Question

Bond energies of few bonds are given below: \(\mathrm{Cl}-\mathrm{Cl}=242.8 \mathrm{~kJ} \mathrm{~mol}^{-1}, \mathrm{H}-\mathrm{Cl}=431.8 \mathrm{~kJ} \mathrm{~mol}^{-\mathrm{l}}\) \(\mathrm{O}-\mathrm{H}=464 \mathrm{k} \mathrm{J} \mathrm{mol}^{-1}, \mathrm{O}=\mathrm{O}=442 \mathrm{k} \mathrm{J} \mathrm{mol}^{-1}\) Using the B.E., calculate \(\Delta H\) for the following reaction, \(2 \mathrm{Cl}_{2}+2 \mathrm{H}_{2} \mathrm{O} \rightarrow 4 \mathrm{HCl}+\mathrm{O}_{2}\) (a) \(906 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (b) \(172.4 \mathrm{k}] \mathrm{mol}^{-1}\) (c) \(198.8 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (d) \(442 \mathrm{~kJ} \mathrm{~mol}^{-1}\)

Short answer

(b) \(172.4 \mathrm{k} \mathrm{J} \mathrm{mol}^{-1}\)

Step-by-step solution

- Calculate Energy for Breaking Bonds

Determine the total energy required to break all the bonds in the reactants. For this reaction, 2 moles of Cl-Cl bonds and 4 moles of O-H bonds must be broken.

- Calculate Bond Energies of Reactants

Multiply the given bond energies by the number of each type of bond in the reactants. Energy for Cl-Cl bonds: 2 moles * 242.8 kJ/mol = 485.6 kJ. Energy for O-H bonds: 4 moles * 464 kJ/mol = 1856 kJ.

- Calculate Energy for Forming Bonds

Determine the total energy released when the bonds in the products are formed. For this reaction, 4 moles of H-Cl bonds and 1 mole of O=O bond are formed.

- Calculate Bond Energies of Products

Multiply the given bond energies by the number of each type of bond in the products. Energy for H-Cl bonds: 4 moles * 431.8 kJ/mol = 1727.2 kJ. Energy for O=O bond: 1 mole * 442 kJ/mol = 442 kJ.

- Calculate \(\Delta H\) for the Reaction

The enthalpy change \(\Delta H\) for the reaction is the energy for breaking bonds minus the energy for forming bonds. \(\Delta H = (Energy_{reactants}) - (Energy_{products}) = (485.6 kJ + 1856 kJ) - (1727.2 kJ + 442 kJ)\). Calculate the final value.

- Solve for \(\Delta H\)

Substitute the values from the previous steps to get \(\Delta H = (485.6 kJ + 1856 kJ) - (1727.2 kJ + 442 kJ) = 2341.6 kJ - 2169.2 kJ = 172.4 kJ/mol\). Choose the correct answer.

Key concepts

Bond Energy

Bond energy is a measure of the strength of a chemical bond—that is, the amount of energy required to break one mole of a specific type of bond in a chemical compound. This energy is usually expressed in kilojoules per mole (kJ/mol). Understanding bond energy is crucial when we want to calculate the overall energy change during a chemical reaction.

For instance, higher bond energy means stronger bonds, and more energy is required to break them. Conversely, forming a bond with high bond energy releases a significant amount of energy. In the context of our exercise, bond energies are given for several types of bonds, such as Cl-Cl and H-Cl. We use these values to calculate the total energy input needed to break the reactants' bonds and the energy released upon formation of the products' bonds.

Chemical Reaction

A chemical reaction involves the rearrangement of atoms to transform reactants into products. This process often entails breaking existing bonds in reactants and forming new bonds in products. The way atoms are reorganized during a chemical reaction determines the overall energy profile of the reaction.

Different types of chemical reactions include synthesis, decomposition, single replacement, and double replacement. Each of these types has a characteristic energy change associated with it. In our exercise, the reaction is a combination of decomposition and synthesis, as water and chlorine molecules break their bonds and new bonds form to create hydrochloric acid and oxygen.

Thermochemistry

Thermochemistry is the branch of chemistry that deals with the heat energy changes associated with chemical reactions. The key quantity in thermochemistry is the change in enthalpy (ergy change that occurs under constant pressure. The enthalpy change (ergy released or absorbed when a reaction takes place. If the energy needed to break bonds is greater than the energy released from forming new bonds, the reaction is endothermic, and ergy is absorbed.

In contrast, if less energy is required to break the bonds than is released upon forming new bonds, the reaction is exothermic, and ergy is favorable. By applying the given bond energies and the stoichiometry of the reaction in our exercise, we calculate the enthalpy change to derive whether the reaction absorbs or releases heat.