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 is 41.2 kJ, so the answer is (b) 41.2.

Step 1: Understand the Reaction

The reaction given is \( \mathrm{CO}_{2}(\mathrm{~g}) + \mathrm{H}_{2}(\mathrm{~g}) \rightarrow \mathrm{CO}(\mathrm{g}) + \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \). We need to calculate the standard enthalpy change (\( \Delta \mathrm{H}^{\circ} \)) for this reaction using the standard enthalpies of formation for the reactants and products.

Step 2: Write the Enthalpy Change Equation

The standard enthalpy change for the reaction can be calculated using the formula: \( \Delta \mathrm{H}^{\circ}_{\text{reaction}} = \sum \Delta \mathrm{H}_{\mathrm{f}}^{\circ}(\text{products}) - \sum \Delta \mathrm{H}_{\mathrm{f}}^{\circ}(\text{reactants}) \).

Step 3: Substitute Known Values

Substitute the given formation enthalpies into the equation: \( \Delta \mathrm{H}^{\circ}_{\text{reaction}} = \left( (-110.5) + (-241.8) \right) - \left( (-393.5) + 0 \right) \).

Step 4: Calculate Product and Reactant Enthalpies

First, calculate the total enthalpy of the products: \( (-110.5) + (-241.8) = -352.3 \mathrm{~kJ/mol} \). Then, calculate the total enthalpy of the reactants: \( (-393.5) + 0 = -393.5 \mathrm{~kJ/mol} \).

Step 5: Calculate the Standard Enthalpy Change

Calculate the \( \Delta \mathrm{H}^{\circ}_{\text{reaction}} \) by subtracting the total enthalpy of the reactants from the total enthalpy of the products:\( \Delta \mathrm{H}^{\circ}_{\text{reaction}} = -352.3 - (-393.5) = 41.2 \mathrm{~kJ/mol} \).

Step 6: Select the Correct Answer

The calculated enthalpy change for the reaction is \( 41.2 \, \mathrm{kJ} \). The correct answer that matches this value is (b) \( 41.2 \).

Key Concepts

standard enthalpy of formation

The standard enthalpy of formation, denoted as \( \Delta H_f^{\circ} \), is a key concept in thermochemistry. It refers to the amount of energy change when one mole of a compound is formed from its elements in their standard states. For example, consider the formation of carbon dioxide \((\mathrm{CO}_2)\) from carbon and oxygen under standard conditions—this would have a unique \( \Delta H_f^{\circ} \) value.

• Standard states are usually the most stable physical states of elements at 1 atmosphere of pressure and a specified temperature, generally 25°C.
• For an element in its standard state, the \( \Delta H_f^{\circ} \) is zero. This is because there is no change involved in forming an element from itself.

Understanding \( \Delta H_f^{\circ} \) is crucial, as it lays the groundwork for calculating the enthalpies of reactions by knowing the individual enthalpies of the compounds involved.

reaction enthalpy calculation

Calculating the reaction enthalpy, \( \Delta H^{\circ}_{\text{reaction}} \), involves using the enthalpy changes associated with the formation of reactants and products. This is typically determined by the following equation:
\[ \Delta H^{\circ}_{\text{reaction}} = \sum \Delta H_f^{\circ}(\text{products}) - \sum \Delta H_f^{\circ}(\text{reactants}) \]
This equation implies:

• You first sum up the formation enthalpies of the products, which are negative values since they are exothermic reactions when compounds are formed from their most stable elements.
• Then, sum up the formation enthalpies of the reactants.
• Subtract the sum for the reactants from the sum for the products to find the overall reaction enthalpy.

This simple framework helps predict whether a reaction will absorb or release energy, and hence, whether it's endothermic or exothermic.

chemistry problem solving

Solving chemistry problems related to enthalpy and energy changes involves systematic steps. Here’s a practical approach to tackle these problems effectively:
1. **Read and Understand the Problem:** Carefully note the given chemical equation and the known \( \Delta H_f^{\circ} \) values.
2. **Establish Relationships:** Utilize key equations like \( \Delta H^{\circ}_{\text{reaction}} = \sum \Delta H_f^{\circ}(\text{products}) - \sum \Delta H_f^{\circ}(\text{reactants}) \) to relate what you’re given with what you need to find.
3. **Substituting Values:** Plug in the given values or data from tables into your established equations.
4. **Calculate Systematically:** Perform the algebraic calculations carefully while keeping track of units and signs, as these can affect your final answer.
5. **Review the Solution:** After solving, double-check your calculations and whether the answer makes physical sense, especially verifying if it's consistent with expected energy absorption or release.
By methodically following these steps, you can improve your success rate in solving chemistry enthalpy problems, reinforce conceptual understanding, and avoid common pitfalls like incorrect sign convention or unit conversions.