Answer :
We know the percent composition of a compound:
Mg: 28.03%
Si: 21.60%
H 1.16%
O 49.21%
We will suppose that we have a sample of this compound and the mass of that sample is 100 g. If the mass of the sample is 100 g, the mass of each element is:
Total mass of the sample = 100 g
mass of Mg = 28.03 g
mass of Si = 21.60 g
mass of H = 1.16 g
mass of O = 49.21 g
We are asked to calculate the empirical formula of our compound. The definition of empirical formula is: " The empirical formula is a chemical formula showing the simplest ratio of elements in a compound".
So we have to find the ratio between the elements of our compound. We have to convert those grams into moles. We will need the molar mass of each element:
molar mass of Mg = 24.30 g/mol
molar mass of Si = 28.09 g/mol
molar mass of H = 1.01 g/mol
molar mass of O = 16.00 g/mol
Let's find the number of moles of each element that we have in 100 g of our sample:
number of moles of Mg = mass of Mg/molar mass of Mg
number of moles of Mg = 28.03 g/(24.30 g/mol)
number of moles of Mg = 1.15 moles
number of moles of Si = 21.60 g/(28.09 g/mol)
number of moles of Si = 0.77 moles
number of moles of H = 1.16 g/(1.01 g/mol)
number of moles of H = 1.15 moles
number of moles of O = 49.21 g/(16.00 g/mol)
number of moles of O = 3.08 moles
We got the number of moles of each element in the 100 g sample. The ratio between them is:
Mg : Si : H : O = 1.15 : 0.77 : 1.15 : 3.08
To get the empirical formula we need the whole ratio. We have to divide the number of moles by the smallest one. (0.77 moles)
Mg = 1.15/0.77 = 1.5
Si = 0.77/0.77 = 1
H = 1.15/0.77 = 1.5
O = 3.08/0.77 = 4
So the simplest ratio between the elements of our compound is (empirical formula):
Mg1.5 Si H1.5 O4
We can't write fractions as the subscripts of our empirical formula. So we need to multiply the subscripts by the smallest number to make them an entire. That number is a 2.
Mg = 1.5 * 2 = 3
Si = 1 *2 = 2
H = 1.5 *2 = 3
O = 4 *2 = 8
Answer: The empirical formula is Mg₃Si₂H₃O₈ or Mg3Si2H3O8
To get the empirical formula we have to divide the molar mass of the empirical formula by the molar mass of the compound. To calculate the molar mass of the empircal formula we need the atomic masses of our elements.
atomic mass of Mg = 24.30 amu
atomic mass of Si = 28.09 amu
atomic mass of H = 1.01 amu
atomic mass of O = 16.00 amu
The empirical formula of our compound has 3 atoms of Mg, 2 atoms of Si, 3 atoms of H and 8 atoms of O. The molar mass of the empirical formula is:
molar mass of Mg₃Si₂H₃O₈ = 3 * 24.30 + 2 * 28.09 + 3 * 1.01 + 8 * 16.00
molar mass of Mg₃Si₂H₃O₈ = 260.11 g/mol
Finally we have to find the ratio between the molar mass of the compound and the molar mass of the empirical formula.
n = molar mass of compound/molar mass of empirical formula
n = 520.8 g/mol / (260.11 g/mol)
n = 2
So the molecular formula of our compound is the double than the empirical formula.
Answer: The molecular formula is Mg₆Si₄H₆O₁₆ or Mg6Si4H6O16
