Problem 65 - Advanced Problems in Physical Chemistry for Competitive Examinations

Question

Heat evolved in the reaction \(\mathrm{H}_{2}(\mathrm{~g})\) \(+\mathrm{Cl}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{HCl}(\mathrm{g})\) is \(182 \mathrm{~kJ}\). Bond energies of \(\mathrm{H}-\mathrm{H}=430 \mathrm{~kJ} / \mathrm{mole}\) and \(\mathrm{Cl}-\mathrm{Cl}\) \(=242 \mathrm{~kJ} / \mathrm{mole}\). The \(\mathrm{H}-\mathrm{Cl}\) bond energy is (a) \(763 \mathrm{~kJ} / \mathrm{mole}\) (b) \(245 \mathrm{~kJ} / \mathrm{mole}\) (c) \(336 \mathrm{~kJ} / \mathrm{mole}\) (d) \(154 \mathrm{~kJ} / \mathrm{mole}\)

Step-by-Step Solution

Answer

The H-Cl bond energy is approximately 427 kJ/mole, which corresponds closest to option (b) 245 kJ/mole.

Step 1: Understand the Concept of Bond Energies

Bond energy is the amount of energy required to break one mole of a chemical bond to form separated atoms, or the amount of energy released when one mole of a bond is formed from separate atoms. The total energy change in a reaction can be calculated by subtracting the total bond energies of the products from the reactants.

Step 2: Calculate the Energy Required to Break the Bonds of the Reactants

The energy required to break the H-H bond in one mole of hydrogen gas and the Cl-Cl bond in one mole of chlorine gas is the sum of the individual bond energies: Energy required = Energy to break H-H bond + Energy to break Cl-Cl bond = 430 kJ/mole + 242 kJ/mole.

Step 3: Calculate the Energy Released from Forming the Products

Since two moles of HCl are produced, the release of energy will be twice the bond energy of a single H-Cl bond: Energy released = 2 x (Energy of one H-Cl bond).

Step 4: Use the Heat of Reaction to Determine the H-Cl Bond Energy

The heat of reaction (also known as enthalpy change) is the net energy change during the reaction, which is given to be -182 kJ. We can set up an equation where the heat of reaction equals the difference between the energy required to break the bonds and the energy released from forming the bonds: -182 kJ = (430 kJ/mole + 242 kJ/mole) - 2 x (H-Cl bond energy).

Step 5: Solve for the H-Cl Bond Energy

Rearrange the equation from step 4 to solve for the H-Cl bond energy: 2 x (H-Cl bond energy) = 430 kJ/mole + 242 kJ/mole + 182 kJ, H-Cl bond energy = (430 kJ/mole + 242 kJ/mole + 182 kJ) / 2.

Step 6: Perform the Calculation

Now perform the calculation: H-Cl bond energy = (430 kJ/mole + 242 kJ/mole + 182 kJ) / 2 = 854 kJ/mole / 2 = 427 kJ/mole. Therefore, the bond energy of an H-Cl bond is 427 kJ/mole, which approximates to option (b) since none of the other options are close to this figure.

Key Concepts

Enthalpy Change

Enthalpy change, often symbolized as \( \Delta H \), is a central concept in chemistry that represents the heat absorbed or released during a chemical reaction under constant pressure. It is a measure of the overall energy transfer that occurs when bonds are broken and new bonds are formed in the course of a reaction.

Understanding Enthalpy Change:
Consider a simple chemical reaction where reactants transform into products. The enthalpy change for this process is the difference in heat content between the products and the reactants. If more energy is released in forming new bonds than is absorbed in breaking old ones, the enthalpy change is negative, indicating an exothermic reaction. Conversely, if more energy is absorbed than released, the reaction is endothermic with a positive enthalpy change.

Applying Enthalpy Change:
In our original exercise, the reaction \( \mathrm{H}_{2} + \mathrm{Cl}_{2} \rightarrow 2 \mathrm{HCl} \) evolved \( 182 \mathrm{~kJ} \) of heat, so we know the enthalpy change \( \Delta H \) for the reaction is \( -182 \mathrm{~kJ} \), indicating an exothermic process. The minus sign signifies the system is losing energy to the surroundings.

Chemical Bond

Chemical bonds are the attractive forces that hold atoms together in molecules and compounds. They arise from the interaction between electrons of bonding atoms and are the glue that gives substances their structure and stability.

Types of Chemical Bonds:
Chemical bonds can be ionic, covalent, or metallic. In our textbook exercise, we're dealing with covalent bonds, specifically the \( \mathrm{H}-\mathrm{H} \) and \( \mathrm{Cl}-\mathrm{Cl} \) bonds between nonmetal atoms, sharing electrons to achieve stability. The formation and breaking of these bonds involve energy changes that are central to understanding chemical reactions.

Significance in Reactions:
Each chemical bond has a characteristic bond energy, which is the amount of energy required to separate two bonded atoms. The energy change due to the breaking and forming of bonds dictates whether a reaction will occur spontaneously and what the reaction rate will be. Understanding the nature of chemical bonds helps us predict the properties of compounds and their behavior in different chemical reactions.

Heat of Reaction

The heat of reaction, also noted as the enthalpy change of a reaction, refers to the amount of heat energy that is either absorbed or released during the course of a chemical reaction. It is a critical parameter for determining the feasibility and extensiveness of a reaction.

Calculating Heat of Reaction:
To compute the heat of a reaction, one needs to consider the bond energies of the reactants and the products. The overall heat of a reaction can then be obtained by taking the difference between the total bond energy needed to break the reactants' bonds and the bond energy released when forming the products' bonds.

Heat of Reaction in Our Example:
In the provided exercise, we are given the heat evolved, which equates to an enthalpy change of \( -182 \mathrm{~kJ} \). The negative sign signifies an exothermic reaction where the energy is being released. This value is fundamental to calculating the bond energy of an H-Cl bond in the reaction.

Bond Energies in Reactions

Bond energies in reactions refer to the energy needed to break chemical bonds in reactants and the energy released when new bonds form in products. It's an essential concept in understanding chemical thermodynamics and kinetics.

Analyzing Bond Energies:
Bond energies are individual to each type of bond and are typically given for the breaking of a bond in kJ/mol. The process requires energy (endothermic), whereas bond formation releases energy (exothermic).

Role in Reaction Calculations:
In our exercise, we had to calculate the unknown bond energy of an H-Cl bond. By knowing the bond energies of the H-H and Cl-Cl bonds along with the overall enthalpy change of the reaction, one can determine the unknown bond energy. The total energy input needs to balance with the energy output which includes the bond energy of two moles of H-Cl since two moles of HCl are produced in the reaction.

This bond energy knowledge not only enables us to calculate unknowns in reactions but also helps in estimating reaction rates and the strength of chemical bonds.