The molar mass of hydrated sodium carbonate is 268 g/mol. Calculate the number of moles of water of crystallization (x) if the formula for hydrated sodium carbonate is Na2CO3.xH2O.
The Correct Answer and Explanation is:
To find the number of moles of water of crystallization (x) in the formula of hydrated sodium carbonate, Na₂CO₃·xH₂O, given that its molar mass is 268 g/mol, we follow these steps:
Step 1: Determine the molar mass of anhydrous sodium carbonate (Na₂CO₃)
Using atomic masses:
- Na = 23 g/mol
- C = 12 g/mol
- O = 16 g/mol
Molar mass of Na₂CO₃ = (2 × 23) + 12 + (3 × 16)
= 46 + 12 + 48
= 106 g/mol
Step 2: Let x be the number of water molecules.
Each water molecule (H₂O) has a molar mass of:
(2 × 1) + 16 = 18 g/mol
So, molar mass of Na₂CO₃·xH₂O = 106 + 18x
We are told this equals 268 g/mol:
106 + 18x = 268
Step 3: Solve for x
18x = 268 − 106
18x = 162
x = 162 ÷ 18
x = 9
Final Answer:
x = 9
So, the formula is Na₂CO₃·9H₂O
Explanation
Hydrated salts are compounds that contain a specific number of water molecules loosely bonded within their crystal structure. These water molecules, known as water of crystallization, are integral to the composition and properties of the compound. In this case, we are asked to determine how many moles of water molecules are associated with each formula unit of sodium carbonate, Na₂CO₃, in its hydrated form.
The compound is given as Na₂CO₃·xH₂O, and the total molar mass is provided as 268 g/mol. To find the value of x, we start by calculating the molar mass of the anhydrous part—sodium carbonate (Na₂CO₃). By summing the atomic masses of its elements (2 sodium atoms, 1 carbon atom, and 3 oxygen atoms), we find that anhydrous sodium carbonate has a molar mass of 106 g/mol.
Next, we recognize that the remaining mass must come from the x number of water molecules. Each H₂O has a molar mass of 18 g/mol. Thus, the total mass of the hydrated compound can be expressed as:
106 + 18x = 268.
Solving this equation yields x = 9, meaning that there are nine water molecules associated with each formula unit of sodium carbonate in the hydrated compound. Therefore, the full formula is Na₂CO₃·9H₂O, known as sodium carbonate nonahydrate.
This kind of calculation is essential in understanding the composition of hydrates and is widely used in chemistry to determine empirical formulas, calculate yields, and prepare accurate chemical solutions.
