Question

Consider two reactions for the production of ethanol: ${\mathrm{C}}_2{\mathrm{H}}_4(g)+{\mathrm{H}}_2\mathrm{O}(g)⟶{\mathrm{CH}}_3{\mathrm{CH}}_2\mathrm{OH}(l)$ ${\mathrm{C}}_2{\mathrm{H}}_6(g)+{\mathrm{H}}_2\mathrm{O}(g)⟶{\mathrm{CH}}_3{\mathrm{CH}}_2\mathrm{OH}(l)+{\mathrm{H}}_2(g)$ Which would be the more thermodynamically feasible at standard conditions? Why?

Short answer

After calculating the Gibbs free energy changes (ΔG) for both reactions using ΔG = ΔH - TΔS, we compare the ΔG values. The reaction with the lower ΔG value will be more thermodynamically feasible at standard conditions.

Step-by-step solution

Calculate the enthalpy change for each reaction

To calculate the enthalpy change (ΔH) for each reaction, we'll need to find the standard enthalpies of formation (ΔHf°) for the reactants and products. Then, we can use Hess's law to find ΔH for each reaction: ΔH = ΣΔHf°(products) - ΣΔHf°(reactants) For the first reaction: ΔH1 = ΔHf°(CH3CH2OH) - (ΔHf°(C2H4) + ΔHf°(H2O)) For the second reaction: ΔH2 = (ΔHf°(CH3CH2OH) + ΔHf°(H2)) - (ΔHf°(C2H6) + ΔHf°(H2O))

Calculate the entropy change for each reaction

To calculate the entropy change (ΔS) for each reaction, we'll need to find the standard entropies (S°) for the reactants and products. Then, we can calculate ΔS for each reaction: ΔS = ΣS°(products) - ΣS°(reactants) For the first reaction: ΔS1 = S°(CH3CH2OH) - (S°(C2H4) + S°(H2O)) For the second reaction: ΔS2 = (S°(CH3CH2OH) + S°(H2)) - (S°(C2H6) + S°(H2O))

Calculate the Gibbs free energy change for each reaction

Now we can use the ΔH and ΔS values for each reaction to calculate the Gibbs free energy change (ΔG) at standard conditions (T=298 K): ΔG = ΔH - TΔS For the first reaction: ΔG1 = ΔH1 - (298 K)ΔS1 For the second reaction: ΔG2 = ΔH2 - (298 K)ΔS2

Compare the Gibbs free energy changes for the reactions

Finally, we can compare the ΔG values for the two reactions: ΔG1 vs ΔG2 The reaction with the lower ΔG value will be more thermodynamically feasible at standard conditions.

Key concepts

Enthalpy Change

Enthalpy change, represented as $\mathrm{\Delta }H$, is a measure of heat change in a chemical reaction at constant pressure. It reflects the energy absorbed or released when bonds are broken or formed. If $\mathrm{\Delta }H$ is negative, the reaction is exothermic, meaning it releases energy. Conversely, a positive $\mathrm{\Delta }H$ indicates an endothermic reaction, where energy is absorbed. In the given exercise, we are calculating $\mathrm{\Delta }H$ for two reactions: one producing ethanol from ethylene and water, and the other from ethane and water. The calculation involves subtracting the sum of the standard enthalpies of formation of the reactants from those of the products. This step is crucial because it allows us to understand whether energy is taken in or given out during the formation of ethanol under standard conditions. By applying Hess's law, which states that the total enthalpy change in a reaction is the same regardless of the steps taken, we can accurately compute $\mathrm{\Delta }H$ and assess the energy efficiency of each proposed chemical path.

Entropy Change

Entropy, symbolized as $\mathrm{\Delta }S$, measures the disorder or randomness in a chemical system. Most chemical reactions result in an increase or decrease in entropy. A positive $\mathrm{\Delta }S$ signifies greater disorder and typically favors spontaneity, while a negative $\mathrm{\Delta }S$ implies a decrease in randomness. For the reaction exercise provided, we calculate $\mathrm{\Delta }S$ by finding the difference between the sum of standard entropies of the products and reactants. It's important to notice that reactions involving gases or producing more moles of products than reactants generally lead to increases in entropy. In the context of the given reactions producing ethanol, understanding $\mathrm{\Delta }S$ helps us grasp the likelihood of reaction spontaneity from an entropy perspective. This value combined with enthalpy change can offer insight into the overall feasibility of the reactions.

Gibbs Free Energy

Gibbs free energy ($\mathrm{\Delta }G$) combines enthalpy and entropy changes into a single value that predicts the spontaneity of a reaction. A negative $\mathrm{\Delta }G$ suggests a spontaneous reaction under given conditions, while a positive $\mathrm{\Delta }G$ indicates non-spontaneity. The equation used is:$$\mathrm{\Delta }G=\mathrm{\Delta }H-T\mathrm{\Delta }S$$where $T$ is the temperature in Kelvin. In the problem provided, calculating $\mathrm{\Delta }G$ for both ethanol-producing reactions at 298 K standard conditions can tell us which is more thermodynamically favorable. The reaction with the lower $\mathrm{\Delta }G$ value suggests it is more likely to happen without additional input of energy. Therefore, Gibbs free energy helps integrate the effects of enthalpy and entropy into one measure to determine the overall feasibility.

Chemical Reactions

Chemical reactions involve the transformation of reactants into products through the breaking and forming of chemical bonds. This transformation is often accompanied by changes in energy, which can be meticulously analyzed using concepts like enthalpy, entropy, and Gibbs free energy. In this exercise, the reactions of interest are those that produce ethanol either from ethene or ethane. Each reaction has its own set of reactants and products. Understanding the specifics of these reactions - the conditions under which they occur and the energy changes involved - is crucial for predicting which reaction path is more feasible. The concept behind studying these reactions is not only to identify a feasible path for ethanol production but also to understand the fundamental principles of thermodynamics that dictate reaction behavior. This understanding helps chemists and engineers in designing processes that are energy-efficient and cost-effective.

Hess's Law

Hess’s Law is a fundamental principle in thermodynamics used to determine the enthalpy change of a chemical reaction. It states that the total enthalpy change in a reaction is the same regardless of how the reaction is carried out in steps. This is derived from the conservation of energy principle. In the case of the reactions discussed in the exercise, Hess's Law allows us to calculate $\mathrm{\Delta }H$ for each reaction pathway by using the standard enthalpies of formation of products and reactants. This simplification is particularly useful when direct measurement of enthalpy change is difficult or impractical.Hess’s Law plays a crucial role in the analysis of enthalpy changes because it provides a method to algebraically sum up individual enthalpy changes for intermediate steps in a reaction to find the overall heat change, ensuring the calculations remain accurate and consistent even without performing the entire reaction in practice.