Answer:
The empirical formula is C₄H₈O;
The molecular formula is C₈H₁₆O₂.
Step-by-step explanation:
The empiric formula is CxHyOz, and the combustion reaction occurs between the fuel and oxygen gas, so it will be:
CxHyOz + O₂ → CO₂ + H₂O
So, all the carbon will form CO₂ and all hydrogen will form H₂O. So, let's calculated the number of moles of carbon in CO₂ and the number of moles of hydrogen in H₂O. They must be the same number f the moles in the valproic acid.
The molar masses are: C= 12 g/mol, O = 156 g/mol and H = 1 g/mol, so CO₂ = 12 + 2x16 = 44 g/mol, and H₂O = 2x1 + 16 = 18 g/mol.
nCO₂ = 0.403/44 = 9.16x10⁻³ mol
In 1 mol of CO₂ there is 1 mol of C, so nC = 9.16x10⁻³ mol.
nH₂O = 0.166/18 = 9.22x10⁻³ mol.
In 1 mol of H₂O there are 2 moles of H, so nH = 0.018 mol.
The mass of Carbon and the mass of H in the compound must be:
mC = nxM = 9.22x10⁻³ x12 = 0.1106 g
mH = nxM = 0.018x1 = 0.018 g
The mass of oxygen must be then:
mC + mH +mO = 0.165
mO = 0.165 - 0.1106 - 0.018
mO = 0.0364g
And its number of moles:
nO = 0.0364/16 = 2.275x10⁻³ mol
To have the empirical formula, the coefficients must be the smallest, so let's divide the number of moles for the small one: 2.275x10⁻³
nC = (9.16x10⁻³ )/(2.275x10⁻³) = 4 mol
nH = 0.018/(2.275x10⁻³) = 8 mol
nO = (2.275x10⁻³)/(2.275x10⁻³) = 1 mol
The empirical formula is C₄H₈O.
The molecular formula must be a multiple of the empirical, so it will be n(C₄H₈O). Knowing the molar mass, we can calculate n:
4xnx12 + 8xnx1 + 1xnx16 = 144
48n + 8n + 16n = 144
72n = 144
n = 2
The molecular formula is 2(C₄H₈O) = C₈H₁₆O₂.