Question

Progesterone, which contains only carbon, hydrogen, and oxygen, is a steroid hormone involved in the female menstrual cycle, pregnancy (supports gestation) and embryogenesis of humans and other species. Combustion analysis of a 1.893-g sample of progesterone produced 5.563 g of CO2 and 1.627 g H2O. The molar mass of progesterone is 314.46 g/mol What is the molecular formula for progesterone

Answer 1

Let the molecular formula of Progesterone be C_XH_YO_Z

Let us write the combustion reaction

C_XH_YO_Z +    (X+(Y/4)-(Z/2)) O₂       -----------> XCO₂   + (Y/2) H₂O

The above is the balances reaction

Data given : Weight of progesterone = 1.893 grams

      Molar mass of progesterone = 314.46 g/mole

Weight of CO2 produced = 5.563 grams

Weight of H2O produced = 1.627 grams

Molar mass of CO2 = 44 gram/mole

Molar mass of H2O = 18 gram/mole

Moles of progesterone = weight of progesterone / molar mass of progesterone = 1.893/314.46 = 6.0198*10^-3 moles

moles of CO2 = Weight CO2 / Molar mass of CO2 = 5.563/44 = 0.12643 moles

Moles of H2O = weight of water / molar mass of water = 1.627 /18 = 0.09038 moles

Now let us recall the reaction   

C_XH_YO_Z +    (X+(Y/4)-(Z/2)) O₂       -----------> XCO₂   +     (Y/2) H₂O          

6.0198*10^-3                                             0.12643           0.09038

From reaction stoichiometry ,

1 moles of progesterone = x moles of CO2

x* 6.0198*10^-3   = 0.12643    

x= 0.12643/ 6.0198*10^-3 =21

From reaction stoichiometry ,

1 moles of progesterone = (y/2) moles of H2O

(y/2) * 6.0198*10^-3 =0.09038

     y = (2*0.09038 /6.0198*10^-3 ) = 30

Now we know molar mass of progesterone is 314.46 g/moles and molecular formula is C_XH_YO_Z

Hence,    x(12)+ 1(y) + 16(z) = 314.46

               21(12)+ 1(30) +16(z) =314.46

                      16(z) = 314.46 - 21(12) -1(30)=32.46

                             z =32.46/16 = 2.028= approximately 2

Since we now know x =21 ,y=30 and z = 2

Hence molecular formula for progesterone is C₂₁H₃₀O₂