What is the molar mass of calcium chloride dihydrate (CaCl2 • 2H2O)? Be sure to
include the mass of all elements in the formula including the elements in water.
The Correct Answer and Explanation is:
To calculate the molar mass of calcium chloride dihydrate (CaCl₂ • 2H₂O), we need to consider the molar masses of each individual component within the compound.
- Identify the components of the formula:
- Calcium (Ca)
- Chlorine (Cl)
- Water (H₂O)
- Determine the molar masses of each element:
- Calcium (Ca): The atomic mass of calcium is approximately 40.08 g/mol.
- Chlorine (Cl): The atomic mass of chlorine is approximately 35.45 g/mol. Since there are two chlorine atoms in calcium chloride, the total mass for chlorine is:
[
2 \times 35.45 \, \text{g/mol} = 70.90 \, \text{g/mol}
] - Water (H₂O): The molar mass of water can be calculated as follows:
- Hydrogen (H): The atomic mass of hydrogen is approximately 1.01 g/mol. Since there are two hydrogen atoms in water, the total mass for hydrogen is:
[
2 \times 1.01 \, \text{g/mol} = 2.02 \, \text{g/mol}
] - Oxygen (O): The atomic mass of oxygen is approximately 16.00 g/mol. Thus, the molar mass of water is:
[
2.02 \, \text{g/mol} + 16.00 \, \text{g/mol} = 18.02 \, \text{g/mol}
]
Since there are two water molecules in the formula (indicated by the dihydrate), the total mass for water is:
[
2 \times 18.02 \, \text{g/mol} = 36.04 \, \text{g/mol}
]
- Hydrogen (H): The atomic mass of hydrogen is approximately 1.01 g/mol. Since there are two hydrogen atoms in water, the total mass for hydrogen is:
- Calculate the total molar mass:
- Now, we can sum the masses of all the components:
[
\text{Molar mass of CaCl}_2 \cdot 2\text{H}_2\text{O} = \text{mass of Ca} + \text{mass of Cl}_2 + \text{mass of } 2\text{H}_2\text{O}
]
[
= 40.08 \, \text{g/mol} + 70.90 \, \text{g/mol} + 36.04 \, \text{g/mol} = 146.02 \, \text{g/mol}
]
Therefore, the molar mass of calcium chloride dihydrate (CaCl₂ • 2H₂O) is 146.02 g/mol.
In summary, the molar mass calculation involves adding the molar masses of each element and compound present in the formula. Understanding the contributions of both the calcium chloride and the water of hydration is crucial for obtaining the accurate molar mass, which is essential for stoichiometric calculations in chemistry.