Problem 39 - Chemistry: An Atoms-Focused Approach

Question

Is the fuel value of glucose in the linear form the same as that in the cyclic form?

Step-by-Step Solution

Answer

Answer: Yes, the fuel value of glucose is the same in both linear and cyclic forms.

Step 1: Understanding the process of glucose oxidation

To determine the fuel value of glucose, we will examine its oxidation process. When glucose is oxidized, it releases energy that can be used by our cells. The complete oxidation of one molecule of glucose can be represented by the following balanced chemical equation: C6H12O6 + 6O2 → 6CO2 + 6H2O This equation represents the conversion of glucose (either linear or cyclic) and oxygen to carbon dioxide and water, releasing energy in the process.

Step 2: Comparing the energy changes of both forms

To compare the energy changes for both linear and cyclic forms of glucose, we need to consider that the energy change (ΔH) for a reaction is determined by the difference in energy between the products and reactants. This can be calculated using the following formula: ΔH = Σ(ΔHf(products)) - Σ(ΔHf(reactants)) Where ΔHf represents the standard enthalpy of formation of each compound. Now, for both linear and cyclic glucose, the reactants and products are the same (i.e., C6H12O6 oxidizes to 6CO2 and 6H2O). So, to compare their energy changes, we need to know if the linear and cyclic forms of glucose have different standard enthalpies of formation.

Step 3: Standard enthalpy of formation of linear and cyclic glucose

The standard enthalpy of formation (ΔHf) is the change in enthalpy when one mole of a substance in its standard state is formed from its constituent elements in their standard states. Since both linear and cyclic forms have the same molecular formula (C6H12O6) and, importantly, the same chemical connectivity, they will have the same standard enthalpy of formation.

Step 4: Analyzing if the fuel value is the same for both forms

Now that we know that both linear and cyclic forms of glucose have the same enthalpy of formation, we can infer that the energy change (ΔH) during their oxidation process will also be the same, as the difference in enthalpy between the products and reactants remains the same. ΔH_linear = Σ(ΔHf(products)) - Σ(ΔHf(reactants_linear)) ΔH_cyclic = Σ(ΔHf(products)) - Σ(ΔHf(reactants_cyclic)) Since the reactants' enthalpies are the same for both linear and cyclic forms, ΔH_linear and ΔH_cyclic are equal. So, we can conclude that the fuel value of glucose in the linear form is the same as that in the cyclic form.

Key Concepts

Fuel Value

Fuel value refers to the amount of energy that is released during a chemical reaction when a certain substance is completely burned. It is an important measure in understanding how effective a fuel is in releasing energy. In the context of glucose oxidation, when glucose is oxidized in the body, it releases energy that powers cells and supports various bodily functions.

• During its complete oxidation process, glucose converts into carbon dioxide and water.
• This process releases energy which can be captured and used by cells for biological activities.

The fuel value is crucial since it helps us compare different fuels and their efficiency in providing energy. In simple terms, the higher the fuel value, the more energy the fuel provides upon combustion.

Standard Enthalpy of Formation

The standard enthalpy of formation (\(ΔH_f\)) is a thermodynamic property. It refers to the change in enthalpy when one mole of a substance is formed from its elements in their standard states at 1 bar pressure and a specified temperature (typically 25°C or 298 K). For instance, the elements needed to form glucose would be carbon, hydrogen, and oxygen in their natural states.

• The standard enthalpy of formation is usually expressed in kilojoules per mole (kJ/mol).
• It's a standard reference, allowing us to calculate energy changes in chemical reactions.

Both the linear and cyclic forms of glucose have the same molecular formula, meaning they possess identical standard enthalpies of formation. This equivalence implies that any difference in their reactions or energy releases is not influenced by their formation enthalpies.

Chemical Equation

A chemical equation is a symbolic representation of a chemical reaction, with reactants on the left side and products on the right. For glucose oxidation, the equation is:\[ C_6H_{12}O_6 + 6O_2 → 6CO_2 + 6H_2O \]This shows that one molecule of glucose reacts with oxygen to produce carbon dioxide and water. Such equations hold vital information including:

• Reactants and products involved in the reaction.
• Balanced stoichiometry to maintain the law of conservation of mass.

Writing and balancing chemical equations accurately is crucial for calculating energy changes. This is because it ensures that the number of atoms for each element is the same on both sides of the reaction, reflecting what physically occurs during the process.

Energy Change

Energy change in a chemical reaction refers to the difference in energy between the products and the reactants. It is often represented by the symbol ΔH, which denotes the change in enthalpy. For glucose oxidation, this would involve calculating the energy released when glucose converts to carbon dioxide and water.

• The formula for energy change is:\(ΔH = Σ(ΔH_f(products)) - Σ(ΔH_f(reactants))\).
• It indicates whether a reaction is exothermic (releases energy) or endothermic (absorbs energy).

In glucose oxidation, the energy change is the same for both linear and cyclic forms, meaning both forms release the same amount of energy upon oxidation. Understanding energy change is essential because it tells us about the energy efficiency and characteristics of a chemical reaction.