Problem 102 - A Complete Resource Book in Chemistry for JEE Main

Question

The standard enthalpy of combustion at \(25^{\circ} \mathrm{C}\) of \(\mathrm{H}_{2}\), \(\mathrm{C}_{6} \mathrm{H}_{10}\) and cyclohexane \(\left(\mathrm{C}_{6} \mathrm{H}_{12}\right)\) are \(-241,-3800\) and \(-3920 \mathrm{~kJ} \mathrm{~mol}^{-1}\) respectively. Calculate heat of hydrogenation of cyclohexane \(\left(\mathrm{C}_{6} \mathrm{H}_{10}\right) .\) (a) \(-161 \mathrm{kJmol}^{-1}\) (b) \(-131 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (c) \(-121 \mathrm{kJmol}^{-1}\) (d) none

Step-by-Step Solution

Answer

The heat of hydrogenation for cyclohexene is \(-121 \mathrm{kJ/mol}\), so the correct answer is (c).

Step 1: Define the Reaction for Hydrogenation

In the hydrogenation of cyclohexene (\( \mathrm{C}_6 \mathrm{H}_{10} \)) to cyclohexane (\( \mathrm{C}_6 \mathrm{H}_{12} \)), hydrogen gas (\( \mathrm{H}_2 \)) is added. The balanced chemical equation for this reaction is: \( \mathrm{C}_6 \mathrm{H}_{10} + \mathrm{H}_2 \rightarrow \mathrm{C}_6 \mathrm{H}_{12} \).

Step 2: Write the Combustion Reactions

For cyclohexene: \( \mathrm{C}_6 \mathrm{H}_{10} + \frac{17}{2} \mathrm{O}_2 \rightarrow 6 \mathrm{CO}_2 + 5 \mathrm{H}_2\mathrm{O} \) with heat of combustion \(-3800 \mathrm{~kJ/mol}\). For cyclohexane: \( \mathrm{C}_6 \mathrm{H}_{12} + 9 \mathrm{O}_2 \rightarrow 6 \mathrm{CO}_2 + 6 \mathrm{H}_2\mathrm{O} \) with heat of combustion \(-3920 \mathrm{~kJ/mol}\). For hydrogen: \( \mathrm{H}_2 + \frac{1}{2} \mathrm{O}_2 \rightarrow \mathrm{H}_2\mathrm{O} \) with heat of combustion \(-241 \mathrm{~kJ/mol}\).

Step 3: Apply Hess's Law

According to Hess's Law, the heat of the hydrogenation reaction can be calculated using the enthalpy changes of combustion. The formula is: \[ \Delta H_\text{hydrogenation} = \Delta H_\text{combustion}(\mathrm{C}_6 \mathrm{H}_{12}) - \Big( \Delta H_\text{combustion}(\mathrm{C}_6 \mathrm{H}_{10}) + \Delta H_\text{combustion}(\mathrm{H}_2) \Big) \].

Step 4: Perform the Calculation

Substitute the given values into the Hess's Law equation:\[ \Delta H_\text{hydrogenation} = -3920 - (-3800 + -241) \]. Simplify and calculate: \[ \Delta H_\text{hydrogenation} = -3920 + 3800 + 241 = 121 \mathrm{~kJ/mol} \].

Step 5: Determine the Correct Answer

The calculated value for the heat of hydrogenation is \(-121 \mathrm{~kJ/mol}\). Therefore, the correct answer is (c) \(-121 \mathrm{kJ/mol}\).

Key Concepts

Enthalpy

Enthalpy is a fundamental concept in thermodynamics that represents the total heat content of a system. It is denoted by the symbol \( H \). Enthalpy is particularly important when studying chemical reactions, as it helps us understand the energy changes they undergo. Keep in mind that during any chemical reaction, energy is either absorbed or released. Enthalpy changes reflect these energy exchanges.

• When a reaction releases heat to its surroundings, it is exothermic, and the enthalpy change \( (\Delta H) \) is negative.
• When a reaction absorbs heat from its surroundings, it is endothermic, and \( \Delta H \) is positive.

In the context of combustion reactions, we often refer to the "standard enthalpy of combustion." This is the heat change that occurs when one mole of a substance completely burns in oxygen under standard conditions (usually \(25^{\circ} \mathrm{C}\) and 1 atmospheric pressure). The exercise provides the standard enthalpy of combustion for substances involved in the hydrogenation process of cyclohexene, aiding in the calculation of energy changes.

Combustion Reactions

Combustion reactions are chemical processes where a substance combines with oxygen, releasing energy in the form of heat and light. They are typically characterized by products that include carbon dioxide \((\mathrm{CO}_2)\) and water \((\mathrm{H}_2\mathrm{O}) \).
These reactions are highly exothermic, meaning they release significant amounts of energy. This energy release is why combustion is a primary method for generating power, such as in engines or heaters.

• In the context of the exercise, the combustion reactions for cyclohexene \((\mathrm{C}_6\mathrm{H}_{10}) \), cyclohexane \((\mathrm{C}_6\mathrm{H}_{12}) \), and hydrogen \((\mathrm{H}_2)\) were provided with their respective enthalpy changes.
• Each of these reactions was set according to standard combustion equations, which consider the complete conversion of reactants to \( \mathrm{CO}_2\) and \( \mathrm{H}_2\mathrm{O} \).

Understanding the enthalpy changes for these combustion reactions is crucial because they allow us to use Hess's Law effectively to find unknown enthalpy changes in related reactions, such as hydrogenation in this example.

Hess's Law

Hess's Law is a valuable principle in thermodynamics which asserts that the total enthalpy change for a chemical reaction is the same, regardless of whether it occurs in one or multiple steps. This law is based on the conservation of energy principle, implying that energy cannot be created or destroyed.
In practice, Hess's Law allows for the calculation of an unknown enthalpy change by using known enthalpy changes of different steps of a reaction sequence. In the exercise, this is applied to determine the enthalpy change for the hydrogenation of cyclohexene to cyclohexane.

• To use Hess's Law, we compile a series of reactions such that when added together, they yield the desired overall reaction.
• The enthalpy changes for these reactions are algebraically manipulated to give the enthalpy change for the target reaction.

For the hydrogenation process provided, we use the combustion enthalpies of cyclohexene, cyclohexane, and hydrogen to find the overall enthalpy change for hydrogenation. By rearranging the equation for these individual combustion reactions, Hess's Law guides us to the accurate enthalpy calculation.