Question

Find the bond energy of \(\mathrm{S}-\mathrm{S}\) bond from the following data: \(\mathrm{C}_{2} \mathrm{H}_{5}-\mathrm{S}-\mathrm{C}_{2} \mathrm{H}_{5}(\mathrm{~g}) ; \Delta H_{\mathrm{f}}^{\mathrm{o}}=-148 \mathrm{~kJ}\), \(\mathrm{C}_{2} \mathrm{H}_{5}-\mathrm{S}-\mathrm{S}-\mathrm{C}_{2} \mathrm{H}_{5}(\mathrm{~g}) ; \Delta H_{\mathrm{f}}^{\mathrm{o}}=-202 \mathrm{~kJ}\) \(\mathrm{S}(\mathrm{g}) ; \Delta H_{\mathrm{f}}^{\mathrm{o}}=222 \mathrm{~kJ}\) (a) \(276 \mathrm{~kJ} / \mathrm{mol}\) (b) \(128 \mathrm{~kJ} / \mathrm{mol}\) (c) \(168 \mathrm{~kJ} / \mathrm{mol}\) (d) \(222 \mathrm{~kJ} / \mathrm{mol}\)

Short answer

The bond energy of the S-S bond is 128 kJ/mol.

Step-by-step solution

Write down the given data

The enthalpy of formation for diethyl sulfide is \( \Delta H_{f}^{o}_{(C_2H_5-S-C_2H_5(g))} = -148 \: kJ \) and for diethyl disulfide is \( \Delta H_{f}^{o}_{(C_2H_5-S-S-C_2H_5(g))} = -202 \: kJ \) respectively. The enthalpy of formation for sulfur in the gas phase is \( \Delta H_{f}^{o}_{(S(g))} = 222 \: kJ \) per mole of sulfur atoms.

Write the balanced chemical equation for the formation of diethyl sulfide

The chemical reaction for the formation of diethyl sulfide from its elements in their standard states is: \( 2C_2H_6(g) + S(s) \rightarrow C_2H_5-S-C_2H_5(g) \).

Write the balanced chemical equation for the formation of diethyl disulfide

The chemical reaction for the formation of diethyl disulfide from its elements in their standard states is: \( 4C_2H_6(g) + 2S(s) \rightarrow C_2H_5-S-S-C_2H_5(g) \) .

Determine the bond energy of the S-S bond

The bond energy of the S-S bond can be found by comparing the enthalpy of formation of diethyl disulfide to twice the enthalpy of formation of diethyl sulfide and subtracting the enthalpy of formation of sulfur. Specifically, \( 2 \times \Delta H_{f}^{o}_{(C_2H_5-S-C_2H_5(g))} + \Delta H_{f}^{o}_{(S(g))} = \Delta H_{f}^{o}_{(C_2H_5-S-S-C_2H_5(g))} + \text{Bond energy of S-S} \) . Rearrange the equation to solve for the bond energy of S-S.

Calculate the bond energy of the S-S bond

By inserting the known values, we can calculate the bond energy of the S-S bond: \( \text{Bond energy of S-S} = 2 \times (-148 \: kJ) + 222 \: kJ - (-202 \: kJ) \).

Final Calculation

Perform the calculations: \( \text{Bond energy of S-S} = 2 \times (-148) + 222 + 202 \). This simplifies to \( \text{Bond energy of S-S} = -296 + 222 + 202 \), which equals \( 128 \: kJ/mol \) . Therefore, the bond energy of the S-S bond is \( 128 \: kJ/mol \).

Key concepts

Enthalpy of Formation Explained

The concept of enthalpy of formation, denoted as \( \Delta H_{f}^{\circ} \), refers to the change in enthalpy when one mole of a substance is formed from its elements in their standard states under standard conditions (usually 1 atm pressure and 298.15 K temperature).

For instance, the enthalpy of formation for diethyl sulfide (\( C_2H_5-S-C_2H_5(g) \)) is a measure of the energy change when one mole of diethyl sulfide is synthesized from ethane (\( C_2H_6(g) \) and sulfur (\( S(s) \)) in their standard states. A negative value, like \( \Delta H_{f}^{\circ} = -148 \: kJ \), indicates that the formation reaction releases energy, and the substances combine spontaneously.

Understanding the enthalpy of formation is pivotal in predicting reaction outcomes and conducting energy balance calculations in chemical reactions. It represents the bonding energy between atoms when a compound is created from the constituent elements.

Chemical Reaction Equations Demystified

Chemical reaction equations are symbolic representations of chemical reactions. They show the reactants transforming into products, with the equation balanced to reflect the conservation of mass. Each substance is represented by its chemical formula, with the arrangement indicating the number of moles involved in the reaction.

A balanced chemical equation for the formation of diethyl sulfide can be written as: \( 2C_2H_6(g) + S(s) \rightarrow C_2H_5-S-C_2H_5(g) \). This signifies that two moles of ethane gas react with one mole of solid sulfur to produce one mole of diethyl sulfide gas.

To correctly interpret such equations, one must understand stoichiometry, which deals with the quantitative relationships between the reactants and products in chemical reactions. Through stoichiometry, we can predict the amounts of products formed from given reactants or vice versa.

Bond Enthalpy and Its Importance

The term \( \text{bond enthalpy} \) refers to the energy required to break one mole of a specific type of bond in a chemical compound in the gas phase, to produce gaseous atoms or molecules. Typically, it is denoted as the energy change upon breaking the bond under standard conditions.

Bond enthalpy is an essential concept for understanding the strength of chemical bonds; the higher the bond enthalpy, the stronger the bond. For instance, determining the bond enthalpy for the \( \text{S-S} \) bond involves calculating how much energy is required to break the bond between two sulfur atoms in diethyl disulfide, reflecting the strength of the bond.

In the textbook exercise, we're looking at the enthalpy changes associated with the formation and disassociation of molecules containing \( \text{S-S} \) bonds. By comparing these values, we can deduce the bond enthalpy which provides insight into the chemical stability of the substance and its reactivity.