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Chapter 8: Problem 6

Which has the greater bond lengths: \(\mathrm{NO}_{2}^{-}\) or \(\mathrm{NO}_{3}^{-} ?\) Explain.

Short Answer

Expert verified
The ion with greater bond lengths is \(\mathrm{NO}_{3}^{-}\). This is because the average bond order of nitrogen-oxygen bonds in \(\mathrm{NO}_{2}^{-}\) (1.5) is greater than that in \(\mathrm{NO}_{3}^{-}\) (1), and as bond order increases, bond length typically decreases.

Step by step solution

01

Examine the resonance structures of the ions

First, we will examine the resonance structures of \(\mathrm{NO}_{2}^{-}\) and \(\mathrm{NO}_{3}^{-}\) ions. This will help us understand the average bond order of nitrogen-oxygen bonds in these ions. In \(\mathrm{NO}_{2}^{-}\), the nitrogen has one single bond and one double bond with the two oxygen atoms. There are two resonance structures for this ion, where the double bond exists between the nitrogen and either of the oxygen atoms. In \(\mathrm{NO}_{3}^{-}\), the nitrogen atom has single bonds with all three oxygen atoms. The charges are distributed uniformly over all oxygen atoms. There are three resonance structures for this ion, where the single unpaired electron on one of the oxygens is delocalized.
02

Calculate the average bond order

The average bond order is the ratio of the total number of bonds between two atoms and the number of different resonance structures. To find the average bond order of nitrogen-oxygen bonds in the aforementioned ions, we need to divide the total number of bonds between nitrogen and oxygen atoms with the number of resonance structures. For \(\mathrm{NO}_{2}^{-}\): Average bond order = \( \frac{1 + 2}{2} = 1.5 \) For \(\mathrm{NO}_{3}^{-}\): Average bond order = \( \frac{1 + 1 + 1}{3} = 1 \)
03

Compare bond orders and bond lengths

With the bond order values calculated in the previous step, we can now make a comparison between the bond lengths of both ions. Typically, as bond order increases, the bond length decreases. Since the average bond order of nitrogen-oxygen bonds in \(\mathrm{NO}_{2}^{-} (1.5)\) is greater than that in \(\mathrm{NO}_{3}^{-} (1)\), the bond length in \(\mathrm{NO}_{2}^{-}\) is shorter than the bond length in \(\mathrm{NO}_{3}^{-}\). So, the ion with greater bond lengths is \(\mathrm{NO}_{3}^{-}\).

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Most popular questions from this chapter

Write Lewis structures and predict whether each of the following is polar or nonpolar a. \(\mathrm{HOCN}\) (exists as \(\mathrm{HO}-\mathrm{CN} )\) b. \(\mathrm{COS}\) c. \(\mathrm{XeF}_{2}\) d. \(\mathrm{CF}_{2} \mathrm{Cl}_{2}\) e. \(\mathrm{SeF}_{6}\) f. \(\mathrm{H}_{2} \mathrm{CO}(\mathrm{C} \text { is the central atom })\)

Write Lewis structures and predict the molecular structures of the following. (See Exercises 115 and 116.) a. \(\mathrm{OCl}_{2}, \mathrm{KrF}_{2}, \mathrm{BeH}_{2}, \mathrm{SO}_{2}\) b. \(\mathrm{SO}_{3}, \mathrm{NF}_{3}, \mathrm{IF}_{3}\) c. \(\mathrm{CF}_{4}, \mathrm{SeF}_{4}, \mathrm{KrF}_{4}\) d. \(\mathrm{IF}_{5}, \mathrm{AsF}_{5}\)

The standard enthalpies of formation for \(\mathrm{S}(g), \mathrm{F}(g), \mathrm{SF}_{4}(g),\) and \(\mathrm{SF}_{6}(g)\) are \(+278.8,+79.0,-775,\) and \(-1209 \mathrm{kJ} / \mathrm{mol}\) respectively. a. Use these data to estimate the energy of an \(\mathrm{S}-\) F bond. b. Compare your calculated value to the value given in Table \(8.5 .\) What conclusions can you draw? c. Why are the \(\Delta H_{f}^{\circ}\) values for \(\mathrm{S}(g)\) and \(\mathrm{F}(g)\) not equal to zero, since sulfur and fluorine are elements?

Predict the molecular structure (including bond angles) for each of the following. a. \(\mathrm{PCl}_{3}\) b. \(\mathrm{SCl}_{2}\) c. \(\mathrm{SiF}_{4}\)

Which of the following statements is(are) true? Correct the false statements. a. It is impossible to satisfy the octet rule for all atoms in \(\mathrm{XeF}_{2}\) . b. Because \(\mathrm{SF}_{4}\) exists, OF_ should also exist because oxygen is in the same family as sulfur. c. The bond in NO + should be stronger than the bond in \(\mathrm{NO}^{-}\). d. As predicted from the two Lewis structures for ozone, one oxygen-oxygen bond is stronger than the other oxygen-oxygen bond.
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