Problem 5 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The difference between \(\Delta \mathrm{H}\) and \(\Delta \mathrm{U}(\Delta \mathrm{H}-\Delta \mathrm{U})\), when the combustion of one mole of heptane (I) is carried out at a temperature \(\mathrm{T}\), is equal to [Main April \(10, \mathbf{2 0 1 9}\) (II)] (a) \(-4 \mathrm{RT}\) (b) \(-3 \mathrm{RT}\) (c) \(4 \mathrm{RT}\) (d) \(3 \mathrm{RT}\)

Step-by-Step Solution

Answer

The correct answer is (a) -4RT.

Step 1: Understanding the Relation between ΔH and ΔU

The difference between the enthalpy change (ΔH) and the internal energy change (ΔU) for a reaction is given by the relation \[ \Delta H - \Delta U = \Delta n_gRT \]where \( \Delta n_g \) is the change in moles of gas.

Step 2: Determine the Change in Gas Moles (Δng)

For the combustion of heptane (C7H14), the balanced chemical equation is \[ \text{C}_7\text{H}_{16(l)} + 11\text{O}_{2(g)} \rightarrow 7\text{CO}_{2(g)} + 8\text{H}_2\text{O}_{(l)} \]Calculate \( \Delta n_g \):- Initial gas moles: 11 (from O2)- Final gas moles: 7 (from CO2)- \( \Delta n_g = 7 - 11 = -4 \)

Step 3: Calculate the Difference ΔH - ΔU

Substitute \( \Delta n_g = -4 \) into the equation \( \Delta H - \Delta U = \Delta n_gRT \):\[ \Delta H - \Delta U = (-4)RT = -4RT \]

Step 4: Select the Correct Option

Among the given options, match the calculated value:- Option (a) is \(-4RT\)Thus, the answer is (a).

Key Concepts

Enthalpy Change

In thermochemistry, enthalpy change (\( \Delta H \)) is a vital concept. It represents the heat exchanged at constant pressure during a chemical reaction. Often used in calorimetry, it gives us insight into whether a reaction is endothermic (absorbs heat) or exothermic (releases heat).
To determine this change, consider the reactants and products involved. At constant pressure, the enthalpy change can be calculated with the heat capacity and the temperature change of the system.
Some important points:

• If \( \Delta H > 0 \), the reaction is endothermic.
• If \( \Delta H < 0 \), the reaction is exothermic.

Understanding \( \Delta H \) helps to predict the energy needs or releases of reactions, crucial for industries that rely on thermal processes.

Internal Energy Change

Internal energy change (\( \Delta U \)) reflects the total change in energy within a system due to molecular motion and interactions. It encompasses kinetic and potential energy components.
For constant volume processes, the internal energy change is identical to the heat exchanged. Unlike enthalpy, \( \Delta U \) does not consider pressure-volume work directly.

• In a closed system, \( \Delta U \) can be calculated as the sum of heat added to the system minus work done by the system.
• The formula: \( \Delta U = Q - W \)

Clarifying the internal energy gives a deeper understanding on how energy is transformed and conserved within a reaction.

Combustion Reaction

Combustion reactions are a specific type of exothermic reaction where a substance reacts with oxygen, releasing significant heat and light along with products like carbon dioxide and water.
Heptane combustion can be highlighted as an example, with the equation:\[ \text{C}_7\text{H}_{16(l)} + 11\text{O}_{2(g)} \rightarrow 7\text{CO}_{2(g)} + 8\text{H}_2\text{O}_{(l)} \]In this reaction, energy in the form of heat is released due to the breaking and formation of chemical bonds. With a change in the number of gas moles (\( \Delta n_g \)), we can also understand differences in enthalpy and internal energy.
Key points:

• Combustion is generally fast and includes flames or explosions.
• Complete combustion results in carbon dioxide and water, while incomplete combustion may yield carbon monoxide.

Recognizing these elements of combustion processes is essential, particularly in contexts like engines or energy generation.