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Consider the ionic compounds KF, NaCl, NaBr, and LiCl. (a) Use ionic radil (Figure 7.8) to estimate the cation-anion distance for each compound. (b) Based on your answer to part (a), arrange these four compounds in order of decreasing lattice energy. (c) Check your predictions in part (b) with the experimental values of lattice energy from Table \(8.1 .\) Are the predictions from ionic radii correct?

Short Answer

Expert verified
The cation-anion distances for KF, NaCl, NaBr, and LiCl are 252 pm, 264 pm, 279 pm, and 227 pm respectively. Based on these distances, the order of decreasing lattice energy is LiCl, KF, NaCl, and NaBr. This order is confirmed by the experimental lattice energy values from Table 8.1: LiCl (853 kJ/mol), KF (821 kJ/mol), NaCl (787 kJ/mol), and NaBr (747 kJ/mol). Thus, the predictions based on ionic radii are correct.

Step by step solution

01

Calculate the cation-anion distances for each compound

For each compound, add the ionic radii of the cation and anion to find the cation-anion distance. Use Figure 7.8 to find the ionic radii. For KF: - K鈦 radius: 133 pm - F鈦 radius: 119 pm Cation-anion distance = 133 pm + 119 pm = 252 pm For NaCl: - Na鈦 radius: 97 pm - Cl鈦 radius: 167 pm Cation-anion distance = 97 pm + 167 pm = 264 pm For NaBr: - Na鈦 radius: 97 pm - Br鈦 radius: 182 pm Cation-anion distance = 97 pm + 182 pm = 279 pm For LiCl: - Li鈦 radius: 60 pm - Cl鈦 radius: 167 pm Cation-anion distance = 60 pm + 167 pm = 227 pm
02

Arrange compounds in order of decreasing lattice energy

Lattice energy is inversely proportional to the distance between the cation and anion. Smaller cation-anion distance results in stronger attractive forces and thus higher lattice energy. Using the cation-anion distance found above, we can arrange the compounds in order of decreasing lattice energy: 1. LiCl (227 pm) 2. KF (252 pm) 3. NaCl (264 pm) 4. NaBr (279 pm)
03

Compare the predicted order with experimental values

Now, let's compare our prediction with the experimental values of lattice energy from Table 8.1. The lattice energies (in kJ/mol) for the compounds are: - KF: 821 kJ/mol - NaCl: 787 kJ/mol - NaBr: 747 kJ/mol - LiCl: 853 kJ/mol Based on the experimental values, the order of decreasing lattice energy is: 1. LiCl (853 kJ/mol) 2. KF (821 kJ/mol) 3. NaCl (787 kJ/mol) 4. NaBr (747 kJ/mol) This confirms that our predictions based on ionic radii are indeed correct.

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Key Concepts

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

Cation-Anion Distance
The cation-anion distance is crucial in ionic compounds. It refers to the distance between the positively charged cation and the negatively charged anion. This distance is determined by adding the ionic radii of the cation and anion involved. For example:
  • KF: The distance is calculated by adding the radius of K鈦, 133 pm, and F鈦, 119 pm, resulting in 252 pm.
  • NaCl: The distance is the sum of Na鈦, 97 pm, and Cl鈦, 167 pm, totaling 264 pm.
  • NaBr: Here, we add Na鈦, 97 pm, and Br鈦, 182 pm, making 279 pm.
  • LiCl: It combines Li鈦, 60 pm, and Cl鈦, 167 pm, totaling 227 pm.
Understanding this distance is key because it influences the strength of the ionic bond. The shorter the distance, the stronger the electrostatic forces of attraction between ions.
Lattice Energy
Lattice energy represents the energy required to separate one mole of an ionic solid into its gaseous ions. This concept plays a significant role in understanding the stability and properties of ionic compounds. The smaller the cation-anion distance, the greater the lattice energy due to stronger attractions between ions.
  • LiCl: With the shortest distance of 227 pm, has the highest lattice energy and is more stable.
  • KF: Follows with a slightly larger distance of 252 pm.
  • NaCl: Comes next with a distance of 264 pm.
  • NaBr: Has the longest distance, 279 pm, resulting in the lowest lattice energy.
By comparing experimental lattice energies, predictions based on cation-anion distances confirm the inverse relationship between distance and lattice energy.
Ionic Radii
The ionic radii is the measure of an ion's size and plays a pivotal role in determining the distance between ions in an ionic lattice. Ionic radii enable us to predict and calculate the cation-anion distances, influencing both lattice energy and ionic bonding strength.
For instance, an element like lithium (Li鈦) has a smaller ionic radius (60 pm) compared to sodium (Na鈦, 97 pm), making LiCl have a shorter cation-anion distance than NaCl. Similarly, comparing halides, the fluoride ion (F鈦, 119 pm) is smaller than the bromide ion (Br鈦, 182 pm), resulting in variations in bond strength and lattice stability. Recognizing these radii helps in forming robust predictions in chemical behavior.
Ionic Bonds
Ionic bonds form when electrons transfer from one atom to another, especially between metals and nonmetals, leading to the formation of cations and anions. These bonds create the framework of ionic compounds.
The bond strength is governed mainly by the electrostatic forces between the differently charged ions. Key factors affecting ionic bonds include:
  • Charge Magnitude: Higher charges result in stronger bonds due to stronger attractions.
  • Distance Between Ions: As seen with cation-anion distance, shorter distances enhance bond strength.
Ionic bonds yield compounds like NaCl or KF with distinctive properties, such as high melting points and electrical conductivity in molten form. Understanding the nature of these bonds allows insights into the physical and chemical characteristics of ionic compounds.

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Most popular questions from this chapter

(a) Is lattice energy usually endothermic or exothermic? (b) Write the chemical equation that represents the process of lattice energy for the case of NaCl. (c) Would you expect salts like NaCl, which have singly charged ions, to have larger or smaller lattice energies compared to salts like CaO which are composed of doubly-charged ions?

Calculate the formal charge on the indicated atom in each of the following molecules or ions: (a) the central oxygen atom in \(\mathrm{O}_{3},\) (b) phosphorus in \(\mathrm{PF}_{6}^{-},(\mathbf{c})\) nitrogen in \(\mathrm{NO}_{2}\) (d) iodine in ICl_\(\mathrm{ICl}_{3},\) (e) chlorine in \(\mathrm{HClO}_{4}\) (hydrogen is bonded to \(\mathrm{O} )\)

There are many Lewis structures you could draw for sulfuric acid, \(\mathrm{H}_{2} \mathrm{SO}_{4}\) (each \(\mathrm{H}\) is bonded to an O). (a) What Lewis structure(s) would you draw to satisfy the octet rule? (b) What Lewis structure(s) would you draw to minimize formal charge?

(a) Draw the best Lewis structure(s) for the nitrite ion, NO \(_{2}^{-}\) (b) With what allotrope of oxygen is it isoelectonic? (c) What would you predict for the lengths of the bonds in \(\mathrm{NO}_{2}^{-}\) relative to \(\mathrm{N}-\mathrm{O}\) single bonds and double bonds?

In the following pairs of binary compounds, determine which one is a molecular substance and which one is an ionic substance. Use the appropriate naming convention (for ionic or molecular substances) to assign a name to each compound: (a) \(\mathrm{SiF}_{4}\) and \(\mathrm{LaF}_{3},(\mathbf{b}) \mathrm{FeCl}_{2}\) and \(\mathrm{ReCl}_{6},(\mathrm{c}) \mathrm{PbCl}_{4}\) and \(\mathrm{RbCl} .\)

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