Problem 93 - Chemistry Matter and Change

Question

Use Hess' law and the following thermochemical equations to produce the thermochemical equation for the reaction \(\mathrm{C}(\mathrm{s},\) diamond) \(\rightarrow \mathrm{C}(\mathrm{s},\) graphite).What is \(\Delta H\) for the reaction? $$ \begin{array}{ll}{\text { a. } \mathrm{C}(\mathrm{s}, \text { graphite })+\mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{CO}_{2}(\mathrm{g})} & {\Delta H=-394 \mathrm{kJ}} \\ {\text { b. } \mathrm{C}(\mathrm{s}, \text { diamond })+\mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{CO}_{2}(\mathrm{g})} & {\Delta H=-396 \mathrm{kJ}}\end{array} $$

Step-by-Step Solution

Answer

\(\Delta H = -2 \text{kJ}\) for the reaction \(\mathrm{C}(\mathrm{s}, \text{diamond}) \rightarrow \mathrm{C}(\mathrm{s}, \text{graphite})\).

Step 1: Write the Target Reaction

Identify the desired reaction, which in this case is \(\mathrm{C}(\mathrm{s}, \text{diamond}) \rightarrow \mathrm{C}(\mathrm{s}, \text{graphite})\). This is the reaction for which we need to find \(\Delta H\).

Step 2: Analyze Given Reactions

We have two given reactions: 1. \(\mathrm{C}(\mathrm{s}, \text{graphite}) + \mathrm{O}_2(\mathrm{g}) \rightarrow \mathrm{CO}_2(\mathrm{g})\) with \(\Delta H = -394 \text{kJ}\).2. \(\mathrm{C}(\mathrm{s}, \text{diamond}) + \mathrm{O}_2(\mathrm{g}) \rightarrow \mathrm{CO}_2(\mathrm{g})\) with \(\Delta H = -396 \text{kJ}\).

Step 3: Apply Hess's Law

Using Hess's Law, rearrange the given reactions to derive the target reaction. Hess's law states that the total enthalpy change for a reaction is the sum of the enthalpy changes for each step.

Step 4: Invert and Add Reactions

Invert the first reaction: \(\mathrm{CO}_2(\mathrm{g}) \rightarrow \mathrm{C}(\mathrm{s}, \text{graphite}) + \mathrm{O}_2(\mathrm{g})\), changing \(\Delta H\) to \(+394 \text{kJ}\). Add this inverted reaction to the second direct reaction: 1. \(\mathrm{CO}_2(\mathrm{g}) \rightarrow \mathrm{C}(\mathrm{s}, \text{graphite}) + \mathrm{O}_2(\mathrm{g})\) with \(\Delta H = +394 \text{kJ}\)2. \(\mathrm{C}(\mathrm{s}, \text{diamond}) + \mathrm{O}_2(\mathrm{g}) \rightarrow \mathrm{CO}_2(\mathrm{g})\) with \(\Delta H = -396 \text{kJ}\).

Step 5: Derive Desired Reaction and Calculate \(\Delta H\)

Cancel out \(\mathrm{O}_2(\mathrm{g})\) and \(\mathrm{CO}_2(\mathrm{g})\) to obtain the target reaction \(\mathrm{C}(\mathrm{s}, \text{diamond}) \rightarrow \mathrm{C}(\mathrm{s}, \text{graphite})\).Calculate \(\Delta H\) for the target reaction: \[\Delta H = +394 \text{kJ} - 396 \text{kJ} = -2 \text{kJ}\].

Key Concepts

Thermochemical Equations

In chemistry, thermochemical equations serve as a bridge between chemical reactions and energy changes. They link the physical and chemical transformation of substances to enthalpy changes, which are the heat absorbed or released during a reaction under constant pressure. These equations not only represent reactants and products but also include the enthalpy change as part of the equation.
In a thermochemical equation, the enthalpy change (94H) is usually given in kilojoules (kJ) and indicates whether the reaction is exothermic or endothermic. An exothermic reaction releases heat, and 94H has a negative value. Conversely, an endothermic reaction absorbs heat, making 94H positive.
For example, the thermochemical equation for graphite burning in oxygen is:

• 94H = -394 ext{kJ}

This tells us that 394 kJ of heat are released when graphite converts to carbon dioxide. Thermochemical equations help in understanding and calculating energy changes in chemical transformations, guided by principles like Hess's Law.

Enthalpy Change (ΔH)

Enthalpy change is a concept that represents the amount of heat exchanged in a chemical reaction at constant pressure. This concept is vital in understanding how energy transformations occur during chemical processes. It tells us if a reaction will release energy to its surroundings (exothermic) or absorb energy from its surroundings (endothermic).
Using Hess's Law, we can calculate 94H for reactions even when they aren't carried out directly. Hess's Law states that the total enthalpy change of a chemical reaction is the same regardless of the pathway it takes. This means 94H can be computed by summing the enthalpy changes of individual steps that lead to a reaction.
In our given exercise, Hess's Law enabled us to determine the 94H for the conversion of diamond to graphite. By rearranging and summing the enthalpy changes from known reactions, the enthalpy change for this conversion was found to be -2 ext{kJ}. This small but specific value tells us the energy difference between these two forms of carbon.

Carbon Allotropes (Diamond and Graphite)

Carbon is unique because of its ability to exist in different forms or allotropes, such as diamond and graphite. Both are made entirely of carbon atoms, but the arrangement of these atoms results in vastly different properties.
Diamond features a three-dimensional lattice where each carbon atom is tetrahedrally bonded to four others. This structure makes diamond extremely hard and a poor conductor of electricity. In contrast, graphite is composed of layers where carbon atoms are bonded in sheets of hexagonal arrays. These layers can slide over each other, making graphite soft and slippery. It also conducts electricity due to the mobility of electrons between the layers.
The transition between these allotropes involves a small enthalpy change because they are forms of the same element. In the exercise, this transition was calculated to have an 94H of -2 ext{kJ}, indicating a slight energetic preference for the graphite form under standard conditions. Understanding carbon allotropes gives insight into how physical properties can vary remarkably with atomic structure.