Problem 88 - Chemistry A Molecular Approach

Question

Use standard enthalpies of formation to calculate \(\Delta H_{\mathrm{rxn}}^{\circ}\) for each reaction. a. \(2 \mathrm{H}_{2} \mathrm{~S}(g)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(I)+2 \mathrm{SO}_{2}(g)\) b. \(\mathrm{SO}_{2}(g)+{ }^{1} /{ }_{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{SO}_{3}(g)\) c. \(\mathrm{C}(s)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{CO}(g)+\mathrm{H}_{2}(g)\) d. \(\mathrm{N}_{2} \mathrm{O}_{4}(g)+4 \mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)\)

Step-by-Step Solution

Answer

To find \(\Delta H_{\mathrm{rxn}}^\circ\) for each reaction, apply the formula \(\Delta H_{\mathrm{rxn}}^\circ = \sum\Delta H_{\mathrm{f, products}}^\circ - \sum\Delta H_{\mathrm{f, reactants}}^\circ\), inserting the standard enthalpies of formation for all reactants and products. Perform the calculation for each reaction.

Step 1 - Write down the enthalpy change of the reaction formula

The enthalpy change for a reaction, \(\Delta H_{\mathrm{rxn}}^\circ\), can be calculated using the formula: \[\Delta H_{\mathrm{rxn}}^\circ = \sum\Delta H_{\mathrm{f, products}}^\circ - \sum\Delta H_{\mathrm{f, reactants}}^\circ\] where \(\Delta H_{\mathrm{f}}^\circ\) represents the standard enthalpies of formation of the reactants and products.

Step 2 - Find the standard enthalpies of formation

Look up the standard enthalpies of formation for all reactants and products involved in each reaction from a reliable source (such as a chemistry textbook or database).

Step 3 - Apply the enthalpy change of reaction formula to each reaction

For each reaction, insert the relevant standard enthalpies of formation into the equation provided in Step 1, and perform the arithmetic to calculate \(\Delta H_{\mathrm{rxn}}^\circ\).

Step 4 - Calculate for Reaction a

Apply the formula to the first reaction: \[\Delta H_{\mathrm{rxn}}^\circ (a) = [2\Delta H_{\mathrm{f, H2O(l)}} + 2\Delta H_{\mathrm{f, SO2(g)}} ] - [2\Delta H_{\mathrm{f, H2S(g)}} + 3\Delta H_{\mathrm{f, O2(g)}}]\] Note: The standard enthalpy of formation for an element in its standard state, such as \(\mathrm{O2(g)}\), is zero.

Step 5 - Calculate for Reaction b

Apply the formula to the second reaction: \[\Delta H_{\mathrm{rxn}}^\circ (b) = [\Delta H_{\mathrm{f, SO3(g)}}] - [\Delta H_{\mathrm{f, SO2(g)}} + \frac{1}{2}\Delta H_{\mathrm{f, O2(g)}}]\]

Step 6 - Calculate for Reaction c

Apply the formula to the third reaction: \[\Delta H_{\mathrm{rxn}}^\circ (c) = [\Delta H_{\mathrm{f, CO(g)}} + \Delta H_{\mathrm{f, H2(g)}}] - [\Delta H_{\mathrm{f, Carbon(s)}} + \Delta H_{\mathrm{f, H2O(g)}}]\]

Step 7 - Calculate for Reaction d

Apply the formula to the fourth reaction: \[\Delta H_{\mathrm{rxn}}^\circ (d) = [\Delta H_{\mathrm{f, N2(g)}} + 4\Delta H_{\mathrm{f, H2O(g)}}] - [\Delta H_{\mathrm{f, N2O4(g)}} + 4\Delta H_{\mathrm{f, H2(g)}}]\]

Step 8 - Perform the calculations

Substitute standard enthalpies of formation values obtained in Step 2 into the equations from Steps 4-7 to find the enthalpy change for each reaction.

Key Concepts

Standard Enthalpies of Formation

Standard enthalpies of formation, denoted as \(\Delta H_{\mathrm{f}}^\circ\), are a fundamental concept in chemical thermodynamics. Imagine it as the thermal 'price tag' for creating a compound from its elements in their most stable form. One key point is that, for elements in their standard states, like oxygen gas (\(O_2(g)\)), the enthalpy of formation is zero because no creation or breaking of bonds is required. It is crucial to understand that the values are measured under standard conditions, which is usually 1 atmosphere (atm) of pressure and a temperature of 298 K (25 degrees Celsius).

When looking up these values in textbooks or databases, students are essentially finding out the amount of heat energy absorbed or released when 1 mole of a compound is formed from its elements. For instance, the formation of water from hydrogen and oxygen gases releases energy, hence its enthalpy of formation has a negative value. These numbers become the building blocks for calculating the heat of reactions in later steps.

Thermochemical Calculations

Thermochemical calculations allow us to predict whether a reaction will release heat to its surroundings or absorb it. This understanding helps in both academic research and industrial applications where energy changes are of interest. To perform these calculations, we utilize standard enthalpies of formation along with stoichiometry – the quantitative relationship between reactants and products in a chemical reaction.

In practice, this requires careful bookkeeping: you determine the amount of heat required to form the products and subtract the amount needed to break up the reactants. Positive results suggest endothermic reactions where the system absorbs heat, and negative values indicate exothermic reactions that release heat. By employing the principles of conservation of energy and mass, thermochemical calculations keep the energy balance in check during chemical transformations.

Enthalpy Change Calculation

The calculation of enthalpy change, \(\Delta H_{\mathrm{rxn}}^\circ\), ties directly into the heart of problem-solving in chemical thermodynamics. The formula \[\Delta H_{\mathrm{rxn}}^\circ = \sum\Delta H_{\mathrm{f, products}}^\circ - \sum\Delta H_{\mathrm{f, reactants}}^\circ\] expressed in the solution is straightforward but powerful, guiding students through the process of quantifying the heat change for a given reaction.

This method hinges on accurate insertion of standard enthalpies of formation into their respective places for reactants and products, followed by attentive arithmetic. The key improvement advice here would be to meticulously list and verify the standard enthalpies for each species involved in the reaction to minimize potential errors in the final enthalpy change calculations. It's also essential for students to remember that coefficients in balanced reactions must be applied to the enthalpies of formation, reflecting the quantities involved.

Chemical Thermodynamics

Chemical thermodynamics provides the broader framework for understanding how energy is transformed in chemical processes. It is essential for students to recognize that it's not just about figures and formulas; it's the science that helps us analyze the flow of energy in the universe at the molecular level. Core concepts such as enthalpy, entropy, and Gibbs free energy come into play.

When a chemical reaction occurs, there's energy variation in the form of heat, which is where enthalpy change becomes relevant. But it's also about the disorder (entropy) and whether a reaction can occur spontaneously (Gibbs free energy). Providing real-world examples, like the role of thermodynamics in designing engines, refrigerators, or even understanding biological systems, can help in cementing the relevance of these abstract concepts to tangible applications.