Question

A 40.4 g sample of a protein contains 17.16 g of carbon, 3.17 g of hydrogen, 13.71 g of oxygen, and the rest being nitrogen. This 40.4-gram sample is known to be 0.07141 moles. Determine the molecular formula of this protein.

Answer 1

The molecular formula of this protein : C₁₈H₄₂O₁₂N₆

Further explanation  

The empirical formula is the smallest comparison of atoms of compound forming elements.  

A molecular formula is a formula that shows the number of atomic elements that make up a compound.  

(empirical formula) n = molecular formula  

The principle of determining empirical formula and molecular formula  

• Determine the mass ratio of the constituent elements of the compound.  
• Determine the mole ratio by dividing the elemental mass with the relative atomic mass obtained by the empirical formula  
• Determine molecular formulas by looking for values of n  

Find mol ratio for every component :

• C (Ar=12 g/mol):

$\tt \dfrac{17.16}{12}=1.43$

• H(Ar=1 g/mol) :

$\tt \dfrac{3.17}{1}=3.17$

• O(Ar=16 g/mol) :

$\tt \dfrac{13.71}{16}=0.857$

N (r=14 g/mol) :

Mass of Nitrogen :

40.4-(17.16+3.17+13.71)=6.36 g

• N :

$\tt \dfrac{6.36}{14}=0.454$

C : H : O : N = 1.43 : 3.17 : 0.857 : 0.454 = 3.15 : 7 : 1.89 : 1=3:7:2:1

Empirical formula : C₃H₇O₂N

Molecular mass of protein :

$\tt \dfrac{40.4}{0.07141}=565.75$

(C₃H₇O₂N)n=565.75

(12.3+1.7+2.16+14)n=565.75

(89)n=565.75

n=6.4≈6

so the molecular formula : C₁₈H₄₂O₁₂N₆