Question

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

Short answer

Thus, the thermochemical equation for the reaction \(C(s, \text { diamond }) \rightarrow C(s, \text { graphite })\) is: \[C(s, \text { diamond }) \rightarrow C(s, \text { graphite }) \quad \Delta H = -2 \mathrm{kJ}\]

Step-by-step solution

Rearrange equation a.

We want our target equation to look like this: \[C(s, \text { diamond }) \rightarrow C(s, \text { graphite })\] Take equation a and reverse it so that CO2 is on the left side and graphite is on the right side: \[CO_{2}(g) \rightarrow C(s, \text { graphite })+O_{2}(g) \quad \Delta H=394 \mathrm{kJ}\]

Rearrange equation b.

No further changes are needed for equation b, as diamond is already on the left side and CO2 is on the right side: \[C(s, \text { diamond })+O_{2}(g) \rightarrow CO_{2}(g) \quad \Delta H=-396 \mathrm{kJ}\]

Cancel out common terms.

In order to use Hess's Law, we need to cancel out the common terms in our 2 equations. Note that both equations have \(O_2(g)\) and \(CO_2(g)\). We subtract the first equation from the second equation, \[(C(s, \text { diamond })+O_{2}(g) \rightarrow CO_{2}(g)) - (CO_{2}(g) \rightarrow C(s, \text { graphite })+O_{2}(g))\] to get our desired equation: \[C(s, \text { diamond }) \rightarrow C(s, \text { graphite })\]

Calculate the enthalpy change, \(\Delta H\).

Now we apply Hess's Law to find the \(\Delta H\) for the desired reaction. We simply subtract the enthalpy change of reversed equation a from equation b: \[\Delta H_{b} - \Delta H_{a} = -396 \mathrm{kJ} - 394 \mathrm{kJ} = -2 \mathrm{kJ}\] So, the enthalpy change for the reaction is: \[\Delta H = -2 \mathrm{kJ}\]

Key concepts

Understanding Enthalpy Change

In the realm of chemistry, enthalpy change (\(\Delta H\)) is an important concept that refers to the heat energy absorbed or released during a chemical reaction at constant pressure. It helps us predict whether a reaction is endothermic or exothermic. An exothermic reaction means heat is released, resulting in a negative \(\Delta H\), whereas an endothermic reaction means heat is absorbed, leading to a positive \(\Delta H\).In our given exercise, the transformation from diamond to graphite involves calculating the enthalpy change. By using Hess's Law, which states that the total enthalpy change is the same no matter how the reaction occurs, we can find \(\Delta H\) by rearranging the given equations to achieve the equation for the desired reaction. These rearrangements help cancel out intermediate substances, focusing only on the initial and final states of the reaction.Thus, the enthalpy change for converting one allotrope of carbon — diamond — into another — graphite — is calculated as \( -2 \, \text{kJ}\). This negative value indicates that the conversion is exothermic, releasing heat energy.

Unpacking Thermochemical Equations

Thermochemical equations are a type of chemical equation that also include the enthalpy change of the reaction, represented as \(\Delta H\). These equations provide detailed information about the heat changes happening during the reaction.In our example, we have two thermochemical equations:

• The combustion of graphite: \[C(s, \text{ graphite })+\mathrm{O}_2(g) \rightarrow \mathrm{CO}_2(g) \quad \Delta H=-394 \, \text{ kJ} \]
• The combustion of diamond: \[C(s, \text{ diamond })+\mathrm{O}_2(g) \rightarrow \mathrm{CO}_2(g) \quad \Delta H=-396 \, \text{ kJ} \]

These equations were used in conjunction with Hess's Law to deduce the enthalpy change for the transformation from diamond to graphite.By reversing and combining these equations, as illustrated in the step-by-step solution, we can eliminate intermediate steps and directly connect the reactants (diamond) with the products (graphite), thus calculating the desired enthalpy change.

Exploring Carbon Allotropes

Carbon has several allotropes. Allotropes are different structural forms of the same element, and they have different physical and chemical properties. The main allotropes of carbon are graphite, diamond, and a lesser-known form, graphene.Diamonds are transparent and highly prized for their aesthetic value, having a strong lattice structure. They are very hard, making them useful in industrial applications as well. Graphite, on the other hand, is opaque and has a slippery feel, often used as a lubricant or in pencils. Graphite's layers can slide over one another due to weak van der Waals forces, giving it its unique properties.In our example, the thermochemical equation for the transformation of diamond to graphite highlights the conversion between these two allotropes. This reaction involves structural breaking and reforming, where diamond's \(sp^3\) hybridized carbon atoms rearrange into graphite's \(sp^2\) planar layers. Understanding these forms elucidates why the transformation releases energy and why these allotropes have distinct uses in the real world.