Problem 48 - Chemistry The Molecular Science

Question

Hydrogen gas combines with chlorine gas in an exothermic reaction to form \(\mathrm{HCl}(\mathrm{g})\). Consider the decomposition of gaseous hydrogen chloride to hydrogen and chlorine. Without doing any calculations, and basing your prediction on the enthalpy change and the entropy change, is this reaction product-favored at \(25^{\circ} \mathrm{C}\) ? Explain your answer briefly.

Step-by-Step Solution

Answer

The decomposition reaction is not product-favored at 25°C due to the endothermic nature requiring energy input.

Step 1: Understand the Reaction

The given reaction is the combination of hydrogen gas (H2) and chlorine gas (Cl2) to form hydrogen chloride (HCl). Conversely, the reverse reaction involves the decomposition of HCl into H2 and Cl2.

Step 2: Consider Enthalpy Change

Hydrogen chloride formation is known to be exothermic, meaning it releases energy. Therefore, the decomposition of HCl would be the opposite, endothermic, requiring energy input.

Step 3: Consider Entropy Change

The formation of HCl involves a decrease in the number of gas molecules (2 molecules forming 2 molecules), meaning little change in entropy. In the decomposition, however, HCl splits into more disorderly separate gas molecules, increasing entropy.

Step 4: Determine Favorability at 25°C

At a standard temperature of 25°C, product favorability depends on the Gibbs free energy change, which is influenced by both enthalpy and entropy. The endothermic nature (positive enthalpy change) and increase in entropy (positive entropy change) oppose each other's effects. Given the strength of the energy required for bond breaking, the reaction is less likely to be product-favored without external energy.

Key Concepts

Enthalpy Change

In a chemical reaction, **enthalpy change** (\( \Delta H \)) reflects the heat absorbed or released. For exothermic reactions, heat is released, resulting in a negative \( \Delta H \). Conversely, endothermic reactions absorb heat, giving a positive \( \Delta H \).

When hydrogen gas (\( \text{H}_2 \)) and chlorine gas (\( \text{Cl}_2 \)) combine to form hydrogen chloride (\( \text{HCl} \)), the process is exothermic. This means that energy is released as the bonds form, making hydrochloric acid formation a favorable reaction in terms of enthalpy.

If we consider the reverse reaction—decomposition of \( \text{HCl} \)—this process becomes endothermic. Here, energy is required to break the strong \( \text{H-Cl} \) bonds. Thus, \( \Delta H \) for decomposition is positive, suggesting that energy input is necessary.

Entropy Change

**Entropy change** (\( \Delta S \)) measures disorder or randomness. In chemical terms, a positive \( \Delta S \) indicates greater disorder after a reaction.

In the formation of \( \text{HCl} \) from hydrogen and chlorine gases, the number of molecules before and after the reaction is nearly the same. However, when \( \text{HCl} \) decomposes into \( \text{H}_2 \) and \( \text{Cl}_2 \), there is an increase in disorder because two molecules of \( \text{HCl} \) turn into more randomly distributed hydrogen and chlorine molecules.

Thus, the decomposition reaction experiences a positive \( \Delta S \), suggesting that entropy increases favor the formation of separate hydrogen and chlorine gas molecules.

Gibbs Free Energy

The concept of **Gibbs Free Energy** (\( \Delta G \)) helps predict whether a reaction will occur spontaneously. It combines enthalpy (\( \Delta H \)) and entropy (\( \Delta S \)): \(\Delta G = \Delta H - T\Delta S\). A negative \( \Delta G \) means the reaction is spontaneous, while a positive \( \Delta G \) shows it is not.

For the decomposition of \( \text{HCl} \), \( \Delta H \) is positive (endothermic), and \( \Delta S \) is positive (more disorder). At higher temperatures, the \( T\Delta S \) term significantly increases, which can potentially make \( \Delta G \) negative, making the reaction spontaneous. However, at standard room temperature (25^{\circ} \text{C}), the energy input required to overcome bond strength makes \( \Delta G \) remain positive.

Therefore, despite increased entropy, the endothermic nature at this temperature makes the decomposition of \( \text{HCl} \) less likely to occur without added energy. It demonstrates how understanding both \( \Delta H \) and \( \Delta S \) is crucial in determining a reaction's spontaneity.