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Cortisol (molecular weight 362.47 g/mole), one of the major steroid hormones, is a key factor in the synthesis of protein. Its profound effect on the reduction of inflammation explains its use in the treatment of rheumatoid arthritis. Cortisol is 69.9% C, 8.34% H and 22.1 % O by mass. What is its molecular formula?

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The molecular formula of cortisol is C₂₁H₃₀O₅

Explanation:

To find the cortisol formula we use the following algorithm:

divide each element percentage by the atomic weight of the element

for carbon 69.9 / 12 = 5.83

for hydrogen 8.34 / 1 = 8.34

for oxygen 22.2 / 16 = 1.41

now the we divide the obtained numbers by the lowest one, which is 1.41

for carbon 5.83/ 1.41 ≈ 4

for hydrogen 8.34 / 1.41 ≈ 6

for oxygen 1.41 / 1.41 = 1

the empirical formula of cortisol is C₄H₆O

the molecular formula of cortisol is (C₄H₆O)ₓ

70x = 362.47

x = 362.47 / 70

x ≈ 5.2

carbon ≈ 5.2 × 4 ≈ 21

hydrogen = 5 × 6 = 30

oxygen = 5 × 1 = 5

The molecular formula of cortisol is C₂₁H₃₀O₅

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determining the molecular formula of a compound

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