Answer to Question #163608 in Organic Chemistry for fofo

Question

A carbohydrate was isolated from a sample of cow’s milk. The substance was found to have a molecular mass of 342. The unknown carbohydrate can be hydrolyzed to form two isomeric compounds, each with a molecular mass of 180. Using the Rule of Thirteen, determine a molecular formula and an index of hydrogen deficiency for the unknown and for the hydrolysis products. (Hint: Begin by solving the molecular formula for the 180-amu hydrolysis products. These products have one oxygen atom for every carbon atom in the molecular formula. The unknown is lactose. Look up its structure in The Merck Index and confirm its molecular formula.)

Answer 1

The rule of 13 states that the formula of a compound is a multiple n of 13 (the molar mass of CH) plus a remainder r. From here:

180 / 13 = 13r11

The predicted formula is C₁₃H₁₃₊₁₁ or C₁₃H₂₄.

Next, we need to substract CH₄ corresponding to the oxygen atoms. As the molecule has one oxygen per one carbon, one carbon is left indicating the presence of 12 hydrogen atoms. From here, the formula is: C₆H₁₂O₆.

To find the entire formula, we need to multiply the indexes and substract one water molecule due to hydrolysis:

C₁₂H₂₄O₁₂ - H₂O = C₁₂H₂₂O₁₁.

The hydrogen deficiency index is:

index = (2C + 2 - H) / 2 = (24 + 2 - 22) / 2 = 2

Answer: C₁₂H₂₂O₁₁; index 2.