Problem 109 - General Chemistry

Question

Hydrogen sulfide, \(\mathrm{H}_{2} \mathrm{~S}\), is a poisonous gas with the odor of rotten eggs. The reaction for the formation of \(\mathrm{H}_{2} \mathrm{~S}\) from the elements is $$ \mathrm{H}_{2}(g)+\frac{1}{8} \mathrm{~S}_{8}(\text { rhombic }) \longrightarrow \mathrm{H}_{2} \mathrm{~S}(g) $$ Use Hess's law to obtain the enthalpy change for this reaction from the following enthalpy changes: $$ \begin{gathered} \mathrm{H}_{2} \mathrm{~S}(g)+\frac{3}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{SO}_{2}(g) ; \Delta H=-518 \mathrm{~kJ} \\\ \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(g) ; \Delta H=-242 \mathrm{~kJ} \\ \frac{1}{8} \mathrm{~S}_{8}(\text { rhombic })+\mathrm{O}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g) ; \Delta H=-297 \mathrm{~kJ} \end{gathered} $$

Step-by-Step Solution

Answer

The enthalpy change for the formation of \(\mathrm{H}_2\mathrm{~S}\) is \(-21 \text{ kJ}\).

Step 1: Identify Target Reaction

The target reaction for which we need to determine the enthalpy change is \( \mathrm{H}_{2}(g) + \frac{1}{8} \mathrm{~S}_{8}(\text{rhombic}) \rightarrow \mathrm{H}_{2} \mathrm{~S}(g) \). We are asked to use Hess's Law to find the enthalpy change for this reaction.

Step 2: List the Given Reactions

We have three given reactions with their respective enthalpy changes:\( \mathrm{H}_{2} \mathrm{~S}(g) + \frac{3}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{H}_{2} \mathrm{O}(g) + \mathrm{SO}_{2}(g) ; \Delta H=-518 \mathrm{~kJ} \), \( \mathrm{H}_{2}(g) + \frac{1}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{H}_{2} \mathrm{O}(g) ; \Delta H=-242 \mathrm{~kJ} \), and \( \frac{1}{8} \mathrm{~S}_{8}(\text{rhombic}) + \mathrm{O}_{2}(g) \rightarrow \mathrm{SO}_{2}(g) ; \Delta H=-297 \mathrm{~kJ} \).

Step 3: Reverse Required Reactions

Using Hess's law, we reverse the reaction \( \mathrm{H}_{2} \mathrm{~S}(g) + \frac{3}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{H}_{2} \mathrm{O}(g) + \mathrm{SO}_{2}(g) \) to \( \mathrm{H}_{2} \mathrm{O}(g) + \mathrm{SO}_{2}(g) \rightarrow \mathrm{H}_{2} \mathrm{~S}(g) + \frac{3}{2} \mathrm{O}_{2}(g) \) and change the enthalpy sign to \( \Delta H = +518 \mathrm{~kJ} \).

Step 4: Use Hess's Law to Derive Equation

Combine the reversed reaction from Step 3 with the other given reactions to construct the target equation. The equation:\[ \mathrm{H}_{2}(g) + \frac{1}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{H}_{2} \mathrm{O}(g) \] and \[ \frac{1}{8} \mathrm{~S}_{8}(\text{rhombic}) + \mathrm{O}_{2}(g) \rightarrow \mathrm{SO}_{2}(g) \] added to the reversed equation in Step 3:\[ \mathrm{H}_{2} \mathrm{O}(g) + \mathrm{SO}_{2}(g) \rightarrow \mathrm{H}_{2} \mathrm{~S}(g) + \frac{3}{2} \mathrm{O}_{2}(g) \]leads to:\[ \mathrm{H}_{2}(g) + \frac{1}{8} \mathrm{~S}_{8}(\text{rhombic}) \rightarrow \mathrm{H}_{2} \mathrm{~S}(g) \].

Step 5: Calculate Overall Enthalpy Change

Sum the enthalpy changes for the constituent reactions: \(+518 \mathrm{~kJ} + (-242) \mathrm{~kJ} + (-297) \mathrm{~kJ} = -21 \mathrm{~kJ} \). This result, \(-21 \mathrm{~kJ}\), is the enthalpy change for the target reaction.

Key Concepts

Understanding Enthalpy Change

Enthalpy change is an essential concept in chemistry, particularly under Hess's Law. It represents the heat energy change in a system at constant pressure during a chemical reaction. Breaking it down:

• Enthalpy (\( H \)), reflects the total energy of a thermodynamic system, comprised of internal energy and energy required for volume displacement by its pressure.
• The symbol \( \Delta H \) denotes the change in enthalpy during a reaction.
• Reactions can be exothermic (\( \Delta H < 0 \))—energy is released—or endothermic (\( \Delta H > 0 \))—energy is absorbed.

In using Hess's Law, one can determine the \( \Delta H \) for a reaction via combining enthalpy changes of related reactions. Given the enthalpy changes of intermediate steps, we can arrive at the desired reaction's enthalpy change without directly measuring it. This principle underscores the path independence of enthalpy changes, highlighting that the total enthalpy change is the same irrespective of the path taken.

Exploring Chemical Reactions

Chemical reactions are processes where substances, known as reactants, transform to form new substances, called products. Familiarizing with these reactions involves understanding elements and compounds engaging in breaking and forming bonds:

• Chemical reactions involve rearrangement of atoms, maintaining the same number of each type before and after the reaction.
• In our example, hydrogen gas reacts with solid sulfur to form poisonous hydrogen sulfide gas.
• Reactions might require energy input or release energy, reflecting differing bond strengths in reactants and products.

In analysing these reactions with Hess's Law, envision a sequence of steps that take the reactants to the products. Conjoining reactions utilizing known enthalpy changes allows us to comprehend the overall energy transformation happening without recalculating from scratch.

The Role of Thermodynamics

Thermodynamics provides the framework to understand energy changes and transfers in chemical reactions. Central to this field is the conservation of energy principle, underscoring that energy cannot be created or destroyed.

• Thermodynamics encompasses laws that predict the direction and feasibility of reactions based on energy considerations.
• Hess’s Law is rooted in the first law of thermodynamics, which elaborates on internal energy conservation.
• Applying thermodynamics ensures that one can predict reaction spontaneity by calculating changes in enthalpy, entropy, and Gibbs free energy.

In the context of our discussed exercise, thermodynamics illustrates how the calculated enthalpy change provides insights into reaction energetics. By linking different enthalpic paths to achieve the same results, it demonstrates the unyielding consistency of energy transfer principles across chemical processes.