A 15.67gsample of hydrate of magnesium carbonate was carefully heated, without decomposing the carbonate to drive off water. The mass was reduce to 7.58g. What is the formula of the hydrated?
To find the formula of the hydrated compound, we need to determine the number of moles of water that was driven off during the heating process.
Step 1: Calculate the mass of water lost.
Mass of water lost = Initial mass - Final mass
Mass of water lost = 15.67 g - 7.58 g = 8.09 g
Step 2: Convert the mass of water lost to moles.
To convert grams to moles, we need to use the molar mass of water, which is 18.02 g/mol.
Moles of water lost = Mass of water lost / Molar mass of water
Moles of water lost = 8.09 g / 18.02 g/mol = 0.4492 mol
Step 3: Determine the number of moles of the anhydrous (without water) compound.
To do this, we need to assume that all the water in the original hydrate was removed when it was heated.
Moles of anhydrous compound = Moles of water lost
Moles of anhydrous compound = 0.4492 mol
Step 4: Find the molar mass of the anhydrous compound.
Molar mass of anhydrous compound = Mass of anhydrous compound / Moles of anhydrous compound
Molar mass of anhydrous compound = (Initial mass - Mass of water lost) / Moles of anhydrous compound
Molar mass of anhydrous compound = (15.67 g - 8.09 g) / 0.4492 mol = 16.97 g/mol
Finally, we can determine the empirical formula of the hydrated compound by dividing the molar masses of the elements in the anhydrous compound by their molar masses in terms of carbon.
Let's assume the hydrate has the formula MgCOₓ·nH₂O, where x is the number of carbon atoms, and n is the number of water molecules.
The molar mass of carbon is 12.01 g/mol.
Using the given empirical formula, the molar mass of the anhydrous compound is:
16.97 g/mol = molar mass of Mg + (molar mass of C × x) + (molar mass of O × x) + (molar mass of H₂O × n)
The molar mass of magnesium is 24.31 g/mol, and the molar mass of oxygen is 16.00 g/mol.
16.97 g/mol = 24.31 g/mol + (12.01 g/mol × x) + (16.00 g/mol × x) + (18.02 g/mol × n)
Simplifying the equation:
16.97 g/mol = 24.31 g/mol + 28.01 g/mol × x + 18.02 g/mol × n
16.97 g/mol = 24.31 g/mol + (46.03 g/mol × x) + (18.02 g/mol × n)
Since we don't know the values of x and n, we cannot solve for a unique formula using the given information. Additional information, such as the molar mass of the hydrated compound or the percentage composition, would be needed to determine the specific formula of the hydrate.