To lose weight body fat is converted to carbon dioxide and w

To lose weight, body fat is converted to carbon dioxide and water and exhaled through the lungs. Losing 10 kilograms of human fat requires the exahlation of 28 kilograms of carbon dioxide and 11 kilograms of water. What is the empirical formula (CxHyOz) of body fat? (Please show work, thank you!)

Solution

mass of CO2 = 28 Kg = 28000 g
mass of H2O = 11 Kg = 11000 g
mass of fat = 10 Kg = 10000 g

let in compound number of moles of C, H and O be x, y and z respectively

Number of moles of CO2 = mass of CO2 / molar mass CO2
= 28000/44
= 6.364*10^2

Number of moles of H2O = mass of H2O / molar mass H2O
= 11000/18
= 6.111*10^2

Since 1 mol of CO2 has 1 mol of C
Number of moles of C in CO2= 6.364*10^2
so, x = 6.364*10^2

Since 1 mol of H2O has 2 mol of H
Number of moles of H = 2*6.111*10^2 = 1.222*10^3

Molar mass of O = 16 g/mol


mass O = total mass - mass of C and H
= 10000 - 6.364*10^2*12 - 1.222*10^3*1
= 1.141*10^3

number of mol of O = mass of O / molar mass of O
= 1.141*10^3/16.0
= 71.34
so, z = 71.34
Divide by smallest to get simplest whole number ratio:
C: 6.364*10^2/71.34 = 9
H: 1.222*10^3/71.34 = 17
O: 71.34/71.34 = 1


So empirical formula is:C9H17O
Answer:
empirical formula is:C₉H₁₇O