Calculate the formula mass of sodium carbonate decahydrate, Na2CO3·10H2O, in atomic mass units (amu or u).
formula mass:
amu
The Correct Answer and Explanation is:
Formula Mass of Sodium Carbonate Decahydrate (Na₂CO₃·10H₂O)
To calculate the formula mass (also called molecular weight or molar mass) of sodium carbonate decahydrate, we sum the atomic masses of all the atoms in its chemical formula:
Chemical Formula: Na₂CO₃·10H₂O
Step 1: Atomic Masses (rounded to 2 decimal places)
- Sodium (Na) = 22.99 u
- Carbon (C) = 12.01 u
- Oxygen (O) = 16.00 u
- Hydrogen (H) = 1.008 u
Step 2: Count the atoms in the compound
Na₂CO₃:
- 2 Sodium (Na): 2 × 22.99 = 45.98 u
- 1 Carbon (C): 1 × 12.01 = 12.01 u
- 3 Oxygen (O): 3 × 16.00 = 48.00 u
10H₂O (10 Water molecules):
- 10 × (2 Hydrogen + 1 Oxygen) =
- Hydrogen: 10 × 2 × 1.008 = 20.16 u
- Oxygen: 10 × 16.00 = 160.00 u
Step 3: Add all the components together
Total formula mass=45.98+12.01+48.00+20.16+160.00=286.15 amu\text{Total formula mass} = 45.98 + 12.01 + 48.00 + 20.16 + 160.00 = \boxed{286.15\ \text{amu}}
Explanation
The formula mass of a compound, also known as the molecular weight, is the sum of the average atomic masses of all the atoms present in its chemical formula, expressed in atomic mass units (amu or u). In this case, the compound is sodium carbonate decahydrate (Na₂CO₃·10H₂O), which means it contains the regular sodium carbonate unit plus ten water molecules as waters of hydration.
First, we calculate the contribution of each element. Sodium carbonate (Na₂CO₃) consists of two sodium atoms, one carbon atom, and three oxygen atoms. The atomic masses are taken from the periodic table: sodium (22.99 u), carbon (12.01 u), and oxygen (16.00 u). Summing these gives the mass of the anhydrous salt.
Next, we account for the ten water molecules. Each water molecule consists of two hydrogen atoms and one oxygen atom. Multiply the number of each type of atom by their respective atomic masses and then by 10 (for ten molecules), and add the result to the previous subtotal.
The total formula mass combines the contributions from both the salt and the water. This gives a final value of 286.15 amu. This value is crucial in chemistry when determining how much of this compound is needed in a reaction, particularly in stoichiometric calculations and when preparing solutions.
Understanding formula mass also helps in interpreting chemical equations, as it allows conversion between moles and grams, and it is essential for lab-scale calculations and industrial chemistry.
