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) \(-161 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (b) \(-131 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (c) \(-121 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (d) None

Short answer

The heat of hydrogenation is \(-121 \mathrm{~kJ} \mathrm{~mol}^{-1}\), so option (c) is correct.

Step-by-step solution

Understand the Problem

The problem asks us to calculate the heat of hydrogenation for cyclohexane \(\left(\mathrm{C}_6 \mathrm{H}_{10}\right)\). This means we need to find the change in enthalpy when one mole of \(\mathrm{C}_6 \mathrm{H}_{10}\) is converted to cyclohexane \(\mathrm{C}_6 \mathrm{H}_{12}\) by the addition of one mole of \(\mathrm{H}_2\).

Write the Combustion Reactions

First, write the balanced equations for the combustion reactions:1. \(\mathrm{H}_2(g) + \frac{1}{2} \mathrm{O}_2(g) \rightarrow \mathrm{H}_2\mathrm{O}(l)\) with \(\Delta H_1 = -241 \mathrm{~kJ} \mathrm{~mol}^{-1}\).2. \(\mathrm{C}_6 \mathrm{H}_{10}(g) + \frac{17}{2} \mathrm{O}_2(g) \rightarrow 6 \mathrm{CO}_2(g) + 5 \mathrm{H}_2\mathrm{O}(l)\) with \(\Delta H_2 = -3800 \mathrm{~kJ} \mathrm{~mol}^{-1}\).3. \(\mathrm{C}_6 \mathrm{H}_{12}(g) + 9 \mathrm{O}_2(g) \rightarrow 6 \mathrm{CO}_2(g) + 6 \mathrm{H}_2\mathrm{O}(l)\) with \(\Delta H_3 = -3920 \mathrm{~kJ} \mathrm{~mol}^{-1}\).

Develop the Hydrogenation Reaction

The hydrogenation reaction can be formulated as:\(\mathrm{C}_6 \mathrm{H}_{10}(g) + \mathrm{H}_2(g) \rightarrow \mathrm{C}_6 \mathrm{H}_{12}(g)\).We want to find \(\Delta H\) for this reaction, which is the heat of hydrogenation.

Apply Hess's Law

According to Hess's Law, the total enthalpy change for a reaction is the sum of the enthalpy changes for the individual steps. Therefore, we have:\(\Delta H_\text{hydrogenation} = \Delta H_3 - \Delta H_2 - \Delta H_1\).Substituting the given values:\[\Delta H_\text{hydrogenation} = (-3920) - (-3800) - (-241)\].

Calculate the Heat of Hydrogenation

Simplify the expression to compute the heat of hydrogenation:\[\Delta H_\text{hydrogenation} = (-3920 + 3800 + 241)\].This results in:\[\Delta H_\text{hydrogenation} = -121 \mathrm{~kJ} \mathrm{~mol}^{-1}\].

Choose the Correct Answer

From the calculated result, the heat of hydrogenation is \(-121 \mathrm{~kJ} \mathrm{~mol}^{-1}\), which matches option (c).

Key concepts

Heat of Hydrogenation

The heat of hydrogenation is an important thermodynamic measurement. It tells us the change in enthalpy when a chemical compound undergoes hydrogenation. Hydrogenation is the process of adding hydrogen to another molecule. In the context of cyclohexane and its related compounds, understanding the heat of hydrogenation helps chemists determine the stability of unsaturated bonds. This is because more stable compounds generally have smaller heats of hydrogenation.

Here’s a simplified way to understand it:

• You start with an unsaturated compound such as an alkene.
• Hydrogen is added to it, converting it into a more saturated form.
• The resulting compound typically has only single bonds in place of the original double or triple bonds.

The process is exothermic, meaning heat is released. The amount of heat released gives us insights into the potential energy stored in these unsaturated bonds. Thus, the heat of hydrogenation is not only a measure of energy change but also an indicator of chemical stability.

Hess's Law

Hess's Law is a fundamental principle in chemistry that is incredibly useful for calculating enthalpy changes, like in our heat of hydrogenation problem. It states that the total enthalpy change of a chemical reaction is the same, regardless of the pathway taken. This makes it very useful for determining difficult-to-measure enthalpy changes by constructing a series of linked chemical steps for which the enthalpy changes are known.

To break it down further:

• Consider that you can't measure the heat of hydrogenation directly.
• Instead, you know the enthalpies of combustion for the reactant and product.
• Hess's Law allows you to use these known values to calculate the desired enthalpy change.
• Simply sum the enthalpy changes for each step involved in the conversion process of your compounds.

In this exercise, we considered the individual combustion reactions for the reactants and products and then used Hess's Law to find the Δ H of the hydrogenation reaction.

Standard Enthalpy Change

Standard enthalpy change is a vital concept in thermodynamics. It describes the heat change that occurs in a system at standard conditions of 1 atm pressure and a specified temperature, usually at 25°C (298 K). In our exercise, we worked with standard enthalpy changes, denoting heat exchange under these standard conditions.

Understanding standard enthalpy is essential because:

• It provides a way to compare energy changes for different reactions.
• This information is important when predicting reaction behavior and determining reaction spontaneity.
• Standard enthalpy changes are widely tabulated, making them accessible for solving various chemical problems.

In the given problem, the standard enthalpy changes for the combustion of hydrogen, cyclohexene, and cyclohexane were used to calculate the heat of hydrogenation. These values helped to directly apply Hess's Law to do so with accuracy and repeatability.

Combustion Reaction

A combustion reaction is an exothermic reaction where a substance combines with oxygen to release heat, light, and new products like carbon dioxide and water. In this exercise, we examined the combustion of hydrogen, cyclohexene ( C_6 H_10), and cyclohexane ( C_6H_12).

• Each combustion reaction involves the compound reacting with oxygen to produce carbon dioxide, water, and thermal energy.
• These reactions typically release large amounts of energy due to the formation of strong bonds in the production of CO₂ and H₂O.
• The enthalpy changes from these reactions are measurable and are usually negative, indicating the exothermic nature.

Understanding combustion reactions is crucial in energetics calculations, like in our problem. They provide essential data for Hess's Law applications, helping deduce complex thermodynamic quantities like the heat of hydrogenation.