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Chapter 8: Problem 66

Use the following data (in kJ/mol) to estimate \(\Delta H\) for the reaction \(S^{-}(g)+e^{-} \rightarrow S^{2-}(g)\) . Include an estimate of uncertainty. $\begin{aligned} \mathrm{S}(s) \longrightarrow \mathrm{S}(g) & \Delta H=277 \mathrm{kJ} / \mathrm{mol} \\ \mathrm{S}(g)+\mathrm{e}^{-} \longrightarrow \mathrm{S}^{-}(g) & \Delta H=-200 \mathrm{kJ} / \mathrm{mol} \end{aligned}$ Assume that all values are known to \(\pm 1 \mathrm{kJ} / \mathrm{mol}\)

Short Answer

Expert verified
The enthalpy change for the reaction \(S^-(g) + e^- \rightarrow S^{2-}(g)\) is \(\Delta H_\text{target} = 77\,\text{kJ/mol}\), with an estimated uncertainty of \(\pm 2\,\text{kJ/mol}\).

Step by step solution

01

Identify the target reaction and given reactions

The target reaction we want to find the enthalpy change for is \(S^-(g) + e^- \rightarrow S^{2-}(g)\). We are given two reactions: 1. \(S(s) \rightarrow S(g) \quad \Delta H = 277 \,\text{kJ/mol}\) 2. \(S(g) + e^- \rightarrow S^-(g) \quad \Delta H = -200 \,\text{kJ/mol}\)
02

Manipulate the given reactions to match the target reaction

Observe that if we add the two given reactions, we will get the target reaction: 1. \(S(s) \rightarrow S(g) \quad \Delta H = 277 \,\text{kJ/mol}\) 2. \(S(g) + e^- \rightarrow S^-(g) \quad \Delta H = -200 \,\text{kJ/mol}\) + -------------------------------------------- \((1 + 2)\) \(S^-(g) + e^- \rightarrow S^{2-}(g)\)
03

Add the enthalpy changes of the given reactions

To find the enthalpy change for the target reaction, we need to add the enthalpy changes for reactions 1 and 2: \(\Delta H_\text{target} = \Delta H_1 + \Delta H_2\) \(\Delta H_\text{target} = 277\,\text{kJ/mol} - 200\,\text{kJ/mol}\) \(\Delta H_\text{target} = 77\,\text{kJ/mol}\)
04

Calculate the uncertainty

We are given that the uncertainties for both reactions \(\Delta H_1\) and \(\Delta H_2\) are \(± 1\,\text{kJ/mol}\). When adding these values, we should add the uncertainties: \(\Delta H_\text{uncertainty} = \Delta H_{1, \text{uncertainty}} + \Delta H_{2, \text{uncertainty}}\) \(\Delta H_\text{uncertainty} = \pm 1\,\text{kJ/mol} + \pm 1\,\text{kJ/mol}\) \(\Delta H_\text{uncertainty} = \pm 2\,\text{kJ/mol}\)
05

Present the final answer

The enthalpy change for the target reaction \(S^-(g) + e^- \rightarrow S^{2-}(g)\) is \(\Delta H_\text{target} = 77\,\text{kJ/mol}\), with an estimated uncertainty of \(\pm 2\,\text{kJ/mol}\).

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Most popular questions from this chapter

Rank the following bonds in order of increasing ionic character: $\mathrm{N}-\mathrm{O}, \mathrm{Ca}-\mathrm{O}, \mathrm{C}-\mathrm{F}, \mathrm{Br}-\mathrm{Br}, \mathrm{K}-\mathrm{F}$ .

For each of the following groups, place the atoms and/or ions in order of decreasing size. a. \(\mathrm{V}, \mathrm{V}^{2+}, \mathrm{V}^{3+}, \mathrm{V}^{5+}\) b. \(\mathrm{Na}^{+}, \mathrm{K}^{+}, \mathrm{Rb}^{+}, \mathrm{Cs}^{+}\) c. \(\mathrm{Te}^{2-}, \mathrm{I}^{-}, \mathrm{Cs}^{+}, \mathrm{Ba}^{2+}\) d. \(\mathrm{P}, \mathrm{P}^{-}, \mathrm{P}^{2-}, \mathrm{P}^{3-}\) e. \(\mathrm{O}^{2-}, \mathrm{S}^{2-}, \mathrm{Se}^{2-}, \mathrm{Te}^{2-}\)

For each of the following, write an equation that corresponds to the energy given. a. lattice energy of \(\mathrm{NaCl}\) b. lattice energy of \(\mathrm{NH}_{4} \mathrm{Br}\) c. lattice energy of \(\mathrm{MgS}\) d. \(\mathrm{O}=\mathrm{O}\) double bond energy beginning with \(\mathrm{O}_{2}(g)\) as a reactant

Write electron configurations for the most stable ion formed by each of the elements Te, Cl, Sr, and Li (when in stable ionic compounds).

The standard enthalpies of formation for $\mathrm{S}(g), \mathrm{F}(g), \mathrm{SF}_{4}(g),\( and \)\mathrm{SF}_{6}(g)\( are \)+278.8,+79.0,-775,$ and \(-1209 \mathrm{kJ} / \mathrm{mol}\) respectively. a. Use these data to estimate the energy of an \(\mathrm{S}-\) F bond. b. Compare your calculated value to the value given in Table \(8.5 .\) What conclusions can you draw? c. Why are the \(\Delta H_{f}^{\circ}\) values for \(\mathrm{S}(g)\) and \(\mathrm{F}(g)\) not equal to zero, since sulfur and fluorine are elements?
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