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Chapter 6: Problem 25

Suggest an explanation for cach of the following observations. (a) The Cr and \(\mathrm{Ni}\) content of stainless steels used to make knife blades is different from that used in the manufacture of spoons. (b) There is a poor match between experimental and calculated (Born-Land茅) values of the lattice energy for AgI, but a good match for NaI. (c) \(\mathrm{ThI}_{2}\) has been formulated as the \(\mathrm{Th}(\mathrm{IV})\) compound \(\mathrm{Th}^{4+}\left(\mathrm{I}^{-}\right)_{2}\left(\mathrm{c}^{-}\right)_{2} .\) Comment on why this is consistent with the observation of ThI \(_{2}\) having a low electrical resistivity.

Short Answer

Expert verified
Knife steels need higher Cr and different Ni content for hardness versus spoons. AgI has partial covalent bonds, impacting lattice energy agreement, unlike ionic NaI. ThI鈧�'s low resistivity is due to additional mobile ions, enhancing conductivity.

Step by step solution

01

Understanding Composition in Knife and Spoon Stainless Steels

In knife blade manufacturing, the stainless steel requires a higher hardness compared to spoons, which are designed for flexibility and corrosion resistance. Chromium (Cr) is usually added to enhance hardness and corrosion resistance, while Nickel (Ni) contributes to toughness and ductility. Therefore, knife steels often have different Cr and Ni compositions than spoon steels to meet these mechanical property demands.
02

Examining Lattice Energy of AgI and NaI

The Born-Land茅 equation calculates lattice energy assuming purely ionic behavior. AgI likely deviates from this model due to its partial covalent character, affecting the lattice energy measurement accuracy. In contrast, NaI behaves more like a purely ionic compound, hence the calculated lattice energy closely matches experimental observations.
03

Analyzing ThI鈧� Composition and Conductivity

ThI鈧� has been formulated as Th(IV) due to the presence of additional negative ions like Cl鈦�. These excess anions serve to balance the tetravalent Th鈦粹伜 charge. This indicates the presence of mobile ions, which is coherent with the low electrical resistivity of ThI鈧�, as the mobility of these ions facilitates electric current flow, indicating semi-conductive or metallic behavior.

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Key Concepts

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

Stainless Steel Composition
Stainless steel is an alloy known for its high corrosion resistance, durability, and versatility. The composition varies significantly depending on its intended application, such as in the construction of knife blades or spoons.

For knife blades, stainless steel typically contains a higher percentage of Chromium (Cr) and Nickel (Ni).
- **Chromium** helps to increase hardness and resistance to wear, essential traits for the cutting edge of a knife. - **Nickel** adds toughness and ductility, thereby preventing brittleness.
In contrast, spoons prioritize flexibility and durability more than extreme hardness. Consequently, the composition of stainless steel used in spoons has a balanced ratio of Cr and Ni aimed at enhancing corrosion resistance without excessive hardness.
- **Cr in Spoons:** Adequate for corrosion resistance, but not as high as in knife blades. - **Ni in Spoons:** Provides the needed strength and flexibility making spoons resistant to bending or breaking under regular use.
Lattice Energy
Lattice energy is a measure of the strength of forces holding ions together in an ionic solid. It's usually calculated using the Born-Land茅 equation, which assumes the material behaves like a perfect ionic compound. However, deviations from this assumption can occur.

For instance, in the case of Silver Iodide (AgI), the lattice energy calculated by the Born-Land茅 equation does not match experimental values well. This discrepancy is due to the partial covalent character within AgI, which the equation fails to account for.
- **Partial Covalent Character:** Occurs when the electron cloud between atoms is shared rather than transferred, causing deviations from purely ionic behavior.
On the other hand, Sodium Iodide (NaI) aligns more closely with ideal ionic behavior, leading to a good match between the calculated and observed lattice energy.
- **Purely Ionic Compounds:** Like NaI, where electron transfer is complete, allowing for accurate lattice energy predictions using the standard Born-Land茅 method.
ThI鈧� Electrical Conductivity
Thorium (II) iodide, or ThI鈧�, showcases interesting electrical properties due to its formulation as Th(IV) with additional ions such as Cl鈦�. This composition enables a pathway for electrical conduction.

