 × 16.00 = 16.00 g/mol (per water molecule)
So, the molar mass of one water molecule is:
[
2.016 + 16.00 = 18.016 \, \text{g/mol}
]
For 7 water molecules, the total mass is:
[
7 × 18.016 = 126.112 \, \text{g/mol}
]
Step 5: Total Molar Mass of MgSO₄·7H₂O
Finally, the total molar mass of magnesium sulfate heptahydrate is the sum of the molar masses of MgSO₄ and 7H₂O:
[
120.37 + 126.112 = 246.482 \, \text{g/mol}
]
Final Answer:
The molar mass of magnesium sulfate heptahydrate (MgSO₄·7H₂O) is 246.48 g/mol.
Explanation:
This calculation involves adding together the individual atomic masses of magnesium, sulfur, oxygen, and hydrogen, considering their respective counts in the formula. The molecular structure of MgSO₄·7H₂O is made up of one magnesium sulfate unit (MgSO₄) and seven water molecules (7H₂O), with the water contributing significantly to the total molar mass due to its mass being calculated for seven molecules instead of just one. The process of summing the molar masses of these components leads us to the final answer.