Problem 93 - Chemistry The Science in Context

Question

Use the following data to calculate the enthalpy of formation of \(\mathrm{NO}_{2} \mathrm{Cl}\) from \(\mathrm{N}_{2}, \mathrm{O}_{2},\) and \(\mathrm{Cl}_{2}\) $$\begin{aligned} \mathrm{NO}_{2} \mathrm{Cl}(g) \rightarrow \mathrm{NO}_{2}(g)+\frac{1}{2} \mathrm{Cl}_{2}(g) & \Delta H_{\mathrm{rxn}}^{\circ}=+20.6 \mathrm{kJ} \\ \frac{1}{2} \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightarrow \mathrm{NO}_{2}(g) & \Delta H_{f}^{\circ}=+33.2 \mathrm{kJ} \\ \frac{1}{2} \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g)+\frac{1}{2} \mathrm{Cl}_{2}(g) \rightarrow \mathrm{NO}_{2} \mathrm{Cl}(g) & \Delta H_{f}^{\circ}=? \end{aligned}$$

Step-by-Step Solution

Answer

Question: Calculate the enthalpy of formation of NO₂Cl from N₂, O₂, and Cl₂. Answer: The enthalpy of formation of NO₂Cl from N₂, O₂, and Cl₂ is -12.6 kJ.

Step 1: Identify the target reaction

We want to find the enthalpy of formation for the following reaction: ½ N₂(g) + O₂(g) + ½ Cl₂(g) → NO₂Cl(g)

Step 2: Rearrange the given reactions to follow Hess's Law

We want the target reaction to equal a combination of the given reactions: (1) NO₂Cl(g) → NO₂(g) + ½ Cl₂(g), ΔH⁰(1) = +20.6 kJ (2) ½ N₂(g) + O₂(g) → NO₂(g), ΔH_f⁰(2)= +33.2 kJ We want to achieve: Target reaction: ½ N₂(g) + O₂(g) + ½ Cl₂(g) → NO₂Cl(g) Rearrange reaction (1) by reversing it and then adding it to reaction (2): (NO₂(g) + ½ Cl₂(g)) + (½ N₂(g) + O₂(g) → NO₂(g)) = ½ N₂(g) + O₂(g) + ½ Cl₂(g) → NO₂Cl(g)

Step 3: Apply Hess's Law to calculate the enthalpy change for the target reaction

Hess's Law states that ΔH⁰(target reaction) = ΔH⁰(1) - ΔH_f⁰(2) Substitute the given values: ΔH⁰(target reaction) = (+20.6 kJ) - (+33.2 kJ) ΔH⁰(target reaction) = -12.6 kJ The enthalpy of formation of NO₂Cl from N₂, O₂, and Cl₂ is -12.6 kJ.

Key Concepts

Hess's Law

Understanding Hess's Law is like piecing together a puzzle — it helps us determine enthalpy changes in reactions where direct measurement is not possible. This fundamental concept in chemical thermodynamics postulates that the total enthalpy change during a chemical reaction is the same regardless of the number of steps in which the reaction occurs. In essence, whether you take a direct route or a scenic path to your destination, the total distance traveled remains constant.

Hess's Law allows us to use known enthalpy changes of certain chemical reactions to calculate unknown enthalpies. By ensuring that the starting and ending materials are the same (no matter the path taken), we can add or subtract known reaction enthalpies to find the unknown one. The solution to the enthalpy of formation example uses this law by manipulating the given reactions to find the desired reaction's enthalpy.

Stoichiometry

Stoichiometry operates as the mathematical sidekick of chemistry, providing the calculations necessary to balance chemical reactions. It involves the quantitative relationships between the reactants and products in chemical processes. In our example, the coefficients (like the 1/2 in front of \(N_2\) and \(Cl_2\)) are crucial in balancing the equations according to the conservation of mass.

Using stoichiometry, we can quantitatively relate the quantities of reactants and products. It's about understanding the ‘recipe’ that a chemical reaction follows, ensuring that we can predict how much of each substance will partake in the reaction and what amounts of new substances will emerge.

Chemical Thermodynamics

Chemical thermodynamics is the branch of chemistry that deals with the energy changes accompanying chemical reactions. It's concerned with the concepts of enthalpy, entropy, and free energy, providing an understanding of the spontaneity of reactions and the balance between heat and work in chemical processes. These principles are like the rules of a game that dictate how substances react under different temperatures and pressures, and with different amounts of energy.

In the enthalpy of formation calculation, chemical thermodynamics guides us to understand the heat transfer during the creation of a compound from its basic elements. We explore how energy is absorbed or released when bonds are broken and formed, and chemical thermodynamics equips us with knowledge of the ‘before’ and ‘after’ states of energy in a reaction.

Enthalpy Change

Enthalpy change is a measure of the heat change at constant pressure during a chemical reaction and is symbolized as \(\Delta H\). It's a crucial concept in studying reaction energetics because it tells us whether a reaction is giving off energy (exothermic) or absorbing energy (endothermic). In our textbook problem, we're focused on the enthalpy of formation, which is a specific type of enthalpy change. It represents the heat change when one mole of a compound is formed from its elements in their standard states.

To put it simply, picture a chemical reaction as a cooking process. Enthalpy change helps us figure out whether the process will heat up or cool down the kitchen. By calculating the enthalpy of formation, we're essentially measuring how much heat the reaction would give off or absorb if we were to put together the ingredients (elements) to make the final dish (compound).