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Chapter 8: Problem 81

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

Short Answer

Expert verified
It is most likely that the charge on the ion M is 2+ because, among the possible charge combinations, this one yields the best match to the given lattice energy of \(6 \times 10^3 k / mol\).

Step by step solution

01

Consider the proportional factor of the lattice energy

The formula for lattice energy is given by: \[E_{L} \propto \frac{Q_1 Q_2}{r}\] where \(E_{L}\) is the lattice energy, \(Q_1\) and \(Q_2\) are the charges of the two ions, and \(r\) is the distance between the ions.
02

Determine the possible charge combinations for MX

We need to consider the possible combinations of charges for the M and X ions in the compound MX. According to the question, M can be 1+, 2+, or 3+. Since we have assumed that the formula for the substance is MX, the charge on X must be equal but opposite in sign to the charge on M. Therefore, the possible combinations are: 1. M(1+) and X(1-) 2. M(2+) and X(2-) 3. M(3+) and X(3-)
03

Find the proportional factor of the lattice energy for each charge combination

Now, we need to calculate the proportional factor of the lattice energy for each charge combination: 1. For M(1+) and X(1-): \(\frac{(1)(-1)}{r} = -\frac{1}{r}\) 2. For M(2+) and X(2-): \(\frac{(2)(-2)}{r} = -\frac{4}{r}\) 3. For M(3+) and X(3-): \(\frac{(3)(-3)}{r} = -\frac{9}{r}\)
04

Compare the proportional factors to the given lattice energy

The given lattice energy is \(6 \times 10^3 k / mol\). Since we know lattice energy is directly proportional to the product of the charges of the ions, we can compare the proportional factors we calculated in step 3 to the given lattice energy. Considering the proportional factors calculated in Step 3, we find that: 1. For M(1+) and X(1-): Proportional factor is -1. Thus, the lattice energy is too high for this combination. 2. For M(2+) and X(2-): Proportional factor is -4. It is closer to the given lattice energy. Hence, it is more likely. 3. For M(3+) and X(3-): Proportional factor is -9. In this case, the lattice energy seems to be too low compared to the given value. Based on this comparison:
05

Conclude the charge on the ion M

It is most likely that the charge on the ion M is 2+ because, among the possible charge combinations, this one yields the best match to the given lattice energy of \(6 \times 10^3 k / mol\).

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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 8.1 according to their expected lattice energies, listing them from lowest lattice energy to the highest: MgS, Ki, GaN, LiBr.

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?

(a) Draw the dominant Lewis structure for the phosphorus trifluoride molecule, PF \(_{3}\) . (b) Determine the oxidation numbers of the \(P\) and \(F\) atoms. (c) Determine the formal charges of the \(P\) and \(F\) atoms.

(a) Using Lewis symbols, diagram the reaction between magnesium and oxygen atoms to give the ionic substance MgO. (b) How many electrons are transferred? (c) Which atom loses electrons in the reaction?

(a) What is the trend in electronegativity going from left to right in a row of the periodic table? (b) How do electronegativity values generally vary going down a column in the periodic table? (c) True or false: The most easily ionizable elements are the most electronegative.
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