Question

Use Equations a and b to determine ?H for the following reaction. \(2 {CO}({g})+2 {NO}({g}) \rightarrow 2 {CO}_{2}({g})+{N}_{2}({g}) \Delta H=?\) a. \(2 {CO}({g})+{O}_{2}({g}) \rightarrow 2 {CO}_{2}(\\}) \Delta H=-566.0 {kJ}\) b. \(N_{2}(g)+O_{2}(g) \rightarrow 2 N O(g) \Delta H=-180.6 {kJ}\)

Short answer

The enthalpy change for the given reaction, \(2 CO(g) + 2 NO(g) \rightarrow 2 CO_2(g) + N_2(g)\), is \(\Delta H = -385.4\: kJ\).

Step-by-step solution

We are given the following reaction to find the ∆H: \(2 CO(g) + 2 NO(g) \rightarrow 2 CO_2(g) + N_2(g)\) #Step 2: Manipulate given reactions to match the target reaction#

First, let's find the required manipulation for each given reaction: Reaction (a): \(2 CO(g) + O_2(g) \rightarrow 2 CO_2(g) \qquad \Delta H = -566.0\: kJ\) This reaction already has the correct stoichiometry for the CO and CO₂ in the target reaction. No manipulation needed. Reaction (b): \(N_2(g) + O_2(g) \rightarrow 2 NO(g) \qquad \Delta H = -180.6\: kJ\) To match the stoichiometry of the given target reaction, we need to flip the reaction so that the 2 NO are on the reactant side: \(2 NO(g) \rightarrow N_2(g) + O_2(g) \qquad \Delta H = 180.6\: kJ\) #Step 3: Add manipulated reactions#

Now we will add both manipulated reactions to obtain the target reaction: \(2 CO(g) + O_2(g) \rightarrow 2 CO_2(g)\) \(\qquad \Delta H_1 = -566.0\: kJ\) \(2 NO(g) \rightarrow N_2(g) + O_2(g)\) \(\qquad \Delta H_2= 180.6\: kJ\) ----------------------------------------------- \(2 CO (g) + 2 NO (g) \rightarrow 2 CO_2(g) + N_2(g)\) Notice that the \(O_2(g)\) terms cancel out. #Step 4: Calculate the enthalpy change for the target reaction#

According to Hess's Law, the enthalpy change of the target reaction is the sum of the enthalpy changes of each individual reaction: \(\Delta H_{target} = \Delta H_1 + \Delta H_2\) We have: \(\Delta H_{target} = -566.0\, kJ + 180.6\, kJ\) \(\Delta H_{target} = -385.4\, kJ\) So the enthalpy change for the given reaction is: \(2 CO(g) + 2 NO(g) \rightarrow 2 CO_2(g) + N_2(g)\:\: \Delta H = -385.4\: kJ\)

Key concepts

Hess's Law

Understanding Hess's Law is key to mastering enthalpy change calculations in chemical reactions. It states that the total enthalpy change for a chemical reaction is the same, no matter how it is carried out, as long as the initial and final conditions are the same. This law relies on the idea that enthalpy is a state function, which means that its value depends only on the current state of the system and not on the path taken to reach that state.

When solving problems using Hess's Law, we can break down complex reactions into simpler steps whose enthalpy changes are known. By manipulating these steps, such as reversing the direction or changing the coefficients, and then summing the enthalpy changes, we can determine the overall enthalpy change for the reaction. The magic of Hess's Law is that it allows us to indirectly find the enthalpy change of reactions where direct measurement might be difficult or impossible. It's a powerful tool for chemists, allowing the puzzle pieces of known reactions to be assembled in a way that reveals the enthalpy change of a desired reaction.

Chemical Reactions

Let's dive into the basics of chemical reactions. These are processes where substances known as reactants transform into new substances called products. These changes involve breaking and forming chemical bonds, which can either absorb heat (endothermic) or release heat (exothermic). The change in the heat content of the system during this process is quantified as the enthalpy change, represented by \( \Delta H \).

An exothermic reaction, like our example, releases heat and typically has a negative \( \Delta H \) value, indicating that energy is being released to the surroundings. Conversely, an endothermic reaction would absorb heat, reflected in a positive \( \Delta H \). Recognizing these types of reactions and their enthalpy changes is crucial for scientists and engineers to design processes, from creating new materials to developing sustainable energy sources.

Stoichiometry

Moving on to stoichiometry, it focuses on the quantitative relationships between the reactants and products in a chemical reaction. These relationships are dictated by the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction. Therefore, the atoms that start as reactants must all be accounted for in the products.

The coefficients in a balanced chemical equation tell us in what proportions the reactants combine and the products form. Using stoichiometry, we can calculate how much of each reactant is needed to create a certain amount of product or predict how much product will result from given amounts of reactants. It's a bit like following a precise recipe in cooking, where the ingredients need to be mixed in correct proportions to get the desired outcome. In the context of the enigma we tackled, aligning the coefficients correctly was crucial to applying Hess's Law accurately and arriving at the correct calculation of the enthalpy change.