Problem 21 - Chemistry: An Atoms-Focused Approach

Question

Using data in Appendix \(4,\) calculate \(\Delta H^{-}\) for the reaction $$2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}_{2}(g)$$

Step-by-Step Solution

Answer

Question: Calculate the enthalpy change, \(\Delta H^{-}\), for the reaction given below using the enthalpy of formations provided in Appendix 4: $$2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}_{2}(g)$$ Answer: The enthalpy change, \(\Delta H^{-}\), for the given reaction is approximately \(-114.14\text{ kJ/mol}\).

Step 1: Write down the formation enthalpy values for the involved compounds

From Appendix 4, we have the following formation enthalpy values: 1. Formation enthalpy for \(\mathrm{NO}(g)\): \(\Delta H_f^\circ (\text{NO})\) 2. Formation enthalpy for \(\mathrm{O}_{2}(g)\): \(\Delta H_f^\circ (\text{O}_2)\) 3. Formation enthalpy for \(\mathrm{NO}_{2}(g)\): \(\Delta H_f^\circ (\text{NO}_2)\) Since \(\mathrm{O}_{2}(g)\) is an elemental compound, its formation enthalpy would be zero, i.e., \(\Delta H_f^\circ (\text{O}_2) = 0\).

Step 2: Use the enthalpy change formula to calculate the enthalpy change of reaction

We know that the enthalpy change of reaction is given by the formula: $$\Delta H^{-} = \sum \text{(Products)} - \sum \text{(Reactants)}$$ For the reaction: $$2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}_{2}(g)$$ Plugging in the values of formation enthalpies from Step 1, we get: $$\Delta H^{-} = 2\Delta H_f^\circ (\text{NO}_2) - \left[2\Delta H_f^\circ (\text{NO}) + \Delta H_f^\circ (\text{O}_2)\right]$$ Since \(\Delta H_f^\circ (\text{O}_2) = 0\), the equation becomes, $$\Delta H^{-} = 2\Delta H_f^\circ (\text{NO}_2) - 2\Delta H_f^\circ (\text{NO})$$

Step 3: Plug in the values from Appendix 4 and calculate the enthalpy change

Insert the actual values of formation enthalpies for \(\text{NO}\) and \(\text{NO}_2\) from Appendix 4: \(\Delta H_f^\circ (\text{NO})=90.25 \text{ kJ/mol}\) \(\Delta H_f^\circ (\text{NO}_2})=33.18 \text{ kJ/mol}\) The enthalpy change of reaction is then: $$\Delta H^{-} = 2(33.18 \text{ kJ/mol}) - 2(90.25 \text{ kJ/mol})$$ $$\Delta H^{-} = 66.36 \text{ kJ/mol} - 180.50 \text{ kJ/mol}$$ $$\Delta H^{-} = -114.14 \text{ kJ/mol}$$ The enthalpy change, \(\Delta H^{-}\), for the given reaction is approximately \(-114.14\text{ kJ/mol}\).

Key Concepts

Formation Enthalpy

Formation enthalpy, also known as the standard enthalpy of formation, is a key concept in chemistry. It refers to the change in enthalpy when one mole of a compound is formed from its elements in their standard states. Standard states mean the form in which the element is stable at 1 bar of pressure and a specified temperature, often 298 K. This concept is vital because it allows chemists to calculate the heat changes involved in reactions.
When looking at a compound like \( ext{NO}_2\), the formation enthalpy gives insight into the energy needed to form it from nitrogen and oxygen, its elemental components. One important thing to remember is that for any elemental form (like \( ext{O}_2\) gas) the standard formation enthalpy is zero. This simplifies calculations significantly. Here's how it works:

• Formation enthalpies are usually given in units of \( ext{kJ/mol}\).
• If a reaction involves multiple moles of a compound, their formation enthalpies are multiplied by the number of moles in the balanced equation.

Knowing the formation enthalpies of the reactants and products allows for determining the overall enthalpy change of a reaction, helping predict if energy is absorbed or released.

Chemical Reaction

Chemical reactions involve the transformation of one set of chemical substances into another. They are characterized by reactants on the left side and products on the right side of a chemical equation. Understanding these reactions is fundamental in chemistry as they describe how substances interact and change.
The specific reaction we are considering is \(2 \text{NO}(g) + \text{O}_2(g) \rightarrow 2 \text{NO}_2(g)\). Here, nitric oxide (NO) and oxygen (O₂) combine to form nitrogen dioxide (NO₂). This equation must always be balanced, which means the number of atoms for each element must be equal on both the reactant and product sides.

• Balancing ensures conservation of mass and proper stoichiometry.
• Coefficients (like the '2' in front of NO and NO₂) indicate the moles involved, crucial for calculating reaction enthalpies.

Balancing and understanding these transformations allow scientists to predict effects like energy changes and matter transformation.

Thermodynamics

Thermodynamics is the branch of science that deals with the relationships and conversions between heat and other forms of energy. It provides principles and equations that govern chemical reactions and energy changes. One of its primary concerns is studying enthalpy (\( H \)), which represents the heat content of a system.
In chemical reactions, determining enthalpy changes is crucial. This change can reveal whether a reaction is exothermic (releases heat) or endothermic (absorbs heat). In our example reaction, the calculation showed it was exothermic because \( \Delta H^- \) is negative. This means energy is released as heat, warming the surroundings.

• Thermodynamics uses laws to describe how energy enters, leaves, or transforms within reactions.
• The first and second laws are extensively applied; the first law relates to energy conservation while the second law addresses entropy.

Understanding thermodynamics is essential for harnessing energy changes in real-world applications and predicting reaction behavior.

Reaction Enthalpies

Reaction enthalpies refer to the heat changes accompanying a chemical reaction. This is often expressed as \( \Delta H^{-} \), representing the difference in enthalpy between the products and reactants. Calculating reaction enthalpies helps understand the energy profile of a reaction.
The formula used for calculating the enthalpy change of a reaction is \[\Delta H^{-} = \sum \text{(Products)} - \sum \text{(Reactants)}\]This expression utilizes the formation enthalpies of the substances involved in the reaction. In our example, it helps determine how much energy is released when NO reacts with O₂ to form NO₂.

• Products' formation enthalpies are added together.
• Reactants' formation enthalpies are subtracted from the products' total.

The result gives insight into the reaction's energy efficiency and direction, aiding in designing industrial chemical processes and understanding natural ones.