Question

Estimate the average \(\mathrm{S}-\mathrm{F}\) bond energy in \(\mathrm{SF}_{6} .\) The values of standard enthalpy of formation of \(\mathrm{SF}_{6}(\mathrm{~g}), \mathrm{S}(\mathrm{g})\) and \(\mathrm{F}(\mathrm{g})\) are \(-1100,275\) and \(80 \mathrm{~kJ} / \mathrm{mol}\), respectively. (a) \(183.33 \mathrm{~kJ} / \mathrm{mol}\) (b) \(309.17 \mathrm{~kJ} / \mathrm{mol}\) (c) \(366.37 \mathrm{~kJ} / \mathrm{mol}\) (d) \(345 \mathrm{~kJ} / \mathrm{mol}\)

Short answer

183.33 kJ/mol

Step-by-step solution

Write the Chemical Equation for Formation

Write the chemical equation for the formation of SF6 from its elements in their standard states: S(g) + 6F(g) → SF6(g).

Calculate the Enthalpy Change for the Reaction

Use the standard enthalpies of formation to calculate the enthalpy change for the reaction. The enthalpy change (ΔH°_reaction) is the sum of the standard enthalpies of formation of products minus the sum of standard enthalpies of formation of reactants.

Determine the Total Bond Energy Change for S-F Bonds

Calculate the total bond energy change by multiplying the average bond energy of one S-F bond by the number of S-F bonds in SF6, which is 6.

Estimate the Average S-F Bond Energy

Divide the total bond energy change by the number of S-F bonds to obtain the average bond energy for a single S-F bond.

Key concepts

Enthalpy of Formation

Understanding the enthalpy of formation is crucial when dealing with thermochemical equations and plugging in numbers to calculate bond energies. This term, represented by the symbol \( \Delta H_f^\circ \), is a measure of the heat change that occurs when one mole of a compound is formed from its elements in their standard states.

This is valuable because it sets a common reference for comparing how much energy is stored in the bonds of different substances. To calculate the overall energy change for a chemical reaction, you sum up the enthalpy of formation values for all the products and subtract those of the reactants. In the problem at hand, the formation of \( \mathrm{SF}_6 \) (gaseous sulfur hexafluoride) from sulfur and fluorine gases involves using their respective enthalpies of formation to compute the energy involved in forming the bonds.

Chemical Bond Energy

Chemical bond energy is a pivotal concept in physical chemistry problems, as it represents the amount of energy required to break one mole of a bond in a chemical compound. This energy can be a means to quantify the stability of a bond - the higher the required energy, the stronger and more stable the bond.

For instance, understanding bond energy helps explain why certain reactions release heat (exothermic) or absorb heat (endothermic). It's a subtlety that might get lost in a series of equations but holds the key to innovating in fields like energy storage and materials science. In the context of the given problem, calculating the \( \mathrm{S}-\mathrm{F} \) bond energy involves estimating how much energy is associated with formation, and consequently potential breaking, of these specific interatomical interactions within \( \mathrm{SF}_6 \).

Thermochemistry

Digging deeper into thermochemistry allows for an understanding of the heat involved during chemical reactions. This branch of physical chemistry involves studying the energy and heat associated with chemical reactions and physical transformations.

To approach a thermochemical problem like our \( \mathrm{S}-\mathrm{F} \) bond energy calculation, you start with the principle of conservation of energy: energy cannot be created or destroyed. By looking at the enthalpies of reaction and formation, we are essentially bookkeeping the energy shifts within a chemical system. Understanding these energy flows is not only academically interesting but also essential for real-world applications, such as engineering and environmental science.

Physical Chemistry Problems

Solving physical chemistry problems often requires a mix of conceptual understanding and mathematical proficiency. These problems, including bond energy calculations, are generally tackled in a methodical manner, typically illustrated by the step-by-step solution provided.

Important advice for students approaching such problems is to parse the problem into distinct steps and to progress systematically. One should write down the balanced chemical equation, identify known values (like enthalpies of formation), calculate the ΔH° for the reaction, and use stoichiometry to find the desired quantity. Remembering that each physical chemistry problem is an opportunity to apply theoretical concepts to tangible scenarios may help ease the sometimes intimidating complexity of the subject.