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Chapter 8: Problem 5

Calculate the enthalpy change that accompanies the reaction: \\[ \frac{1}{2} \mathrm{Li}_{2}(\mathrm{g})+\mathrm{e}^{-}-\mathrm{Li}^{-}(\mathrm{g}) \\] given that the bond enthalpy for \(L_{i}\), is \(110 \mathrm{kJ} \mathrm{mol}^{-1}\) and \(E A_{1}\) for lithium is \(60 \mathrm{kJ} \mathrm{mol}^{-1}\)

Short Answer

Expert verified
The enthalpy change for the reaction is \(-5 \mathrm{kJ/mol}\).

Step by step solution

01

Understand the Reaction

The reaction given is \( \frac{1}{2} \mathrm{Li}_{2} (\mathrm{g}) + \mathrm{e}^{-} \rightarrow \mathrm{Li}^{-} (\mathrm{g}) \). It involves breaking the bond in diatomic lithium (Li2) and adding an electron to form \( \mathrm{Li}^{-} \). The enthalpy change associated with this reaction includes both the bond dissociation energy and the electron affinity of lithium.
02

Calculate Bond Dissociation Energy

The bond enthalpy for diatomic lithium (\( \mathrm{Li}_2 \)) is given as \( 110 \mathrm{kJ/mol} \). For \( \frac{1}{2} \mathrm{Li}_2 \), the bond dissociation energy is thus \( \frac{110}{2} \mathrm{kJ/mol} = 55 \mathrm{kJ/mol} \). This is the energy required to break \( \frac{1}{2} \) of the \( \mathrm{Li}_2 \) bond to form \( \mathrm{Li} \) atoms.
03

Add Electron Affinity

Electron affinity (EA1) is the amount of energy released when an atom gains an electron. For lithium, this value is given as \( -60 \mathrm{kJ/mol} \). Electron affinity is negative because energy is released when the electron is added.
04

Calculate the Total Enthalpy Change

The enthalpy change for the reaction is the sum of the energy required for bond dissociation and the electron affinity. Thus, \( \Delta H = 55 \mathrm{kJ/mol} - 60 \mathrm{kJ/mol} = -5 \mathrm{kJ/mol} \).
05

Conclusion

The total enthalpy change for the reaction \( \frac{1}{2} \mathrm{Li}_{2} (\mathrm{g}) + \mathrm{e}^{-} \rightarrow \mathrm{Li}^{-} (\mathrm{g}) \) is \( -5 \mathrm{kJ/mol} \). This indicates that the reaction is exothermic.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Bond Dissociation Energy
Bond dissociation energy (BDE) is a critical concept in understanding chemical reactions. It is defined as the energy required to break a particular bond between two atoms in a molecule. For diatomic molecules like \( \mathrm{Li}_2 \), this refers to the bond holding the two lithium atoms together. When you consider a reaction that involves breaking bonds, such as in the provided exercise, you need to account for this energy expenditure.
  • For diatomic lithium, the bond enthalpy is \( 110 \mathrm{kJ/mol} \).
  • Since the reaction involves breaking \( \frac{1}{2} \) of this bond, the BDE used for the calculation is \( 55 \mathrm{kJ/mol} \).
Understanding BDE is essential because it is an endothermic process鈥攎eaning energy is consumed to break the bond.
Electron Affinity
Electron affinity (EA) measures the energy change when an atom in the gas phase gains an electron to form an anion. It is often expressed as the energy released, which is why it is typically negative. This process is crucial in assessing reactions where atoms gain electrons, as seen in forming \( \mathrm{Li}^{-} \).
  • The electron affinity for lithium is \( -60 \mathrm{kJ/mol} \).
  • Since energy is released when an atom gains an electron, the enthalpy change due to EA is negative, contributing to the reaction's exothermic nature.
This energy release offsets the energy required for bond dissociation, playing a significant role in the total enthalpy change of the reaction.
Exothermic Reaction
Exothermic reactions are processes that release energy, usually in the form of heat, to the surroundings. In chemical reactions, this release happens when products are at a lower energy state compared to reactants. For the given reaction, the overall enthalpy change result is \( \Delta H = -5 \mathrm{kJ/mol} \), indicating an exothermic process.
  • In exothermic reactions, the released energy from forming new bonds or electron affinities exceeds the energy consumed in breaking initial bonds.
  • Such reactions often feel warm to the touch or can produce light as a byproduct of the released energy.
Understanding whether a reaction is exothermic helps predict the feasibility and spontaneity of chemical processes.
Chemical Thermodynamics
Chemical thermodynamics is a branch of physical chemistry that deals with energy changes in chemical reactions. It encompasses concepts like enthalpy, entropy, and Gibbs free energy, explaining why reactions occur the way they do. The concepts of bond dissociation energy and electron affinity discussed above are fundamental parts of this field.
  • Thermodynamics provides a framework to calculate the energy economics of a reaction, helping to predict the direction and extent of chemical changes.
  • In the context of the provided problem, the enthalpy change was calculated, showing that chemical thermodynamic principles can determine whether a reaction is endothermic or exothermic.
This knowledge allows chemists to manipulate conditions to favor desired reactions, harnessing energy changes for practical applications.

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Most popular questions from this chapter

With reference to the oxygen atom, explain what you understand by the (a) first ionization energy, (b) second ionization energy, (c) first electron affinity, (d) second electron affinity and (e) enthalpy change associated with the attachment of an electron.

A bromide of indium, \(\operatorname{In} \mathrm{Br}_{x},\) adopts the NaCl lattice but only one-third of the metal ion sites are occupied. What is the oxidation state of indium in this compound?

The first five ionization energies of a gaseous atom \(X\) are 589,1148,4911,6494 and \(8153 \mathrm{kJ} \mathrm{mol}^{-1},\) To what group is this element likely to belong?

Calculate the enthalpy change that accompanies the process: \\[ \frac{1}{2} \mathrm{Li}_{2}(\mathrm{g})-\mathrm{Li}^{+}(\mathrm{g})+\mathrm{e}^{-} \\] given that the bond enthalpy for dilithium is \(110 \mathrm{kJ} \mathrm{mol}^{-1}\) and \(I E_{1}\) for lithium is \(520 \mathrm{kJ} \mathrm{mol}^{-1}\)

(a) Gallium phosphide is used is solar energy conversion, and it crystallizes with the zinc blende lattice. What is the formula of gallium phosphide? Rationalize this formula in terms of the positions of Ga and \(P\) in the periodic table. (b) Crystalline cerium(IV) oxide contains 4-coordinate \(\mathrm{O}^{2-}\) ions. What is the coordination number of the Ce(IV) centres? The oxide adopts one of the lattices described in Chapter \(8 .\) Suggest which lattice it is.
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