Problem 96 - A Complete Resource Book in Chemistry for JEE Main

Question

The \(\Delta \mathrm{H}_{\mathrm{f}}^{\circ}\) for \(\mathrm{CO}_{2}(\mathrm{~g}), \mathrm{CO}(\mathrm{g})\) and \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) are \(-393.5\), \(-110.5\) and \(-241.8 \mathrm{~kJ} \mathrm{~mol}^{-1}\) respectively. The standard enthalpy change (in \(\mathrm{kJ}\) ) for the reaction \(\mathrm{CO}_{2}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) is (a) \(524.1\) (b) \(41.2\) (c) \(-262.5\) (d) \(-41.2\)

Step-by-Step Solution

Answer

The standard enthalpy change for the reaction is 41.2 kJ/mol, option (b).

Step 1: Understand the Reaction

We are given the reaction \(\mathrm{CO}_{2}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\). Our task is to find the standard enthalpy change for this reaction using the given standard enthalpy of formation values.

Step 2: Recall Enthalpy of Reaction Formula

The standard enthalpy change of a reaction \((\Delta H_{\text{rxn}})\) can be calculated using the formula: \[ \Delta H_{\text{rxn}}^{\circ} = \sum \Delta H_{f}^{\circ}(\text{products}) - \sum \Delta H_{f}^{\circ}(\text{reactants}) \]

Step 3: Gather Given Data

We have the following standard enthalpies of formation :- \(\Delta H_{f}^{\circ}(\mathrm{CO}_{2}(\mathrm{~g})) = -393.5\, \mathrm{kJ}\,\mathrm{mol}^{-1}\)- \(\Delta H_{f}^{\circ}(\mathrm{CO}(\mathrm{g})) = -110.5\, \mathrm{kJ}\,\mathrm{mol}^{-1}\)- \(\Delta H_{f}^{\circ}(\mathrm{H}_{2}\mathrm{O}(\mathrm{g})) = -241.8\, \mathrm{kJ}\,\mathrm{mol}^{-1}\)\(\Delta H_{f}^{\circ}(\mathrm{H}_{2}(\mathrm{~g})) = 0\, \mathrm{kJ}\,\mathrm{mol}^{-1}\)\, since \(\mathrm{H}_{2}\) is in its elemental state.

Step 4: Apply the Formula for Products

Calculate the sum of \(\Delta H_{f}^{\circ}\) for products, which are \(\mathrm{CO}(\mathrm{g})\) and \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\):\[ \sum \Delta H_{f}^{\circ}(\text{products}) = \Delta H_{f}^{\circ}(\mathrm{CO}(\mathrm{g})) + \Delta H_{f}^{\circ}(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})) = (-110.5) + (-241.8) = -352.3 \text{ kJ/mol} \]

Step 5: Apply the Formula for Reactants

Calculate the sum of \(\Delta H_{f}^{\circ}\) for reactants, which are \(\mathrm{CO}_{2}(\mathrm{~g})\) and \(\mathrm{H}_{2}(\mathrm{~g})\):\[ \sum \Delta H_{f}^{\circ}(\text{reactants}) = \Delta H_{f}^{\circ}(\mathrm{CO}_{2}(\mathrm{~g})) + \Delta H_{f}^{\circ}(\mathrm{H}_{2}(\mathrm{~g})) = (-393.5) + 0 = -393.5 \text{ kJ/mol} \]

Step 6: Calculate Enthalpy Change

Substitute the sums obtained earlier into the enthalpy of reaction formula:\[ \Delta H_{\text{rxn}}^{\circ} = (-352.3) - (-393.5) = -352.3 + 393.5 = 41.2 \text{ kJ/mol} \]

Step 7: Determine the Correct Option

Compare the calculated \(\Delta H_{\text{rxn}}^{\circ}\) of 41.2 \(\text{kJ/mol}\) with the options given. The correct answer is option (b) 41.2.

Key Concepts

Enthalpy of Formation

The enthalpy of formation (\( \Delta H_{f}^{\circ} \)) is the amount of energy needed to form a compound from its elements. To standardize, it is usually measured under specific conditions: 1 atmosphere of pressure and a temperature of 298 K (25°C). This value is crucial because it provides a baseline understanding of the energy content of compounds.
Think of enthalpy of formation as a map that shows the energy landscape of creating a molecule. More negative values indicate that forming the compound from its elements releases more energy, making it more stable. For instance, the formation of \( \mathrm{CO}_{2}(\mathrm{~g}) \) releases a substantial amount of energy, evidenced by its negative enthalpy of formation value of \(-393.5 \, \mathrm{kJ \, mol}^{-1}\). Understanding these values can help predict the behavior of substances in chemical reactions.

Standard Enthalpy Change

The standard enthalpy change (\( \Delta H_{\text{rxn}}^{\circ} \)) is a measure of heat absorbed or released during a reaction. It tells us how much energy the reaction takes in or gives off when proceeding under standard conditions (1 atm pressure, 298 K).
This value indicates whether a reaction is endothermic or exothermic. In an exothermic reaction, energy is released, and the \( \Delta H_{\text{rxn}}^{\circ} \) is negative. In an endothermic reaction, energy is absorbed, making \( \Delta H_{\text{rxn}}^{\circ} \) positive. For our example reaction \( \mathrm{CO}_{2}(\mathrm{~g}) + \mathrm{H}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CO}(\mathrm{g}) + \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \), the calculated enthalpy change is \( 41.2/ \mathrm{kJ/mol}\), indicating the reaction absorbs heat.

Chemical Reactions

Chemical reactions are processes in which substances, known as reactants, transform into different substances, called products. This transformation involves breaking and forming bonds, which changes the energy state of the system.
Every chemical reaction involves changes in energy. For example, the oxidation of hydrogen gas by oxygen to form water releases energy. Similarly, when \( \mathrm{CO}_{2} \) and \( \mathrm{H}_{2} \) react to produce \( \mathrm{CO} \) and evaporated water, energy balance must be considered to understand the shift in enthalpy.
Understanding the enthalpy of the reactants and products can help predict the direction and extent of a reaction. It also has practical applications in calculating how much energy is needed to initiate a reaction or how much is stored in certain bonds.

Thermodynamics in Chemistry

Thermodynamics is the branch of physical sciences that deals with energy and its transformations. In chemistry, it helps us understand processes that proceed with energy changes.
Several basic principles govern thermodynamics in chemistry:

• **First Law of Thermodynamics** (conservation of energy): Energy cannot be created or destroyed, only transformed.
• **Second Law of Thermodynamics**: The entropy of a system tends to increase over time, meaning processes naturally progress towards disorder.

Applying these principles, chemists can determine if a reaction is feasible under given conditions. For example, even if a reaction releases energy (\( \Delta H < 0 \)), it may not occur spontaneously unless the entropy change (\( \Delta S \)) favors the reaction.