Problem 64 - Chemistry and Chemical Reactivity

Question

The enthalpy change for the oxidation of styrene, \(\mathrm{C}_{8} \mathrm{H}_{8},\) is measured by calorimetry. \(\mathrm{C}_{\mathrm{s}} \mathrm{H}_{\mathrm{s}}(\ell)+10 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 8 \mathrm{CO}_{2}(\mathrm{g})+4 \mathrm{H}_{2} \mathrm{O}(\ell)\) $$ \Delta_{r} H^{\circ}=-4395.0 \mathrm{kJ} / \mathrm{mol}-\mathrm{rxn} $$ Use this value, along with the standard enthalpies of formation of \(\mathrm{CO}_{2}(\mathrm{g})\) and \(\mathrm{H}_{2} \mathrm{O}(\ell),\) to calculate the enthalpy of formation of styrene, in \(\mathrm{kJ} / \mathrm{mol}\).

Step-by-Step Solution

Answer

The enthalpy of formation of styrene is 103.8 kJ/mol.

Step 1: Write the Reaction Equation

The enthalpy change we have is for the oxidation reaction of styrene represented by the equation: \[ \mathrm{C}_{8}\mathrm{H}_{8}(\ell)+10 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 8 \mathrm{CO}_{2}(\mathrm{g})+4 \mathrm{H}_{2} \mathrm{O}(\ell) \] This equation will be used to understand the transformation and enthalpy changes.

Step 2: Recall Enthalpy of Reaction Formula

Enthalpy of reaction, \( \Delta_{r} H^{\circ} \), is related to the enthalpies of formation \( \Delta_f H^{\circ} \) of reactants and products: \[ \Delta_{r} H^{\circ} = \sum \Delta_f H^{\circ}_{\text{products}} - \sum \Delta_f H^{\circ}_{\text{reactants}} \] We'll use this formula to find styrene's formation enthalpy.

Step 3: Insert Enthalpy Values for Products

The enthalpies of formation for the products are known: \( \Delta_f H^{\circ} (\mathrm{CO}_{2}(\mathrm{g})) = -393.5 \mathrm{kJ/mol} \) and \( \Delta_f H^{\circ} (\mathrm{H}_{2} \mathrm{O}(\ell)) = -285.8 \mathrm{kJ/mol} \).

Step 4: Calculate Total Enthalpy for Products

Now, calculate the total enthalpy of formation for the products: \[ 8\Delta_f H^{\circ} (\mathrm{CO}_{2}) + 4\Delta_f H^{\circ} (\mathrm{H}_{2} \mathrm{O}) = 8(-393.5) + 4(-285.8) = -3148.0 - 1143.2 = -4291.2 \mathrm{kJ} \]

Step 5: Solve for Styrene Enthalpy of Formation

Using the reaction enthalpy \( \Delta_{r} H^{\circ} = -4395.0 \mathrm{kJ/mol} \): \[ -4395.0 = -4291.2 - \Delta_f H^{\circ} (\mathrm{C}_{8}\mathrm{H}_{8}) \] Solve for \( \Delta_f H^{\circ} (\mathrm{C}_{8}\mathrm{H}_{8}) \): \[ \Delta_f H^{\circ} (\mathrm{C}_{8}\mathrm{H}_{8}) = -4291.2 + 4395.0 = 103.8 \mathrm{kJ/mol} \]

Step 6: Determine Final Result

The enthalpy of formation of styrene, \( \Delta_f H^{\circ} (\mathrm{C}_{8}\mathrm{H}_{8}) \), is calculated to be \( 103.8 \mathrm{kJ/mol} \).

Key Concepts

Calorimetry

Calorimetry is a fascinating technique used to measure the heat of chemical reactions or physical changes. It plays an essential role in determining the enthalpy change of a reaction, which is crucial in understanding energy exchanges between systems and their surroundings. In the exercise mentioned, calorimetry is used to measure the enthalpy change for the oxidation of styrene. This involves using a calorimeter to determine the amount of heat absorbed or released during the reaction.

A calorimeter typically consists of an insulated container filled with water, where the reaction occurs. As the reaction proceeds, the temperature change of the water is recorded. From this data, the heat transfer is calculated, allowing the enthalpy change of the reaction to be determined accurately.

• Calorimetry helps understand reaction energetics.
• It involves precise measurement using a calorimeter.
• Applications include determining fuel energy and chemical process efficiency.

By accurately measuring temperature changes, calorimetry provides a practical way to understand the thermodynamics of chemical processes, enhancing our grasp of these energetic transformations.

Oxidation Reaction

The oxidation reaction of styrene involves the transformation of styrene (\(\mathrm{C}_{8}\mathrm{H}_{8}\)) with oxygen to produce carbon dioxide and water. It is a type of combustion reaction that is highly exothermic, releasing a substantial amount of energy, making it quite powerful.

In a typical oxidation reaction, a substance reacts with oxygen, often accompanied by heat and light production. In the case of styrene's oxidation, the reaction is balanced as follows: \[ \mathrm{C}_{8}\mathrm{H}_{8} + 10 \mathrm{O}_{2} \rightarrow 8 \mathrm{CO}_{2} + 4 \mathrm{H}_{2} \mathrm{O} \] This reaction showcases the fundamental principle of conservation of mass and energy, with the substance undergoing oxidation by losing electrons, commonly to oxygen, forming various oxides.

Oxidation reactions are pivotal in numerous industries and natural processes. They encompass simple burning practices to complex biochemical processes, aiding in our understanding of energy transformations and chemical changes.

Enthalpy Change

Enthalpy change, denoted as \( \Delta H \), is a key concept in thermodynamics describing the heat change occurring at constant pressure during a chemical reaction. In the context of the exercise, the enthalpy change for the oxidation of styrene is -4395.0 \( \mathrm{kJ/mol} \), which tells us the reaction is highly exothermic, meaning it releases energy into the surroundings.

Calculating the enthalpy change involves using the known enthalpies of formation for reactants and products. The general formula is: \[ \Delta_{r} H^{\circ} = \Sigma \Delta_f H^{\circ}_{\text{products}} - \Sigma \Delta_f H^{\circ}_{\text{reactants}} \] This formula indicates how energy is absorbed or released during the conversion of reactants to products.

• \( \Delta H \) is considered negative for exothermic processes.
• Positive \( \Delta H \) represents endothermic processes.
• An understanding of \( \Delta H \) helps predict reaction energetics and feasibility.

Comprehending enthalpy changes is crucial for understanding how energy is conserved and transformed in chemical reactions.

Enthalpies of Formation

Enthalpies of formation are fundamental values representing the heat change when one mole of a compound is formed from its elements in their standard states. These values are key for calculating reaction enthalpies and, ultimately, assessing reaction energetics.

In the exercise provided, the enthalpies of formation for carbon dioxide \( (\mathrm{CO}_{2}) \) and water \( (\mathrm{H}_{2} \mathrm{O}) \) are given as \(-393.5 \mathrm{kJ/mol}\) and \(-285.8 \mathrm{kJ/mol}\), respectively. These standardized values are vital in enthalpy calculations, allowing chemists to determine the change in heat during different reactions.

The enthalpy of formation for styrene was calculated indirectly using these known values and the measured overall reaction enthalpy. This highlights the importance of:

• Standard enthalpy values for various substances.
• Utilizing standard conditions for consistent and comparable results.
• The application of thermodynamic principles to derive unknown enthalpies.

By applying these principles, scientists can predict and analyze chemical processes' energetic behavior, critical for industrial applications and our understanding of chemical thermodynamics.