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CHEM 12B—Trego

Calculating Average Molar Mass of Fatty

Animal and vegetable are composed of triglycerides. A consists of a molecule of (propane-1,2,3-triol) condensed with three fatty carboxylic . A naturally occurring will be composed of a number of different fatty acids, varying in the length of the parent chain (~C4-C24). Additionally, some fatty acids contain 1 or more C-C double bonds (unsaturated fatty acids). Because a fat consists of various fatty acids, the triglyceride molecules will have various molecular masses.

O

O O (CH2)nCH3

(CH )nCH Glycerol O 2 3 Fatty Acids O

O (CH2)nCH3

One approach to dealing with the variability in the molar mass is to calculate an average molar mass. The composition of most naturally occurring fats has been determined. Using this data, we can calculate a weighed average molar mass as shown below.

Average Molar Mass = 3 x Average Molar Masses of Fatty Acids + Molar Mass of C3H2 (glycerol skeleton)

Example:

Consider a hypothetical fat with the following fatty acid composition.

C10 C12 C14 C16 C18 (mono unsaturated) Mol % 5.0 15.0 25.0 25.0 30.0

Fatty acids are often identified by their atom count, since all the structures are straight chain.

C10 = CH3(CH2)8CO2H MM = 172.3 g/mol

The average molar mass of the fatty acid components of the triglycerides can be calculated in a similar fashion to the manner in which average atomic mass is calculated. Multiply the molar mass of each fatty acid by the decimal equivalent of its percent abundance. The sum of these products will yield the average molar mass.

Fatty Acid Mol % / x Molar Mass g/mol = Product 100 CH3(CH2)8CO2H 0.050 172.3 8.62 g/mol CH3(CH2)10CO2H 0.150 200.4 30.06 g/mol CH3(CH2)12CO2H 0.250 228.4 57.10 g/mol CH3(CH2)14CO2H 0.250 256.5 64.13 g/mol CH3(CH2)14CHCHCO2H 0.300 282.5 84.75 g/mol Sum 244.7 g/mol

Continued on back…

Average molar mass of the triglycerides:

(3 x 244.7 g/mol) + 38.03 g/mol = 772.0 g/mol ↑ ↑ molar mass of glycerol CH skeleton ↑ avg. molar mass of free fatty acids

Fatty Acid Composition of Determined by FAME Analysis

Mol-%† Pavia Hexanoic Acid () 1.1 Octanoic acid () 11.0 10-22 Decanoic Acid () 9.7 Dodecanoic Acid () 39.6 45-51 Tetradecanoic Acid () 18.9 17-20 Hexadecanoic Acid () 9.2 4-10 9-Octadecenoic Acid () 6.2 2-10 Octadecanoic Acid (Steric Acid) 4.3 1-5

†Determined by /mass spectrometry at Laney College, Spring Semester, 2014