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Chapter 8: Problem 81

An ionic substance of formula MX has a lattice energy of \(6 \times 10^{3} \mathrm{k} \mathrm{J} / \mathrm{mol}\). Is the charge on the ion \(\mathrm{M}\) likely to be \(1+\), \(2+\) or \(3+?\) Explain your reasoning.

Short Answer

Expert verified
The charge on the ion M in the ionic compound MX is most likely 2+. The given lattice energy of \(6 \times 10^3 kJ/mol\) is a moderate value, which suggests that the charge on M should be 2+ according to Coulomb's Law.

Step by step solution

01

Understanding lattice energy and its trend

Lattice energy is the energy required to break one mole of an ionic compound into its separate gaseous ions. Lattice energy increases with the charge of the ions and decreases with the increase in the size of the ions. The relationship between lattice energy, charge, and size of ions can be described by Coulomb's law. In this case, we are given the lattice energy, and we need to determine the charge on the ion M.
02

Coulomb's Law

Coulomb's law states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. In the context of lattice energy in ionic compounds, this can be written as: \(E_{lattice} = k \frac{Q_1Q_2}{r}\) where \(E_{lattice}\) is the lattice energy, \(Q_1\) and \(Q_2\) are the charges of the ions, r is the distance between the ions, and k is a proportionality constant.
03

Comparing lattice energies for different charges

Now let's analyze the lattice energy trend with respect to the charges of the ions. Suppose we have three ionic compounds: MX, M₂X, and M₃X, where M represents the ion with charges 1+, 2+, and 3+ respectively, and X is a constant ion. Using Coulomb's law and assuming that the distance between the ions and the constant k are equal in all three cases, we can compare the lattice energies of the three ionic compounds as follows: • For MX (M with a charge of 1+), the lattice energy would be proportional to \(1 \times Q_2\) • For M₂X (M with a charge of 2+), the lattice energy would be proportional to \(2 \times Q_2\) • For M₃X (M with a charge of 3+), the lattice energy would be proportional to \(3 \times Q_2\)
04

Analyzing the given lattice energy

The given lattice energy is \(6 \times 10^3 kJ/mol\). Comparing this value to the lattice energy trend we analyzed in the previous step, we can make some predictions: • If M has a charge of 1+, the lattice energy of MX should be relatively low • If M has a charge of 2+, the lattice energy of MX should be moderate • If M has a charge of 3+, the lattice energy of MX should be relatively high
05

Predicting the charge on M

Based on our analysis of the lattice energy trend and the given lattice energy, we can now say that the charge on the ion M in the ionic compound MX is most likely 2+. The reason for this conclusion is that the given lattice energy of \(6 \times 10^3 kJ/mol\) is a moderate value, which suggests that the charge on M should be 2+ according to Coulomb's Law. So the charge on the ion M is likely to be 2+.

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Most popular questions from this chapter

Barium azide is \(62.04 \% \mathrm{Ba}\) and \(37.96 \% \mathrm{~N}\). Each azide ion has a net charge of \(1-\) (a) Determine the chemical formula of the azide ion. (b) Write three resonance structures for the azide ion. (c) Which structure is most important? (d) Predict the bond lengths in the ion.

Consider the following statement: "For some molecules and ions, a Lewis structure that satisfies the octet rule does not lead to the lowest formal charges, and a Lewis structure that leads to the lowest formal charges does not satisfy the octet rule." Illustrate this statement using the hydrogen sulfite ion, \(\mathrm{HSO}_{3}^{-}\), as an example (the \(\mathrm{H}\) atom is bonded to one of the \(\mathrm{O}\) atoms).

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(a) Triazine, \(\mathrm{C}_{3} \mathrm{H}_{3} \mathrm{~N}_{3}\), is like benzene except that in triazine every other \(\mathrm{C}-\mathrm{H}\) group is replaced by a nitrogen atom. Draw the Lewis structure(s) for the triazine molecule. (b) Estimate the carbon-nitrogen bond distances in the ring.

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