5.4 Thermochemistry and Nutrition

The thermochemical quantities that you probably encounter most often are the caloric values of food. Food supplies the raw materials that your body needs to replace cells and the energy that keeps those cells functioning. About 80% of this energy is released as heat to maintain your body temperature at a sustainable level to keep you alive.

The nutritional CalorieA unit used to indicate the caloric content of food. It is equal to 1 kilocalorie (1 kcal). (with a capital C) that you see on food labels is equal to 1 kcal (kilocalorie). The caloric content of food is determined from its enthalpy of combustion (ΔH_comb) per gram, as measured in a bomb calorimeter, using the general reaction

There are two important differences, however, between the caloric values reported for foods and the ΔH_comb of the same foods burned in a calorimeter. First, the ΔH_comb described in joules (or kilojoules) are negative for all substances that can be burned. In contrast, the caloric content of a food is always expressed as a positive number because it is stored energy. Therefore,

Second, when foods are burned in a calorimeter, any nitrogen they contain (largely from proteins, which are rich in nitrogen) is transformed to N₂. In the body, however, nitrogen from foods is converted to urea [(H₂N)₂C=O], rather than N₂ before it is excreted. The ΔH_comb of urea measured by bomb calorimetry is −632.0 kJ/mol. Consequently, the enthalpy change measured by calorimetry for any nitrogen-containing food is greater than the amount of energy the body would obtain from it. The difference in the values is equal to the ΔH_comb of urea multiplied by the number of moles of urea formed when the food is broken down. This point is illustrated schematically in the following equations:

All three ΔH values are negative, and, by Hess’s law, ΔH₃ = ΔH₁ + ΔH₂. The magnitude of ΔH₁ must be less than ΔH₃, the calorimetrically measured ΔH_comb for a food. By producing urea rather than N₂, therefore, humans are excreting some of the energy that was stored in their food.

Because of their different chemical compositions, foods vary widely in caloric content. As we saw in Example 5, for instance, a fatty acid such as palmitic acid produces about 39 kJ/g during combustion, while a sugar such as glucose produces 15.6 kJ/g. Fatty acids and sugars are the building blocks of fats and carbohydrates, respectively, two of the major sources of energy in the diet. Nutritionists typically assign average values of 38 kJ/g (about 9 Cal/g) and 17 kJ/g (about 4 Cal/g) for fats and carbohydrates, respectively, although the actual values for specific foods vary because of differences in composition. Proteins, the third major source of calories in the diet, vary as well. Proteins are composed of amino acids, which have the following general structure:

General structure of an amino acid. An amino acid contains an amine group (−NH₂) and a carboxylic acid group (−CO₂H).

In addition to their amine and carboxylic acid components, amino acids may contain a wide range of other functional groups: R can be hydrogen (–H); an alkyl group (e.g., –CH₃); an aryl group (e.g., –CH₂C₆H₅); or a substituted alkyl group that contains an amine, an alcohol, or a carboxylic acid (Figure 5.16 "The Structures of 10 Amino Acids"). Of the 20 naturally occurring amino acids, 10 are required in the human diet; these 10 are called essential amino acids because our bodies are unable to synthesize them from other compounds. Because R can be any of several different groups, each amino acid has a different value of ΔH_comb. Proteins are usually estimated to have an average ΔH_comb of 17 kJ/g (about 4 Cal/g).

Figure 5.16 The Structures of 10 Amino Acids

Essential amino acids in this group are indicated with an asterisk.

Example 11

Calculate the amount of available energy obtained from the biological oxidation of 1.000 g of alanine (an amino acid). Remember that the nitrogen-containing product is urea, not N₂, so biological oxidation of alanine will yield less energy than will combustion. The value of ΔH_comb for alanine is −1577 kJ/mol.

Given: amino acid and ΔH_comb per mole

Asked for: caloric content per gram

Strategy:

A Write balanced chemical equations for the oxidation of alanine to CO₂, H₂O, and urea; the combustion of urea; and the combustion of alanine. Multiply both sides of the equations by appropriate factors and then rearrange them to cancel urea from both sides when the equations are added.

B Use Hess’s law to obtain an expression for ΔH for the oxidation of alanine to urea in terms of the ΔH_comb of alanine and urea. Substitute the appropriate values of ΔH_comb into the equation and solve for ΔH for the oxidation of alanine to CO₂, H₂O, and urea.

