Problem 19 - Basic Principles of Organic Chemistry

Question

The heat of combustion of glucose(s) to \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(l)\) is \(670 \mathrm{kcal} \mathrm{mol}^{-1}\), whereas that of 2 oxopropanoic acid \((l)\) is \(280 \mathrm{kcal} \mathrm{mol}^{-1}\). Neglecting the heats of solution of the compounds in water, estimate the energy of glucose \((a q)+\mathrm{O}_{2} \rightarrow 2 \mathrm{CH}_{3} \mathrm{COCO}_{2} \mathrm{H}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) .\)

Step-by-Step Solution

Answer

The reaction energy change is approximately 110 kcal.

Step 1: Understand the Reaction

We need to estimate the change in energy for the reaction of glucose in aqueous solution with oxygen to form 2-oxopropanoic acid and water. The reaction can be represented as: \( \text{Glucose(aq)} + O_2 \rightarrow 2 \text{CH}_3\text{COCO}_2\text{H}(aq) + 2 \text{H}_2\text{O}(l) \).

Step 2: Use Given Combustion Data

Identify the given heats of combustion: the heat of combustion for glucose (s) is \( 670 \text{ kcal mol}^{-1} \), and for 2-oxopropanoic acid (l) it is \( 280 \text{ kcal mol}^{-1} \). These values will be used to estimate the reaction energy change.

Step 3: Calculate Energy Change for Products

From the reaction, 2 moles of 2-oxopropanoic acid are produced. The total energy release for the combustion of these 2 moles is calculated from their given heat of combustion: \( 2 \times 280 \text{ kcal} = 560 \text{ kcal} \).

Step 4: Calculate Total Energy Release

Using the heat of combustion of glucose: \( 670 \text{ kcal} \). For the products' total energy (from Step 3): \( 560 \text{ kcal} \). The change in energy for the reaction is the difference between these two values.

Step 5: Estimate Reaction Energy Change

The energy required to transform glucose into the products (excluding the combustion with oxygen which is constant for both sides): \( 670 \text{ kcal} - 560 \text{ kcal} = 110 \text{ kcal} \).

Step 6: Conclusion: Determine Reaction Energy

The energy change for the reaction \( \text{Glucose(aq)} + O_2 \rightarrow 2 \text{CH}_3\text{COCO}_2\text{H}(aq) + 2 \text{H}_2\text{O}(l) \) is estimated as \( 110 \text{ kcal} \).

Key Concepts

Heat of Combustion

When we talk about the heat of combustion, we're discussing how much energy is released when a substance is burned completely in the presence of oxygen. Imagine burning a piece of paper. As it burns, it releases heat and leaves behind ash.
Just like paper, chemical substances also release energy when they combust, but in a more controlled and measurable way.
For glucose (a sugar), the heat of combustion is quite high, which means it releases a lot of energy. Specifically, glucose has a heat of combustion of 670 kcal/mol. This tells us how much energy is produced when one mole of glucose is fully combusted.

• High heat of combustion typically means high energy release.
• This heat is important in understanding the energy potential of different fuels and substances.

When we look at substances in reactions, considering their heat of combustion helps us understand how much energy will be involved.

Energy change calculation

Calculating the energy change in chemical reactions is essential for predicting how much energy is required or released during a reaction. To figure this out, we often start by noting the heat of combustion of the reactants and products.
In our example, glucose reacts in a way where it transforms into 2-oxopropanoic acid. For this, we consider the heat of combustion of the initial glucose (670 kcal/mol) and compare it to that of the final product, 2-oxopropanoic acid (280 kcal/mol). However, since 2 moles of 2-oxopropanoic acid are produced, we multiply its heat of combustion by 2, giving 560 kcal.

• We first calculate individual combustion energies.
• Then, we sum energies for similar products if needed.
• Finally, find the difference to understand the net change.

In this case, the energy change is calculated by subtracting the products' total energy from that of the glucose: 670 kcal - 560 kcal = 110 kcal. This result shows us that by transforming glucose into the products, 110 kcal of energy is absorbed.

Chemical reactions

Chemical reactions involve the transformation of substances through breaking and forming of chemical bonds. These reactions can either absorb or release energy.
The reaction we are considering involves glucose reacting with oxygen, resulting in a complex outcome of 2-oxopropanoic acid and water. Assessing the reaction involves understanding both the reactants and products, along with the energy exchanges in the process.
Every reaction has its unique reactants and products, and this interplay describes the overall energy dynamics. When glucose breaks down (combusts) and is converted into other substances, energy is released, which can be harnessed for different uses, like within biological systems or industrial processes.

• Make sure to account for all reactants and products.
• Understand that different substances interact differently, thus giving unique energy changes.
• Balance the chemical equation to reflect accurate energy changes.

The type of chemical reaction (such as combustion) will heavily influence how much energy is needed or released, affecting the overall energy balance of the reaction.