Question

Acrylonitrile is the starting material used in the manufacture of acrylic fibers (U.S. annual production capacity is more than two million pounds). Three industrial processes for the production of acrylonitrile are given below. Using data from Appendix 4, calculate \(\Delta S^{\circ}, \Delta H^{p},\) and \(\Delta G^{\circ}\) for each process. For part a, assume that \(T=25^{\circ} \mathrm{C} ;\) for part \(\mathrm{b}, T=70 .^{\circ} \mathrm{C} ;\) and for part \(\mathrm{c}, T=700 .^{\circ} \mathrm{C}\) Assume that \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) do not depend on temperature.

Short answer

Using the data from Appendix 4 and the balanced chemical equations, calculate the change in entropy (\(\Delta S^{\circ}\)) and change in enthalpy (\(\Delta H^{\circ}\)) for each process using the formulas: \[\Delta H^{\circ} = \sum H^{\circ}_{\text{products}} - \sum H^{\circ}_{\text{reactants}}\] \[\Delta S^{\circ} = \sum S^{\circ}_{\text{products}} - \sum S^{\circ}_{\text{reactants}}\] Then, convert the given temperatures from Celsius to Kelvin and calculate the change in Gibbs free energy (\(\Delta G^{\circ}\)) for each process using the equation: \[\Delta G^{\circ} = \Delta H^{\circ} - T\Delta S^{\circ}\]

Step-by-step solution

Find \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) for each process

Using the Appendix 4, we need to find the standard enthalpies of formation and standard entropies of all reactants and products involved in the reactions for processes a, b, and c. Once we have found these values, we can calculate \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) for each process using the following formulas: \[\Delta H^{\circ} = \sum H^{\circ}_{\text{products}} - \sum H^{\circ}_{\text{reactants}}\] \[\Delta S^{\circ} = \sum S^{\circ}_{\text{products}} - \sum S^{\circ}_{\text{reactants}}\]

Calculate \(\Delta G^{\circ}\) for each process

Now that we have the values of \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) for each process at the given temperatures, we can calculate \(\Delta G^{\circ}\) using the following equation: \[\Delta G^{\circ} = \Delta H^{\circ} - T\Delta S^{\circ}\] where \(T\) is the temperature in Kelvin. Remember to convert the given temperatures in Celsius to Kelvin by adding 273.15 to the Celsius temperatures before plugging them into the equation. Calculate \(\Delta G^{\circ}\) for each process with their respective temperatures: a) For part a, \(T = 25^{\circ}\mathrm{C} \Rightarrow T = 298.15 \mathrm{K}\): \[\Delta G^{\circ}_a = \Delta H^{\circ}_a - (298.15 \mathrm{K})(\Delta S^{\circ}_a)\] b) For part b, \(T = 70^{\circ}\mathrm{C} \Rightarrow T = 343.15 \mathrm{K}\): \[\Delta G^{\circ}_b = \Delta H^{\circ}_b - (343.15 \mathrm{K})(\Delta S^{\circ}_b)\] c) For part c, \(T = 700^{\circ}\mathrm{C} \Rightarrow T = 973.15 \mathrm{K}\): \[\Delta G^{\circ}_c = \Delta H^{\circ}_c - (973.15 \mathrm{K})(\Delta S^{\circ}_c)\] With these equations, we can find the \(\Delta G^{\circ}\) values for each of the three processes.

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 \(H\) and is measured in joules or kilojoules. It gives us insight into how much energy is absorbed or released during a chemical reaction. In terms of chemical reactions, enthalpy change (\(\Delta H\)) can be used to determine if a reaction is exothermic (releases heat) or endothermic (absorbs heat). A positive \(\Delta H\) indicates that the reaction requires heat, meaning it's endothermic. A negative \(\Delta H\) suggests that the reaction gives off heat, categorizing it as exothermic. In calculations, the enthalpy change for a reaction can be found using the standard enthalpies of formation for the products and reactants:

• \(\Delta H^{\circ} = \sum H^{\circ}_{\text{products}} - \sum H^{\circ}_{\text{reactants}}\)

This equation allows us to determine the heat change under standard conditions (1 bar and 298 K). Understanding enthalpy helps predict the energy requirements or releases in industrial processes, like the production of acrylonitrile.

Entropy

Entropy, symbolized as \(S\), is a measure of the disorder or randomness in a system. In chemical thermodynamics, it's crucial for understanding how energy spreads in a process or reaction. The second law of thermodynamics states that in any spontaneous process, the total entropy of the system and its surroundings always increases.When examining reactions, the change in entropy (\(\Delta S\)) tells us how the disorder of the system changes:

• \(\Delta S^{\circ} = \sum S^{\circ}_{\text{products}} - \sum S^{\circ}_{\text{reactants}}\)

A positive \(\Delta S\) indicates that the products are more disordered than the reactants, which is typically favorable for spontaneity. Conversely, a negative \(\Delta S\) suggests greater order in the products.Entropy change is a significant factor when predicting whether reactions occur spontaneously, as its interplay with enthalpy will determine the reaction's overall Gibbs free energy change.

Gibbs Free Energy

Gibbs free energy, represented by \(G\), combines enthalpy and entropy to determine the spontaneity of a reaction. It is a critical concept providing insight into whether a reaction can proceed on its own under constant pressure and temperature. The change in Gibbs free energy, \(\Delta G\), defines this spontaneity:

• \(\Delta G^{\circ} = \Delta H^{\circ} - T\Delta S^{\circ}\)

Here, \(T\) is the temperature in Kelvin. A negative \(\Delta G\) indicates a spontaneous process, while a positive \(\Delta G\) suggests a non-spontaneous one. When \(\Delta G = 0\), the system is in equilibrium.The clever marriage of enthalpy and entropy through Gibbs free energy helps chemists and engineers predict and control chemical reactions, especially significant in deciding the viability of industrial processes like synthesizing acrylonitrile at different temperatures.

Temperature Conversion

Temperature conversion is essential in thermodynamics for consistent and accurate calculations, especially when determining properties like Gibbs free energy that require absolute temperature scales. The standard conversion from Celsius to Kelvin is simple and necessary:

• To convert from Celsius to Kelvin, add 273.15 to the Celsius temperature.
• For example, \(25^{\circ}C\) converts to \(298.15 K\), \(70^{\circ}C\) to \(343.15 K\), and \(700^{\circ}C\) to \(973.15 K\).

Using Kelvin, a unit explained by absolute zero where all thermal motion stops, ensures that all thermodynamic equations, including \(\Delta G^{\circ} = \Delta H^{\circ} - T\Delta S^{\circ}\), are correctly applicable without negative temperatures that complicate calculations. Understanding and accurately converting temperatures is fundamental to reliable thermodynamic assessments and calculations.