C Calculate the amount of energy released per gram by dividing the value of ΔH by the molar mass of alanine.

Solution:

The actual energy available biologically from alanine is less than its ΔH_comb because of the production of urea rather than N₂. We know the ΔH_comb values for alanine and urea, so we can use Hess’s law to calculate ΔH for the oxidation of alanine to CO₂, H₂O, and urea.

A We begin by writing balanced chemical equations for (1) the oxidation of alanine to CO₂, H₂O, and urea; (2) the combustion of urea; and (3) the combustion of alanine. Because alanine contains only a single nitrogen atom, whereas urea and N₂ each contain two nitrogen atoms, it is easier to balance Equations 1 and 3 if we write them for the oxidation of 2 mol of alanine:

$$\begin{array}{l}(1){\text{ 2C}}_{\text{3}}{\text{H}}_{\text{7}}{\text{NO}}_{\text{2}}\text{(s)}+{\text{6O}}_{\text{2}}\text{(g)}\to {\text{5CO}}_{\text{2}}\text{(g)}+{\text{5H}}_{\text{2}}\text{O(l)}+{{\text{(H}}_{\text{2}}\text{N)}}_{\text{2}}\text{C=O(s)}\\ {\text{(2) (H}}_{\text{2}}{\text{N)}}_{\text{2}}\text{C=O(s)}+\frac{3}{2}{\text{O}}_{\text{2}}\text{(g)}\to {\text{CO}}_{\text{2}}\text{(g)}+{\text{2H}}_{\text{2}}\text{O(l)}+{\text{N}}_{\text{2}}\text{(g)}\\ {\text{(3) 2C}}_{\text{3}}{\text{H}}_{\text{7}}{\text{NO}}_{\text{2}}\text{(s)}+\frac{15}{2}{\text{O}}_{\text{2}}\text{(g)}\to {\text{6CO}}_{\text{2}}\text{(g)}+{\text{7H}}_{\text{2}}\text{O(l)}+{\text{N}}_{\text{2}}\text{(g)}\end{array}$$

Adding Equations 1 and 2 and canceling urea from both sides give the overall chemical equation directly:

$$\begin{array}{ccc}\text{(1)}{\text{2C}}_{\text{3}}{\text{H}}_{\text{7}}{\text{NO}}_{\text{2}}\text{(s)}+{\text{6O}}_{\text{2}}\text{(g)}& \to & {\text{5CO}}_{\text{2}}\text{(g)}+{\text{5H}}_{\text{2}}\text{O(l)}+\cancel{{{\text{(H}}_{\text{2}}\text{N)}}_{\text{2}}\text{C }=\text{ O(s)}}\Delta H_{\text{1}}\\ \cancel{\text{(2)}{{\text{(H}}_{\text{2}}\text{N)}}_{\text{2}}\text{C }=\text{ O(s)}}+\frac{3}{2}{\text{O}}_{\text{2}}\text{(g)}& \to & {\text{CO}}_{\text{2}}\text{(g)}+{\text{2H}}_{\text{2}}\text{O(l)}+{\text{N}}_{\text{2}}\text{(g)}\Delta H_{\text{2}}\\ \text{(3)}{\text{2C}}_{\text{3}}{\text{H}}_{\text{7}}{\text{NO}}_{\text{2}}\text{(s)}+\frac{15}{2}{\text{O}}_{\text{2}}\text{(g)}& \to & {\text{6CO}}_{\text{2}}\text{(g)}+{\text{7H}}_{\text{2}}\text{O(l)}+{\text{N}}_{\text{2}}\text{(g)}\Delta H_{\text{3}}\end{array}$$

B By Hess’s law, ΔH₃ = ΔH₁ + ΔH₂. We know that ΔH₃ = 2ΔH_comb (alanine), ΔH₂ = ΔH_comb (urea), and ΔH₁ = 2ΔH (alanine → urea). Rearranging and substituting the appropriate values gives

$$\begin{array}{ll}\Delta H_{\text{1}}=\Delta H_{\text{3}}-\Delta H_{\text{2}}\hfill & =\text{ 2}\Delta H_{\text{comb}}\text{(alanine)}-\Delta H_{\text{comb}}\text{(urea) }\hfill \\ \hfill & =\text{ 2(}-\text{1577 kJ/mol)}-\text{(}-\text{632}\text{.0 kJ/mol)}\hfill \\ \hfill & =-\text{2522 kJ/(2 mol alanine) }\hfill \end{array}$$

Thus ΔH (alanine → urea) = −2522 kJ/(2 mol of alanine) = −1261 kJ/mol of alanine. Oxidation of alanine to urea rather than to nitrogen therefore results in about a 20% decrease in the amount of energy released (−1261 kJ/mol versus −1577 kJ/mol).

