Problem 57 - Chemistry: An Atoms-Focused Approach

Question

Acid Precipitation Aerosols (fine droplets) of sulfuric acid form in the atmosphere as a result of the following combination reaction:$$\mathrm{SO}_{3}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightarrow \mathrm{H}_{2} \mathrm{SO}_{4}(\ell)$$.Use the appropriate \(\Delta G_{f}^{\circ}\) data in Appendix 4 to calculate \(\Delta G_{\mathrm{rxn}}^{\circ}\) for this reaction.

Step-by-Step Solution

Answer

Question: Calculate the standard Gibbs free energy change (ΔG°) for the reaction of sulfur trioxide (SO3) and water (H2O) forming sulfuric acid (H2SO4), using the given standard Gibbs free energy of formation (ΔGf°) data. Answer: The standard Gibbs free energy change (ΔG°) for the reaction is -145.5 kJ/mol.

Step 1: 1. Write down the given reaction

The given reaction is: $$\mathrm{SO}_{3}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightarrow \mathrm{H}_{2} \mathrm{SO}_{4}(\ell)$$

Step 2: 2. Consult Appendix 4 for the standard Gibbs free energy of formation values (ΔGf°) for the substances involved in the reaction

Search for the ΔGf° values of the substances: ΔGf° (SO3) = -370.4 kJ/mol ΔGf° (H2O) = -228.6 kJ/mol ΔGf° (H2SO4) = -744.5 kJ/mol

Step 3: 3. Calculate the standard Gibbs free energy change of the reaction (ΔG°) using the formula

Apply the formula: ΔG° (reaction) = Σ ΔGf° (products) - Σ ΔGf° (reactants) So, ΔG° (reaction) = ΔGf° (H2SO4) - [ΔGf° (SO3) + ΔGf° (H2O)]

Step 4: 4. Substitute the values and compute the result

Insert the values found in step 2: ΔG° (reaction) = (-744.5 kJ/mol) - [(-370.4 kJ/mol) + (-228.6 kJ/mol)] ΔG° (reaction) = (-744.5 kJ/mol) - (-599 kJ/mol) = -145.5 kJ/mol The standard Gibbs free energy change (ΔG°) for the reaction is -145.5 kJ/mol.

Key Concepts

Gibbs Free Energy

Gibbs Free Energy, often symbolized as \(G\), is a thermodynamic property that indicates the maximum reversible work obtainable from a chemical reaction at constant pressure and temperature. It essentially tells us whether a chemical process can occur naturally. If the change in Gibbs Free Energy (∆G) is negative, the reaction is spontaneous. On the other hand, a positive ∆G means the reaction is non-spontaneous and requires energy input.

The formula to calculate Gibbs Free Energy change is:

• \(∆G = ∆H - T ∆S\)

where \(∆H\) is the change in enthalpy, \(T\) is the temperature in Kelvin, and \(∆S\) is the change in entropy. In a simplified context for standard reactions, we use the formula:

• \(∆G°_{rxn} = ∑ ∆G_f°(products) - ∑ ∆G_f°(reactants)\)

This highlights the change in free energy given the formation energies (\(∆G_f°\)) of the substances involved.

In the exercise, we used this concept to calculate the spontaneous nature of the reaction forming sulfuric acid. By comparing the Gibbs Free Energy of reactants and products, we determined that \(∆G°_{rxn}= -145.5\,kJ/mol\), signifying a spontaneous process.

Chemical Reaction

A chemical reaction involves the transformation of reactants to products through the breaking and formation of chemical bonds. In the context of our exercise, the reaction can be represented as:

• \(\text{SO}_3(g) + \text{H}_2\text{O}(g) \to \text{H}_2\text{SO}_4(l)\)

This particular reaction is a type of combination reaction where the gaseous sulfur trioxide (\(\text{SO}_3\)) and water vapor (\(\text{H}_2\text{O}\)) combine to form liquid sulfuric acid (\(\text{H}_2\text{SO}_4\)).

Key characteristics of chemical reactions include:

• Reactants: These are the starting materials that undergo change. For our reaction, \(\text{SO}_3\) and \(\text{H}_2\text{O}\) are the reactants.
• Products: These are the new substances formed as a result of the reaction. In this case, \(\text{H}_2\text{SO}_4\) is the product.
• Energy Change: Chemical reactions can either release energy or absorb it, which is reflected in the signs of \(∆G\) or \(∆H\).

This reaction involves a release of energy as indicated by the negative \(∆G\) value of -145.5 kJ/mol, suggesting that the reaction is exothermic and spontaneous.

Sulfuric Acid Formation

Sulfuric acid (\(\text{H}_2\text{SO}_4\)) is a strong acid formed from sulfur trioxide (\(\text{SO}_3\)) and water. Its formation plays a significant role in acid precipitation, a type of acid rain that arises from atmospheric chemical processes.

The basic chemical reaction for sulfuric acid formation can be summarized by:

• \(\text{SO}_3(g) + \text{H}_2\text{O}(g) \to \text{H}_2\text{SO}_4(l)\)

This reaction is critical in understanding environmental processes as well as industrial applications. In the atmosphere, \(\text{SO}_3\) often arises from the combustion of fossil fuels that contain sulfur, contributing to environmental pollution.

Some essential facts about sulfuric acid formation include:

• It leads to the formation of acid rain, which can have harmful effects on ecosystems, soil, water bodies, and human-made structures.
• Industrial processes often mimic natural sulfuric acid formation to produce \(\text{H}_2\text{SO}_4\) for use in producing fertilizers, chemicals, and in refining processes.
• The process is energetically favorable, as shown by the spontaneously negative \(∆G\) calculated in the reaction.

Understanding how sulfuric acid forms helps us mitigate environmental impacts and efficiently harness its industrial benefits.