NaCl has a lattice energy of -787 kJ/mol. Consider a hypothetical salt XY. X 3+ has the same radius of Na + and Y 3- has the same radius as Cl - . Estimate the lattice energy of XY.

Welcome back everyone in this example we have two unknown salts A. B. And C. D. The radius of Catalan A. Is equal to the Caspian sea two plus and the radius of the an ion B minus is equal to the radius of an eye on D three minus, determine the lattice energy of salt C. D. If it was found that the lattice energy of salt A. B. Is negative 4 56 kg jewels Permal. So we want to recall that our symbol for lattice energy is this use symbol here and is expressed in units of jewels or kilo jewels. And this is Permal. So it's important that they mention that these are salts because we recall that salts are ionic compounds or ionic solids. And we would recall our definition for lattice energy which is going to be the entropy change when one mole and sorry about that. So when one mole of a ionic solid, A. K. A crystalline lattice or crystalline solid is formed from its constituent gaseous ions at standard conditions. So at standard temperature and pressure. And this should say an we also should recall that lattice energy is found by taking the force that is required to pull these ions together from infinity and is typically expressed in units of newtons. And this is multiplied by the distance between these ions, which is typically in units of meters. And when it comes to force, we want to recall columns law. So we can integrate this with our understanding of lattice energy by saying that our lattice energy is equal to columns law. Which we should recall is where force is equal to columns constant K. Multiplied by the charge of particle one by times the charge of particle to and divided by the radius squared. So the radius of our ions here. And this is all still multiplied by distance because we're integrating this in our formula for lattice energy, recall that for columns constant K. Here the units are going to be jewels times meters divided by columns squared. And that's how we end up with units of jewels for our lattice energy. And so we can simplify this to say that our lattice energy is equal to columns constant times the charge of particle one times the charge of particle two divided by our distance between our ions. And so according to the prompt, we're told that our lattice energy for salt A. B. Is equal to negative 4 56 kg jewels per mole. And so when we think of the ions making up the salt, we have the ape plus one ion and the B minus one ion. And so the product of these two charges would be plus one times negative one. And that would give us just negative one. Since this charge is pretty low there shouldn't be too much force needed to bring these two ions to form A. And B. Together. On the other hand we have salt C. D. And according to the prompt we have the carry on C. Two plus and the an ion D. Three minus. So to bring these two ions together we're gonna find their product. And so we have the plus two charge multiplied by the minus three charge. And that would give us minus six. And based on that value here we would say we have a large amount of force required to bring these ions together. And that means that therefore our salt C. D. Should have a high lattice energy value versus our salt A. B. Which had just a charge of minus one overall which is a much lower amount of force required to bring these ions together. And if we know the lattice energy of salt A. B. And we know that the lattice energy of salt C. D. Should be large. We would say that the lattice energy of salt C. D. Is just going to be the lattice energy of salt A. B. Negative 4 56. Kill it jules Permal. And then we would just multiply it by the product of the charges for salt C. D. Which we said is negative six. And that would give us our lattice energy of salt C. D. Equal to a value of negative 2736 kg joules per mole. So this is actually going to be our final answer here for our lattice energy of salt C. D. And we see it's a much more negative value here versus our value given in the prompt for salt A. B. And that means that we have more energy released when the ions of salt C. D. Form our compound C. D. As assault. And so what's highlighted in yellow here is our final answer. I hope that everything I went through is clear, but if you have any questions just leave them down below and I will see everyone in the next practice video.

Ch.10 - Chemical Bonding I: The Lewis Model

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Ch.10 - Chemical Bonding I: The Lewis Model

Problem 94

Chapter 10, Problem 94

NaCl has a lattice energy of -787 kJ/mol. Consider a hypothetical salt XY. X³⁺ has the same radius of Na⁺ and Y^3- has the same radius as Cl^-. Estimate the lattice energy of XY.

Verified step by step guidance

insert step 1: Understand the concept of lattice energy, which is the energy required to separate one mole of an ionic solid into its gaseous ions. It is influenced by the charges of the ions and the distance between them.

insert step 2: Recognize that the lattice energy is proportional to the product of the charges of the ions and inversely proportional to the distance between them. This can be expressed as: \( U \propto \frac{q_1 \cdot q_2}{r} \), where \( q_1 \) and \( q_2 \) are the charges of the ions, and \( r \) is the distance between the ions.

insert step 3: Compare the charges of the ions in NaCl and XY. In NaCl, Na+ has a charge of +1 and Cl- has a charge of -1. In XY, X3+ has a charge of +3 and Y3- has a charge of -3.

insert step 4: Calculate the ratio of the product of the charges for XY to that of NaCl. For NaCl, the product is \( (+1) \times (-1) = -1 \). For XY, the product is \( (+3) \times (-3) = -9 \). The ratio is \( \frac{-9}{-1} = 9 \).

insert step 5: Estimate the lattice energy of XY by multiplying the lattice energy of NaCl by the ratio of the charge products. Since the lattice energy of NaCl is -787 kJ/mol, the estimated lattice energy of XY would be \( -787 \times 9 \) kJ/mol.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Lattice Energy

Lattice energy is the amount of energy released when gaseous ions combine to form an ionic solid. It is a measure of the strength of the forces between the ions in an ionic compound. A more negative lattice energy indicates a more stable ionic compound, as it reflects stronger ionic interactions. The lattice energy can be estimated using the charges and sizes of the ions involved.

Ionic Radii

Ionic radii refer to the effective size of an ion in a crystal lattice. The size of an ion affects the distance between ions in the lattice, which in turn influences the lattice energy. For example, smaller ions can pack more closely together, leading to stronger electrostatic attractions and higher lattice energy. Understanding the ionic radii of the ions involved is crucial for estimating lattice energy.

Coulomb's Law

Coulomb's Law describes the electrostatic interaction between charged particles. It states that the force between two charged ions is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. This principle is fundamental in calculating lattice energy, as it helps to quantify the strength of the ionic bonds based on the charges and distances of the ions in the lattice.