C The energy released per gram by the biological oxidation of alanine is

$$\left(\frac{-\text{1261 kJ}}{\text{1 }\cancel{\text{mol}}}\right)\left(\frac{\text{1 }\cancel{\text{mol}}}{\text{89}\text{.094 g}}\right)=-\text{14}\text{.15 kJ/g}$$

This is equal to −3.382 Cal/g.

Exercise

Calculate the energy released per gram from the oxidation of valine (an amino acid) to CO₂, H₂O, and urea. Report your answer to three significant figures. The value of ΔH_comb for valine is −2922 kJ/mol.

Answer: −22.2 kJ/g (−5.31 Cal/g)

The reported caloric content of foods does not include ΔH_comb for those components that are not digested, such as fiber. Moreover, meats and fruits are 50%−70% water, which cannot be oxidized by O₂ to obtain energy. So water contains no calories. Some foods contain large amounts of fiber, which is primarily composed of sugars. Although fiber can be burned in a calorimeter just like glucose to give carbon dioxide, water, and heat, humans lack the enzymes needed to break fiber down into smaller molecules that can be oxidized. Hence fiber also does not contribute to the caloric content of food.

We can determine the caloric content of foods in two ways. The most precise method is to dry a carefully weighed sample and carry out a combustion reaction in a bomb calorimeter. The more typical approach, however, is to analyze the food for protein, carbohydrate, fat, water, and “minerals” (everything that doesn’t burn) and then calculate the caloric content using the average values for each component that produces energy (9 Cal/g for fats, 4 Cal/g for carbohydrates and proteins, and 0 Cal/g for water and minerals). An example of this approach is shown in Table 5.4 "Approximate Composition and Fuel Value of an 8 oz Slice of Roast Beef" for a slice of roast beef. The compositions and caloric contents of some common foods are given in Table 5.5 "Approximate Compositions and Fuel Values of Some Common Foods".

Because the Calorie represents such a large amount of energy, a few of them go a long way. An average 73 kg (160 lb) person needs about 67 Cal/h (1600 Cal/day) to fuel the basic biochemical processes that keep that person alive. This energy is required to maintain body temperature, keep the heart beating, power the muscles used for breathing, carry out chemical reactions in cells, and send the nerve impulses that control those automatic functions. Physical activity increases the amount of energy required but not by as much as many of us hope (Table 5.6 "Approximate Energy Expenditure by a 160 lb Person Engaged in Various Activities"). A moderately active individual requires about 2500−3000 Cal/day; athletes or others engaged in strenuous activity can burn 4000 Cal/day. Any excess caloric intake is stored by the body for future use, usually in the form of fat, which is the most compact way to store energy. When more energy is needed than the diet supplies, stored fuels are mobilized and oxidized. We usually exhaust the supply of stored carbohydrates before turning to fats, which accounts in part for the popularity of low-carbohydrate diets.

The calculations in Example 12 ignore various factors, such as how fast the person is climbing. Although the rate is irrelevant in calculating the change in potential energy, it is very relevant to the amount of energy actually required to ascend the stairs. The calculations also ignore the fact that the body’s conversion of chemical energy to mechanical work is significantly less than 100% efficient. According to the average energy expended for various activities listed in Table 5.6 "Approximate Energy Expenditure by a 160 lb Person Engaged in Various Activities", a person must run more than 4.5 h at 10 mph or bicycle for 6 h at 13 mph to burn off 1 lb of fat (1.0 lb × 454 g/lb × 9.0 Cal/g = 4100 Cal). But if a person rides a bicycle at 13 mph for only 1 h per day 6 days a week, that person will burn off 50 lb of fat in the course of a year (assuming, of course, the cyclist doesn’t increase his or her intake of calories to compensate for the exercise).