Question

Bond dissociation energies of \(\mathrm{H}_{2}, \mathrm{Cl}_{2}\) and \(\mathrm{HCl}_{(g)}\) are 104,58 and \(103 \mathrm{kcal} \mathrm{mol}^{-1}\) respectively. Calculate the enthalpy of formation of \(\mathrm{HCl}\) gas. (a) \(-22 \mathrm{kcal}\) (b) \(+22 \mathrm{kcal}\) (c) \(+184 \mathrm{kcal}\) (d) \(-184 \mathrm{kcal}\)

Short answer

-22 kcal

Step-by-step solution

Understand the concept of bond dissociation energy

The bond dissociation energy is the energy required to break a bond in a molecule to form isolated atoms in the gas phase. To form HCl from hydrogen and chlorine, we'll consider breaking the bonds in H2 and Cl2 and then forming the bonds in HCl.

Calculate the total energy needed to break the bonds

Calculate the energy needed to break the molecular bonds in H2 and Cl2. This is given by the sum of their bond dissociation energies: for H2 it's 104 kcal/mol and for Cl2 it's 58 kcal/mol.

Calculate the energy released in forming HCl bonds

When two moles of HCl are formed, the energy released is twice the bond dissociation energy of one mole of HCl due to two H-Cl bonds being formed. Hence, the energy released is 2 * 103 kcal/mol.

Calculate the enthalpy of formation of HCl gas

The enthalpy of formation is the total energy needed to break the initial bonds minus the energy released from forming the new bonds. This represents the net energy change during the chemical reaction.

Write the chemical reaction and apply Hess's law

The reaction to form 2 moles of HCl gas from hydrogen and chlorine is: H2(g) + Cl2(g) -> 2HCl(g). The enthalpy of formation is given by (Energy to break H2 + Energy to break Cl2) - (Energy released by forming HCl).

Key concepts

Bond Dissociation Energy

Bond dissociation energy is a term used in chemical thermodynamics to describe the energy needed to break a single bond within a molecule and separate the atoms completely without causing any change to the rest of the molecule. This energy varies for different types of bonds and different molecules. In the context of an exercise, understanding bond dissociation energy is crucial for calculating the enthalpy of formation of a new compound.

For the formation of HCl gas from hydrogen (H_2) and chlorine (Cl_2), we start by breaking their respective bonds. The bond dissociation energy for H_2 is 104 kcal/mol, while for Cl_2 it's 58 kcal/mol. Knowing these energies, students can better grasp why certain reactions release or absorb energy and how to apply this understanding to enthalpy calculations.

Hess’s Law

Hess's law, also known as the law of constant heat summation, states that the total enthalpy change for a reaction is the same, no matter how the reaction occurs, as long as the initial and final conditions are the same. This principle allows for the enthalpy of a reaction to be calculated even if it cannot be measured directly by using known enthalpies of other related reactions.

To apply Hess's law in our problem, we look at the formation of HCl gas. The overall enthalpy change of the reaction can be found by adding the enthalpies of breaking the H_2 and Cl_2 bonds and then subtracting the energy released when two moles of HCl bond are formed. Thus, Hess's law provides a pathway to understand and solve complex thermodynamic problems by breaking them down into simpler steps.

Chemical Thermodynamics

Chemical thermodynamics is the study of the relationship between heat, work, temperature, and chemical reactions or physical changes. The enthalpy of formation is a key concept here, which refers to the heat change that occurs when one mole of a compound is formed from its elements in their standard states.

The importance of this concept lies in its ability to predict reaction spontaneity and feasibility. By understanding the principles of chemical thermodynamics, and specifically the enthalpy of a system, students can rationalize why some reactions occur naturally while others do not. Moreover, these concepts empower students with the necessary tools to calculate energy changes and better understand the energetic implications of reactions, as illustrated in the provided textbook exercise solving for the enthalpy of formation of HCl gas.