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

Question

Given the following standard heats of reactions: (i) heat of formation of water \(=-68.3 \mathrm{kcal}\); (ii) heat of combustion of acetylene \(=-310.6 \mathrm{kcal}\); (iii) heat of combustion of ethylene \(=-337.2 \mathrm{kcal}\); Calculate the heat of reaction for the hydrogenation of acetylene at constant volume \(\left(25^{\circ} \mathrm{C}\right)\).

Step-by-Step Solution

Answer

The heat of reaction for the hydrogenation of acetylene is -26.6 kcal.

Step 1: Understand the Reaction

We need to calculate the heat of reaction for the hydrogenation of acetylene. The reaction is:\[ \text{C}_2\text{H}_2 + \text{H}_2 \rightarrow \text{C}_2\text{H}_4 \]which means one mole of acetylene reacts with one mole of hydrogen to form ethylene.

Step 2: Apply Hess's Law

According to Hess's Law, we can find the heat of the target reaction by rearranging the given reactions in such a way that they add up to our target reaction. The known reactions are:1. Combustion of acetylene: \[ \text{C}_2\text{H}_2 + \dfrac{5}{2}\text{O}_2 \rightarrow 2\text{CO}_2 + \text{H}_2\text{O} \quad \Delta H = -310.6 \text{kcal} \]2. Combustion of ethylene: \[ \text{C}_2\text{H}_4 + 3\text{O}_2 \rightarrow 2\text{CO}_2 + 2\text{H}_2\text{O} \quad \Delta H = -337.2 \text{kcal} \]3. Formation of water: \[ \text{H}_2 + \dfrac{1}{2}\text{O}_2 \rightarrow \text{H}_2\text{O} \quad \Delta H = -68.3 \text{kcal} \]

Step 3: Calculate Heat Change Based on Combustion Reactions

Substitute known combustions:1. \( \text{C}_2\text{H}_2 + \dfrac{5}{2}\text{O}_2 \rightarrow 2\text{CO}_2 + \text{H}_2\text{O} \)2. \( 2\text{CO}_2 + 2\text{H}_2\text{O} \rightarrow \text{C}_2\text{H}_4 + 3\text{O}_2 \)Adding these, we get:\[ \text{C}_2\text{H}_2 + \dfrac{5}{2}\text{O}_2 + 2\text{CO}_2 + 2\text{H}_2\text{O} \rightarrow 2\text{CO}_2 + \text{H}_2\text{O} + \text{C}_2\text{H}_4 + 3\text{O}_2 \]Simplifying this:\[ \text{C}_2\text{H}_2 + \text{H}_2 \rightarrow \text{C}_2\text{H}_4 \]with the heat change:\[ \Delta H = (-337.2 - (-310.6)) = -26.6 \text{kcal} \]

Step 4: Consider Standard Conditions

Since the change in volume at these conditions is often negligible and no gases are consumed or produced besides those equal volumes, the calculation does not alter. The heat at constant pressure and constant volume is essentially the same under standard conditions for this type of reaction.

Key Concepts

Heat of Reaction

In the world of thermochemistry, the **heat of reaction** is a fundamental concept. It represents the heat change that occurs as a result of a chemical reaction. This heat change can either be absorbed or released by the system. Whether heat is absorbed or released depends on the nature of the reaction: if the heat is released, it’s an exothermic reaction, whereas if the heat is absorbed, it’s endothermic.

To calculate the heat of a reaction, you can use

• Standard heats of formation, which are the heat changes associated with forming one mole of a compound from its elements in their standard states.
• Hess's Law, which allows you to use known reactions to calculate the heat of an unknown reaction.

In the exercise above, we determine the heat of hydrogenation of acetylene by considering the given standard heats of formation and combustion reactions.

Hess's Law

Hess's Law is a very useful principle in thermochemistry. It allows the calculation of the heat of reaction by using the heats of reaction from other related reactions. This can be explained by the fact that the overall heat change of a chemical reaction is the same no matter how many steps it takes, thanks to its path-independent nature. Essentially, it means that you can sum the heats of several individual reactions to find the total heat change for a final reaction.

Using Hess’s Law involves:

• Identifying known reactions and their corresponding heat changes (enthalpies).
• Reversing reactions if necessary, which changes the sign of the enthalpy.
• Scaling the reactions if needed, meaning the enthalpy is multiplied by the same factor as the reaction coefficients.
• Adding up all the reactions to arrive at the desired overall reaction.

In our specific problem, we use Hess’s Law to rearrange given combustion reactions to calculate the heat change for our target reaction.

Combustion Reactions

Combustion reactions are an important class of reactions often associated with explosive or energy-releasing processes. These reactions usually involve a fuel (often a hydrocarbon like acetylene or ethylene) reacting with oxygen to produce carbon dioxide and water. The energy released during combustion reactions is generally large due to the formation of strong bonds in the products.

Key features of combustion reactions include:

• The presence of oxygen as a reactant.
• The production of energy, often light or heat.
• The frequent output of carbon dioxide and water as typical products.

In the textbook problem, the combustion of acetylene and ethylene are used to provide necessary heats of reactions for calculating the heat change of the hydrogenation of acetylene, demonstrating the practical use of combustion reactions in thermochemical computations.