Answer:
C₅H₁₀O₅
Explanation:
1. Calculate the mass of each element in 2.78 mg of X.
(a) Mass of C
[tex]\text{Mass of C} = \text{5.13 g CO}_{2}\times \dfrac{\text{12.01 g C}}{\text{44.01 g }\text{CO}_{2}}= \text{1.400 g C}[/tex]
(b) Mass of H
[tex]\text{Mass of H} = \text{2.10 g H$_{2}$O}\times \dfrac{\text{2.016 g H}}{\text{18.02 g H$_{2}$O}} = \text{0.2349 g H}[/tex]
(c) Mass of O
Mass of O = 3.5 - 1.400 - 0.2349 = 1.87 g
2. Calculate the moles of each element
[tex]\text{Moles of C = 1400 mg C}\times\dfrac{\text{1 mmol C}}{\text{12.01 mg C }} = \text{116.6 mmol C}\\\\\text{Moles of H = 234.9 mg H} \times \dfrac{\text{1 mmol H}}{\text{1.008 mg H}} = \text{233.1 mmol H}\\\\\text{Moles of O = 1870 mg O} \times \dfrac{\text{1 mmol O}}{\text{16.00 mg O}} = \text{116 mmol O}[/tex]
3. Calculate the molar ratios
Divide all moles by the smallest number of moles.
[tex]\text{C: } \dfrac{116.6}{116.6}= 1\\\\\text{H: } \dfrac{233.1}{116.6} = 1.999\\\\\text{O: } \dfrac{116}{116.6} = 1.00[/tex]
4. Round the ratios to the nearest integer
C:H:O = 1:2:1
5. Write the empirical formula
The empirical formula is CH₂O.
6. Calculate the molecular formula.
EF Mass = (12.01 + 2.016 + 16.00) u = 30.03 u
The molecular formula is an integral multiple of the empirical formula.
MF = (EF)ₙ
[tex]n = \dfrac{\text{MF Mass}}{\text{EF Mass }} = \dfrac{\text{150 u}}{\text{30.03 u}} = 5.00 \approx 5[/tex]
MF = (CH₂O)₅ = C₅H₁₀O₅
The molecular formula of X is C₅H₁₀O₅.
