Question

Use standard enthalpies of formation to calculate \(\Delta H_{\mathrm{rxn}}^{\circ}\) for each reaction. \begin{equation}\begin{array}{l}{\text { a. } \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)} \\ {\text { b. } \mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g)} \\ {\text { c. } 3 \mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{HNO}_{3}(a q)+\mathrm{NO}(g)} \\ {\text { d. } \mathrm{Cr}_{2} \mathrm{O}_{3}(s)+3 \mathrm{CO}(g) \longrightarrow 2 \mathrm{Cr}(s)+3 \mathrm{CO}_{2}(g)}\end{array} \end{equation}

Short answer

To find \(\Delta H_{\mathrm{rxn}}^\circ\) for each reaction, calculate the difference between the sum of the standard enthalpies of formation of the reactants and the products using their respective standard enthalpies of formation.

Step-by-step solution

Explanation of the Process

To calculate the standard enthalpy of reaction (\(\Delta H_{\mathrm{rxn}}^\circ\)) for each chemical reaction, we use the standard enthalpies of formation (\(\Delta H_{\mathrm{f}}^\circ\)) of the reactants and products. The standard enthalpy of reaction can be determined by summing the standard enthalpies of formation of the products and then subtracting the sum of the standard enthalpies of formation of the reactants using the formula: \[\Delta H_{\mathrm{rxn}}^\circ = \sum (\Delta H_{\mathrm{f}}^\circ \text{ of products}) - \sum (\Delta H_{\mathrm{f}}^\circ \text{ of reactants})\].

Calculate \(\Delta H_{\mathrm{rxn}}^\circ\) for reaction (a)

Use the standard enthalpies of formation for each species in reaction (a) to calculate the enthalpy change: \[\Delta H_{\mathrm{rxn}}^\circ = \Delta H_{\mathrm{f}}^\circ(\mathrm{C}_{2}\mathrm{H}_{6}(g)) - (\Delta H_{\mathrm{f}}^\circ(\mathrm{C}_{2}\mathrm{H}_{4}(g)) + \Delta H_{\mathrm{f}}^\circ(\mathrm{H}_{2}(g)))\]. Since the standard enthalpy of formation for elemental substances in their standard states (like \(\mathrm{H}_{2}(g)\)) is zero, this term is not included if it applies.

Calculate \(\Delta H_{\mathrm{rxn}}^\circ\) for reaction (b)

Similar to reaction (a), calculate the enthalpy change for reaction (b) using the formula: \[\Delta H_{\mathrm{rxn}}^\circ = (\Delta H_{\mathrm{f}}^\circ(\mathrm{H}_{2}(g)) + \Delta H_{\mathrm{f}}^\circ(\mathrm{CO}_{2}(g))) - (\Delta H_{\mathrm{f}}^\circ(\mathrm{CO}(g)) + \Delta H_{\mathrm{f}}^\circ(\mathrm{H}_{2}\mathrm{O}(g)))\].

Calculate \(\Delta H_{\mathrm{rxn}}^\circ\) for reaction (c)

For reaction (c), the enthalpy change is: \[\Delta H_{\mathrm{rxn}}^\circ = (2 \Delta H_{\mathrm{f}}^\circ(\mathrm{HNO}_{3}(aq)) + \Delta H_{\mathrm{f}}^\circ(\mathrm{NO}(g))) - (3 \Delta H_{\mathrm{f}}^\circ(\mathrm{NO}_{2}(g)) + \Delta H_{\mathrm{f}}^\circ(\mathrm{H}_{2}\mathrm{O}(l)))\].

Calculate \(\Delta H_{\mathrm{rxn}}^\circ\) for reaction (d)

For reaction (d), apply the enthalpy change calculation: \[\Delta H_{\mathrm{rxn}}^\circ = (2 \Delta H_{\mathrm{f}}^\circ(\mathrm{Cr}(s)) + 3 \Delta H_{\mathrm{f}}^\circ(\mathrm{CO}_{2}(g))) - (\Delta H_{\mathrm{f}}^\circ(\mathrm{Cr}_{2}\mathrm{O}_{3}(s)) + 3 \Delta H_{\mathrm{f}}^\circ(\mathrm{CO}(g)))\]. Since \(\Delta H_{\mathrm{f}}^\circ\) is zero for \(\mathrm{Cr}(s)\) as an element in its standard state, it is not included in the calculation.

Key concepts

Enthalpy Change Calculation

Understanding the calculation of enthalpy change, denoted as \( \Delta H \), is crucial when examining chemical reactions. Enthalpy change refers to the heat absorbed or released during a chemical process at constant pressure, which is a fundamental concept in thermochemistry.

For enthalpy change calculations involving chemical reactions, we rely on the principle that enthalpy is a state function. This means that the total change in enthalpy depends only on the initial and final states of the system, not on the path taken. The standard enthalpy of formation, \( \Delta H_{\mathrm{f}}^\circ \), of a compound is the change in enthalpy when one mole of the compound is formed from its elements in their standard states.

The formula to calculate the standard enthalpy of reaction, \( \Delta H_{\mathrm{rxn}}^\circ \), is as follows:
\[\Delta H_{\mathrm{rxn}}^\circ = \sum (\Delta H_{\mathrm{f}}^\circ \text{ of products}) - \sum (\Delta H_{\mathrm{f}}^\circ \text{ of reactants})\]
This equation signifies that you sum up all the standard enthalpies of formation of the products and subtract the sum of the standard enthalpies of formation of the reactants. An important thing to remember is that the standard enthalpy of formation for any element in its standard state is zero. Therefore, elements in their standard state do not contribute to the calculation of the reaction enthalpy.

Chemical Reactions

Chemical reactions are the processes in which substances, known as reactants, transform into new substances called products. These reactions often involve changes in energy, and one of the primary types of energy changes is heat.

Types of Reactions

There are various types of chemical reactions, such as synthesis, decomposition, single-replacement, double-replacement, and combustion reactions. Each type has a specific pattern in terms of reactant interaction and product formation. For example:

• Synthesis reactions combine two or more simple substances to form a more complex compound.
• Combustion reactions typically involve a hydrocarbon reacting with oxygen to produce carbon dioxide and water.

Role of Enthalpy Change

The role of enthalpy change in these reactions is significant. It can tell us whether a reaction is exothermic (releases heat) or endothermic (absorbs heat). Enthalpy change provides insights into the energy required for reactants to transform into products and influences factors like reaction spontaneity and equilibrium.

Thermochemistry

Thermochemistry is the study of the heat involved in chemical reactions and physical transformations. It's a branch of thermodynamics, which looks at the relationships between heat, work, temperature, and energy.

In the context of chemical reactions, thermochemistry focuses on how heat transfer is associated with chemical changes. This involves the application of the first law of thermodynamics, which states that energy cannot be created or destroyed, only transformed.

Understanding Heat in Reactions

The amount of heat absorbed or released in a reaction at constant pressure is called enthalpy. When we measure the heat change directly related to the reactants and products at standard conditions (1 atm pressure and, typically, 298.15 K), we refer to standard enthalpy changes, such as \( \Delta H_{\mathrm{f}}^\circ \).

Thermochemical equations are a way to depict both the chemical reaction and the associated enthalpy change. They serve as a valuable tool for scientists and engineers to design processes, understand reaction mechanisms, and predict the energy efficiency of chemical transformations.