Problem 43 - Chemical Principles: The Quest for Insight

Question

The standard enthalpies of combustion of graphite and diamond are \(-393.51\) and \(-395.41 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}\), respectively. Calculate the change in molar enthalpy for the graphite \(\rightarrow\) diamond transition.

Step-by-Step Solution

Answer

The change in molar enthalpy for the transition from graphite to diamond is -1.90 kJ/mol.

Step 1: Identify the Known Values

We know the standard enthalpies of combustion for graphite and diamond, which are -393.51 kJ/mol and -395.41 kJ/mol respectively.

Step 2: Apply Hess's Law

Hess's Law states that the total enthalpy change for a chemical reaction is the same, no matter how it is carried out, as long as initial and final conditions are the same. In this case, we want to find the change in molar enthalpy for the transition, which can be thought of as the difference between the enthalpy of combustion of diamond and graphite.

Step 3: Calculate the Change in Molar Enthalpy

Subtract the standard molar enthalpy of combustion of graphite from that of diamond to find the change in enthalpy for the graphite to diamond transition: c(Diamond) - c(Graphite) = (-395.41 kJ/mol) - (-393.51 kJ/mol) = -1.90 kJ/mol.

Key Concepts

Standard Enthalpy of Combustion

The standard enthalpy of combustion is a measure of the energy released when one mole of a substance combusts completely with oxygen under standard conditions. It is typically expressed in kilojoules per mole (\( kJ/mol \)). This term is paramount for understanding chemical thermodynamics because it represents how much heat is given off during the combustion process of substances. For example, the standard enthalpies of combustion of graphite and diamond are \( -393.51 \ kJ/mol \) and \( -395.41 \ kJ/mol \) respectively, indicating that diamond releases slightly more energy upon complete combustion than graphite.

Students should note that these values are negative because combustion is an exothermic process where heat is released into the surrounding environment. This concept is crucial for calculating energy changes in chemical reactions, like the transition from graphite to diamond. Remember, the more negative the enthalpy of combustion, the more heat is released.

Hess's Law

When solving problems related to thermochemistry, Hess's Law can be an incredibly helpful guideline. It asserts that the total enthalpy change for a reaction is the same no matter how the process is conducted, provided it goes from a specific set of reactants to a specific set of products. This principle is used to calculate enthalpy changes of reactions that are difficult to measure directly. By using known enthalpy changes of related reactions, Hess's Law enables us to find unknown values with the help of simple arithmetic.

In application, if you're dealing with the enthalpy change for the graphite to diamond transition, you don't need to measure this directly. Instead, you can use the combustion enthalpies of both substances. By subtracting the standard enthalpy of combustion of graphite from that of diamond (\( -395.41 \ kJ/mol \) - \( -393.51 \ kJ/mol \)), you can find the enthalpy change for the reaction which turns out to be \( -1.90 \ kJ/mol \), indicating that the transition from graphite to diamond is slightly endothermic in nature.

Graphite to Diamond Transition

Transitioning from graphite to diamond is an example of an allotrope transition involving carbon, where both graphite and diamond are forms of pure carbon differing in structure. Graphite has a layered, planar structure while diamond forms a rigid lattice, making it one of the hardest materials. The conversion is accompanied by a change in enthalpy reflecting the difference in energy content and structural stability between the two.

The transition as a physical change involves overcoming significant energy barriers and usually requires high pressure and temperatures to occur naturally. In a laboratory or industrial setting, this process can be facilitated through various technological interventions. Calculating the enthalpy change provides insight into the energy requirement or release during this transition, essential for synthesizing diamonds. The marginal enthalpy change of \( -1.90 \ kJ/mol \) in the graphite to diamond conversion indicates that slightly more energy is stored in the diamond structure compared to graphite due to the more compact and ordered lattice.