Since their discovery in 1985, fullerenes have received the attention of many chemical researchers. Kolesov et al. reported the standard enthalpy of combustion and of formation of crystalline \(\mathrm{C}_{60}\) based on calorimetric measurements (V.P. Kolesov, S.M. Pimenova, V.K. Pavlovich, N.B. Tamm, and A.A. Kurskaya, \(J\). Chem. Thermodynamics \(\mathbf{2 8}, 1121(1996)\) ). In one of their runs, they found the standard specific internal energy of combustion to be \(-36.0334 \mathrm{~kJ} \mathrm{~g}^{-1}\) at \(298.15 \mathrm{~K}\) Compute \(\Delta_{\mathrm{c}} H^{\Theta}\) and \(\Delta_{\mathrm{f}} H^{\Theta}\) of \(\mathrm{C}_{60}\)

The standard enthalpy of combustion (Δ_cH^Θ) is a fundamental thermodynamic quantity representing the heat released when one mole of a substance combusts completely with oxygen under standard conditions (usually at 1 atm pressure and a reference temperature of 298.15 K). Essentially, it tells us how much energy you can get from burning a substance.

For instance, in the combustion of fullerene C60, the reaction would typically involve C60 reacting with O2 to form CO2. Calculating the standard enthalpy of combustion for C60 requires knowing the molar mass of the molecule—which you obtain by counting the number of carbon atoms and multiplying by the atomic weight of carbon—and the specific internal energy of combustion provided per gram. Afterward, you must convert this value to a per mole basis as illustrated in the exercise solution, using the molar mass calculated.

The standard enthalpy of formation (Δ_fH^Θ) indicates the heat change associated with the formation of one mole of a compound from its elements in their most stable forms at standard conditions. For pure elements like graphite (the most stable form of carbon), the standard enthalpy of formation is by definition zero, as elements are considered to be formed from themselves.

Calculating the standard enthalpy of formation for a compound like C60 involves using Hess's Law, which states that the total enthalpy change for a chemical reaction is the same, no matter how the reaction is carried out in steps. So, you would use the enthalpy changes from the combustion of both graphite and C60 to determine the enthalpy of formation for C60. This process requires a solid understanding of chemical equations and stoichiometry to ensure the correct application of Hess's Law.

Calorimetry is a technique used to measure the amount of heat involved in a chemical reaction or a physical change. This measurement is crucial for determining thermodynamic properties like enthalpy changes. A calorimeter is an insulated device that minimizes energy exchange with its environment, ensuring that the heat measured is solely due to the reaction occurring inside.

In the context of fullerenes and their enthalpy calculations, calorimetric measurements are taken to precisely determine the heat released during the combustion of C60. The specific internal energy of combustion provides an insight into the energy change on a per gram basis, which can then be extrapolated to a per mole basis to find the standard enthalpy of combustion, a key step exemplified in the specific exercise provided.

Molar mass calculation is an essential step in many chemical computations and involves determining the mass of one mole of a substance. The molar mass (usually expressed in grams per mole, g/mol) is calculated by adding up the atomic masses of all the atoms present in one molecule of the substance. The atomic mass of an element is listed in the periodic table and represents the average mass of the atoms of that element, accounting for the various isotopes and their abundances.

For fullerene C60, with 60 carbon atoms, the calculation is straightforward: multiply the atomic mass of carbon by 60. Knowing the molar mass is critical for converting per gram measurements, like the specific internal energy of combustion given in the exercise, to a per mole basis, which is more useful for stoichiometric calculations and understanding the energy content of a substance.