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Chapter 8: Problem 2

Illustrated are four ions \(-\mathrm{A}, \mathrm{B}, \mathrm{X},\) and \(\mathrm{Y}-\) showing their relative ionic radii. The ions shown in red carry positive charges: \(2+\) charge for \(A\) and a \(1+\) charge for \(B\). Ions shown in blue carry negative charges: a 1 - charge for \(\mathrm{X}\) and a 2 - charge for \(\mathrm{Y}\). (a) Which combinations of these ions produce ionic compounds where there is a 1:1 ratio of cations and anions? (b) Among the combinations in part (a), which leads to the ionic compound having the largest lattice energy? (c) Which combination of ions leads to the ionic compound having the smallest lattice energy? [Section 8.2\(]\)

Short Answer

Expert verified
(a) The combinations of ions that produce ionic compounds in a 1:1 ratio of cations to anions are AY and BX. (b) The combination with the largest lattice energy is AY, as it has a higher product of charges. (c) The combination with the smallest lattice energy is BX, as it has a smaller product of charges.

Step by step solution

01

(a) Finding ionic compounds in 1:1 ratio

To find the combinations of ions that produce a 1:1 ratio, we need to match the positive charges of the cations with the negative charges of the anions, resulting in a net zero charge. This can be done as follows: 1. Ion A has a charge of +2, so it can be paired with ion Y, which has a charge of -2. Thus, one possible combination is: AY 2. Ion B has a charge of +1, so it can be paired with ion X, which has a charge of -1. The second possible combination is: BX These combinations result in a net charge of zero and a 1:1 ratio of cations to anions.
02

(b) Finding the combination with the largest lattice energy

Recall that lattice energy increases as the ionic charges increase and as the ionic radii decrease. To find the combination with the largest lattice energy among AY and BX, let's consider their charges and radii. 1. AY: Ion A has a charge of +2 and ion Y has a charge of -2, giving a product of charges of +4. 2. BX: Ion B has a charge of +1 and ion X has a charge of -1, giving a product of charges of -1. Comparing these, the combination AY has a higher product of charges and so it has the largest lattice energy among the two ionic compounds.
03

(c) Finding the combination with the smallest lattice energy

Since we already know that the ionic compound AY has the largest lattice energy, it implies that the ionic compound BX will have the smallest lattice energy, as it has the smaller product of charges between the two.

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Most popular questions from this chapter

(a) Does the lattice energy of an ionic solid increase or decrease (i) as the charges of the ions increase, (ii) as the sizes of the ions increase? (b) Arrange the following substances not listed in Table 8.2 according to their expected lattice energies, listing them from lowest lattice energy to the highest: \(\mathrm{MgS}, \mathrm{KI}\), \(\mathrm{GaN}, \mathrm{L} \mathrm{iBr}\)

(a) What is the octet rule? (b) How many electrons must a sulfur atom gain to achieve an octet in its valence shell? (c) If an atom has the electron configuration \(1 s^{2} 2 s^{2} 2 p^{3},\) how many electrons must it gain to achieve an octet?

(a) Write the chemical equations that are used in calculating the lattice energy of \(\mathrm{SrCl}_{2}(s)\) via a Born-Haber cycle. (b) The second ionization energy of \(\operatorname{Sr}(g)\) is \(1064 \mathrm{~kJ} / \mathrm{mol}\). Use this fact along with data in Appendix \(\mathrm{C}\), Figure 7.9 , Figure \(7.11,\) and Table 8.2 to calculate \(\Delta H_{f}^{\circ}\) for \(\operatorname{Sr} \mathrm{Cl}_{2}(s)\)

Predict the chemical formula of the ionic compound formed between the following pairs of elements: (a) \(\mathrm{Al}\) and \(\mathrm{F}\), (b) \(\mathrm{K}\) and \(\mathrm{S},(\mathrm{c}) \mathrm{Y}\) and \(\mathrm{O},\) (d) \(\mathrm{Mg}\) and \(\mathrm{N}\).

(a) Using average bond enthalpies, predict which of the following reactions will be most exothermic: (i) \(\mathrm{C}(g)+2 \mathrm{~F}_{2}(g) \longrightarrow \mathrm{CF}_{4}(g)\) (ii) \(\mathrm{CO}(g)+3 \mathrm{~F}_{2} \longrightarrow \mathrm{CF}_{4}(g)+\mathrm{OF}_{2}(g)\) (iii) \(\mathrm{CO}_{2}(g)+4 \mathrm{~F}_{2} \longrightarrow \mathrm{CF}_{4}(g)+2 \mathrm{OF}_{2}(g)\) (b) Explain the trend, if any, that exists between reaction exothermicity and the extent to which the carbon atom is bonded to oxygen.
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