Problem 84 - Chemistry: Atoms First

Question

The oxidation of the sugar glucose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\), is described by the following equation: \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g) \longrightarrow 6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) \quad \Delta H=-2816 \mathrm{kJ}\) The metabolism of glucose gives the same products, although the glucose reacts with oxygen in a series of steps in the body. (a) How much heat in kilojoules can be produced by the metabolism of \(1.0 \mathrm{g}\) of glucose? (b) How many Calories can be produced by the metabolism of \(1.0 \mathrm{g}\) of glucose?

Step-by-Step Solution

Answer

The metabolism of 1.0 g of glucose can produce approximately 15.64 kJ of heat energy or about 3.74 Calories.

Step 1: Determine the Heat Released Per Mole of Glucose

The given chemical equation shows that the oxidation of 1 mole of glucose releases \(2816 \text{kj}\). Since the molecular weight of glucose \(C_6H_{12}O_6\) is approximately 180 g/mol, we can calculate the heat released per gram by dividing the total heat release by the molar mass.

Step 2: Calculate Heat Energy Released for 1.0 g of Glucose

To find out how much energy is released when 1.0 g of glucose is metabolized, use the heat released per mole of glucose and convert it into heat per gram of glucose. Then multiply this value by 1.0 g.

Step 3: Convert Heat Energy from Kilojoules to Calories

1 dietary Calorie (with a capital C) is equal to 4.184 kilojoules. To convert the energy value obtained in step 2 from kilojoules to Calories, divide the energy in kilojoules by 4.184.

Key Concepts

Cellular Respiration

Understanding how our bodies extract energy from food is central to biology and health sciences. Cellular respiration is the fundamental process through which cells convert the biochemical energy from nutrients into adenosine triphosphate (ATP), a molecule that powers numerous cellular activities. This intricate process occurs in the mitochondria of cells through a series of biochemical reactions.

Glucose, a six-carbon sugar, is a principal fuel for cellular respiration. The complete breakdown of glucose to carbon dioxide and water releases energy, captured in the form of ATP. The overall reaction can be represented simply as:
\[\textrm{C}_6\textrm{H}_{12}\textrm{O}_6 + 6\textrm{O}_2 \rightarrow 6\textrm{CO}_2 + 6\textrm{H}_2\textrm{O} + \textrm{ATP}\text{ (energy)}\]

The steps of cellular respiration include glycolysis, the citric acid cycle (Krebs cycle), and oxidative phosphorylation via the electron transport chain. Together, these processes systematically degrade glucose and transfer the stored energy into ATP, making it available for the cell's needs.

Energy Conversion in the Body

Our body is an expert in energy conversion. This is highlighted in the metabolism of glucose, where chemical energy is converted into a usable form. During metabolism, energy from food is initially stored in the high-energy phosphate bonds of ATP. The body then uses ATP to perform work, such as muscle contraction, nerve impulse propagation, and active transport across cell membranes.

In terms of energy output, the process is quantifiable. For example, the oxidation of 1 gram of glucose releases approximately \(15.6 \text{kJ} \), which is the amount of energy you get from metabolizing a tiny sugar cube. By understanding this conversion, we can infer not only how much energy is stored in the food we eat but also how efficiently our bodies can turn that energy into work, the ultimate goal of cellular respiration.

Chemical Equations in Biochemistry

Chemical equations are integral to the field of biochemistry as they help us understand the stoichiometry – the quantitative relationships between reactants and products in a chemical reaction. In the context of glucose metabolism, the balanced chemical equation represents the amount of glucose and oxygen molecules required to produce carbon dioxide, water, and energy. The equation from the original exercise,\[\textrm{C}_6\textrm{H}_{12}\textrm{O}_6(s) + 6\textrm{O}_2(g) \rightarrow 6\textrm{CO}_2(g) + 6\textrm{H}_2\textrm{O}(l) \]indicates that one molecule of glucose reacts with six molecules of oxygen to produce six molecules each of carbon dioxide and water.

From this equation, one can deduce various thermodynamic properties, such as change in enthalpy (\(\textrm{\text{Δ}}H\)), which signifies the amount of heat energy released or absorbed during the reaction. This quantitative aspect is fundamental when estimating the energy content of foods, understanding metabolic pathways, and exploring the thermodynamics of biological systems.