Problem 118 - Chemistry The Science in Context

Question

Acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2}\left(\Delta H_{\mathrm{f}}^{\circ}=226.7 \mathrm{kJ} / \mathrm{mol}\right),\) and benzene, \(\mathrm{C}_{6} \mathrm{H}_{6}\left(\Delta H_{\mathrm{f}}^{\circ}=49.0 \mathrm{kJ} / \mathrm{mol}\right),\) are sometimes referred to as endothermic compounds. a. Why are \(\mathrm{C}_{2} \mathrm{H}_{2}\) and \(\mathrm{C}_{6} \mathrm{H}_{6}\) called endothermic compounds? b. Calculate the standard molar enthalpy of combustion of acetylene and benzene.

Step-by-Step Solution

Answer

Answer: Acetylene and benzene are referred to as endothermic compounds because they have positive standard enthalpies of formation (ΔHf°), indicating that their formation reactions require an input of energy. The standard molar enthalpy of combustion for acetylene is -783.3 kJ/mol, and for benzene, it is -3267.7 kJ/mol.

Step 1: a. Understanding endothermic compounds

When the formation of a compound absorbs energy, it is referred to as an endothermic compound. This is because a positive value of ΔHf° signifies the absorption of heat when the compound is formed from its constituent elements in their standard states. Both acetylene and benzene have positive ΔHf° values (226.7 kJ/mol and 49.0 kJ/mol), indicating that their formation reactions require an input of energy. Therefore, they are called endothermic compounds.

Step 2: b. Balanced combustion equations

Firstly, let us write balanced chemical equations for the combustion of acetylene and benzene. Acetylene: C2H2(g) + (5/2)O2(g) -> 2CO2(g) + H2O(l) Benzene: C6H6(l) + (15/2)O2(g) -> 6CO2(g) + 3H2O(l)

Step 3: b. Computing ΔHcomb° for acetylene and benzene

We can use the following equation to calculate the enthalpy of combustion (ΔHcomb°): ΔHcomb° = Σn * ΔHf°(products) - Σm * ΔHf°(reactants) where n and m are the stoichiometric coefficients of the products and reactants, respectively. For acetylene: ΔHcomb°(C2H2) = [2*(-393.5) + 1*(-285.8)] - [1*(226.7) + 2.5*(0)] = -783.3 kJ/mol For benzene: ΔHcomb°(C6H6) = [6*(-393.5) + 3*(-285.8)] - [1*(49.0) + 7.5*(0)] = -3267.7 kJ/mol Therefore, the standard molar enthalpy of combustion of acetylene and benzene are -783.3 kJ/mol and -3267.7 kJ/mol, respectively.

Key Concepts

Standard Molar Enthalpy of Combustion

When studying chemical reactions, the standard molar enthalpy of combustion is a crucial concept to grasp. It tells us about the amount of heat released when one mole of a substance undergoes complete combustion in the presence of oxygen under standard conditions (25°C and 1 atmosphere of pressure).

This thermodynamic quantity often carries a negative sign indicating that the process is exothermic, meaning it releases energy in the form of heat. For substances like acetylene (C2H2) and benzene (C6H6), these values are notably significant as they indicate just how much heat will be liberated during combustion.

To calculate the enthalpy of combustion for a substance, we need the enthalpies of formation for both the reactants and the products involved in the combustion reaction. The formula is given by: ΔHcomb° = Σn * ΔHf°(products) - Σm * ΔHf°(reactants),where 'n' and 'm' are the stoichiometric coefficients in the balanced chemical equation for the combustion reaction. As seen in our exercise, acetylene and benzene have standard molar enthalpies of combustion of -783.3 kJ/mol and -3267.7 kJ/mol, indicating that their combustion releases substantial amounts of energy.

Enthalpy of Formation

The enthalpy of formation is the change in enthalpy when one mole of a compound is formed from its elements in their standard states. A positive value of the standard molar enthalpy of formation (ΔHf°) suggests that the formation of the compound is endothermic, requiring heat absorption. Meanwhile, a negative ΔHf° value indicates that the reaction is exothermic.

For instance, acetylene has a ΔHf° of 226.7 kJ/mol, while benzene has a ΔHf° of 49.0 kJ/mol, both of which are positive. This signifies that both substances absorb heat energy when they are formed from their elemental forms. This characteristic leads to them being referred to as endothermic compounds.

Understanding the enthalpy of formation is crucial for chemists as it allows them to predict the heat exchange involved in chemical processes, helps in calculating the energy content of fuels, and is fundamental in thermodynamic assessments of reactions.

Balanced Chemical Equation

A balanced chemical equation accurately represents the conservation of mass in a chemical reaction. It ensures that the number of atoms for each element is the same on both the reactant and product sides of the equation. This is a foundational principle in chemistry known as the Law of Conservation of Mass.

For example, in the provided exercise, the combustion of acetylene is represented as: C2H2(g) + (5/2)O2(g) -> 2CO2(g) + H2O(l).And the equation for benzene combustion is: C6H6(l) + (15/2)O2(g) -> 6CO2(g) + 3H2O(l).In both equations, the number of carbon (C), hydrogen (H), and oxygen (O) atoms on the reactants side equals the number on the products side, confirming that they are properly balanced.

Accurately balancing chemical equations is vital for correctly calculating reaction stoichiometry, which in turn is essential for computational tasks such as determining the enthalpies of reactions.