In the ThI鈧� structure: - **Th鈦粹伜 ions**: Require balancing through excess negative ions, which contributes to the overall charge balance. - **Extra anions (such as Cl鈦�)**: Create pathways for ionic movement, thereby facilitating electrical conductance.
This movement of ions helps lower electrical resistivity, implying that ThI鈧� can conduct electricity better than typical ionic compounds. Such behavior can indicate that the material possesses characteristics of semiconductors or even metallic nature, attributed to the mobility and presence of excess anions within the structure which promote the movement of electric charge easily.
- **Semi-conductive Nature:** These mixed ion conditions and mobile charges signify why ThI鈧� has a low resistivity, allowing it to conduct electricity more efficiently.

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Most popular questions from this chapter

Which of the following processes are expected to be exothermic? Give reasons for your answers. (a) \(\mathrm{Na}^{+}(\mathrm{g})+\mathrm{Br}^{-}(\mathrm{g}) \rightarrow\) NaBr(s) (b) \(\mathrm{Mg}(\mathrm{g}) \rightarrow \mathrm{Mg}^{2+}(\mathrm{g})+2 \mathrm{e}^{-}\) (c) \(\operatorname{Mg} \mathrm{Cl}_{2}(\mathrm{s})-\mathrm{Mg}(\mathrm{s})+\mathrm{Cl}_{2}(\mathrm{g})\) (d) \(\mathrm{O}(\mathrm{g})+2 \mathrm{e}^{-}-\mathrm{O}^{2-}(\mathrm{g})\) (c) \(\mathrm{Cu}(\mathrm{l})-\mathrm{Cu}(\mathrm{s})\) (f) \(\mathrm{Cu}(\mathrm{s})-\mathrm{Cu}(\mathrm{g})\) \((\mathrm{g}) \mathrm{KF}(\mathrm{s}) \rightarrow \mathrm{K}^{+}(\mathrm{g})+\mathrm{F}^{-}(\mathrm{g})\)

Discuss the interpretation of the following: (a) \(\Delta_{\mathrm{f}} H^{\circ}(298 \mathrm{K})\) becomes less negative along the series \(\mathrm{LiF}, \mathrm{NaF}, \mathrm{KF}, \mathrm{RbF}, \mathrm{CsF},\) but more negative along the series \(\mathrm{LiI}, \mathrm{NaI}, \mathrm{KI}, \mathrm{RbI}, \mathrm{CsI}\) (b) The thermal stability of the isomorphous sulfates of \(\mathrm{Ca}, \mathrm{Sr}\) and \(\mathrm{Ba}\) with respect to decomposition into the metal oxide (MO) and SO jucreases in the sequence \(\mathrm{CaSO}_{4}<\mathrm{SrSO}_{4}<\mathrm{BaSO}_{4}\).

With reference to the NaCl, CsCl and TiO structure types, explain what is meant by (a) coordination number, (b) unit cell, (c) ion sharing between unit cells, and (d) determination of the formula of an ionic salt from the unit cell.

Outline the similarities and differences between cubic and hexagonal close- packed arrangements of spheres, paying particular attention to (a) coordination numbers, (b) interstitial holes and (c) unit cells.

(a) \(\mathrm{VO}, \mathrm{TiO}\) and \(\mathrm{NiO}\) all have defect rock salt structures. Explain what this statement means. (b) In \(\mathrm{NiO}\), the \(\mathrm{Ni}-\mathrm{O}\) internuclear separation is 209 pm. Determine the volume of a unit cell of \(\mathrm{NiO}\), and its density, assuming a non- defect structure, Given that the observed density of \(\mathrm{NiO}\) is \(6.67 \mathrm{g} \mathrm{cm}^{-3},\) determine the extent of vacancies in the NiO lattice. Express your answer as a percentage.
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