A hydrated aluminium sulphate A12(SO4)3.xH2O, contains 8.10% of
aluminium by mass.
Find the value of x
Find the molmass of the hydrated molecule.
molmass=12Al+3S+12O+xH2+XO where the element symbols are atomic masses.
but x*molmassH2O/above= .0810
solve for X, and have fun with algebra.
To find the value of x in the hydrated aluminium sulphate formula A12(SO4)3.xH2O, we can use the given information that the compound contains 8.10% of aluminium by mass.
Step 1: Calculate the molar mass of aluminium (Al).
The molar mass of Al is 26.98 g/mol.
Step 2: Calculate the molar mass of the compound A12(SO4)3.xH2O.
The molar mass of A12(SO4)3 is:
2 * (26.98 g/mol) + 3 * [(32.07 g/mol) + (4 * 16.00 g/mol)] = 342.14 g/mol.
Step 3: Calculate the molar mass of water (H2O).
The molar mass of H2O is 18.02 g/mol.
Step 4: Write the equation to calculate the mass of aluminium in the compound.
(8.10g Al / 100g of compound) * (342.14 g/mol) = mass of Al.
Step 5: Solve for x.
Let's assume there are 'y' moles of Al in the compound, which means there are also 'y' moles of xH2O. The total moles of the compound is then equal to y + y = 2y.
Using the mole ratio, we can set up the equation:
(y moles Al / 2y moles of compound) * (342.14 g/mol) = (mass of Al) / (molar mass of Al).
Step 6: Convert the moles of xH2O to mass.
The molar mass of xH2O is:
2 * (1.01 g/mol) + 16.00 g/mol + x * [2 * (1.01 g/mol) + 16.00 g/mol] = 18.02 g/mol + 18.02x g/mol (since there are two hydrogen atoms per molecule of water).
Step 7: Set up the equation for the mass of xH2O.
[(mass of Al) + (mass of xH2O)] = 100g (since the total mass of the compound is 100g).
Step 8: Solve the equation to find x.
Substitute the previously calculated values into the equation:
(mass of Al) + [18.02 g/mol + 18.02x g/mol] = 100g.
Solving this equation will give you the value of x, the number of water molecules in hydrated aluminium sulphate.