5.100. Arctic Exploration Food contains three main categories of compounds: carb

Question

5.100. Arctic Exploration Food contains three main categories of compounds: carbohydrate, protein, and fat. Arctic explorers often eat a high-fat diet because fats have a high food value. The average food values for carbohydrate, protein, and fat are 4 Cal/g, 4 Cal/g, and 9 Cal/g, respectively Consider a typical fat to have the chemical formula Ci8H3602, glucose (CoHI206) to be a representative carbohydrate, and the amino acid alanine (CaHsNO2) a building block of proteins. Express the food values given above as Hcomb in kJ/mol.

Explanation / Answer

From carbohydrate,

C6H12O6 + 6 O2 ----------> 6 CO2 + 6 H2O

Energy from 1 g. of glucose = 4 cal

Then, 180 g. ( 1mol) of glucose = 180 * 4 = 720 cal. = 720 * 4.184 = 3012.5 J = 3.01 kJ/mol

From protein,

2 C3H6NO2 + 7 O2 ----------> 6 CO2 + 6 H2O + N2

Molar mass of C3H6NO2 = 3(12)+6(1)+1(14)+2(16) = 88 g/mol

energy from 1 g. of protein = 4 cal

then,

energy from 2 * 88 g. of protein = 4 * 2 * 88 = 704 cal = 704 * 4.184 = 2945.5 J = 2.94 kJ

For 1 mol of protein 2.94 / 2 = 1.47 kJ/mol

From fat,

C18H36O2 + 26 O2 ----------> 18 CO2 + 18 H2O

Molar mass of C18H36O2 = 18(12)+36(1)+2(16) = 284 g/mol

Energy from 1 g. of fat = 9 cal

then,

energy from 284 g. of fat = 284 * 9 = 2556 * 4.184 = 10694 J = 10.7 kJ/mol

Therefore,

Total food value = 3.01 + 1.47 + 10.7 = 15.18 kJ/mol

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