Based on Lewis structures, predict the ordering, from shortest to longest, of \(N-O\) bond lengths in \(N O^{+}, N O_{2}^{-},\) and \(N O_{3}^{-} .\)

Short Answer

Expert verified
The N-O bond lengths are ordered as NO₊ < NO₂⁻ < NO₃⁻ (from shortest to longest), based on their Lewis structures and corresponding bond orders of 2, 1.5, and approximately 1.33, respectively.

Step by step solution

01

Draw the Lewis structures for NO₊, NO₂⁻, and NO₃⁻

First, we'll draw the Lewis structures for each molecule/ion: 1. NO₊: Nitrogen (N) has 5 valence electrons, and oxygen (O) has 6 valence electrons. In NO₊, the molecule has a +1 charge overall, meaning it loses 1 electron. Thus, there are a total of 10 (5+6-1) valence electrons available. Nitrogen forms a double bond with oxygen, and both atoms have complete octets. 2. NO₂⁻: Nitrogen (N) has 5 valence electrons, and each of the two oxygen atoms (O) has 6 valence electrons. In NO₂⁻, the molecule has a -1 charge overall, meaning it gains one electron. Thus, there are a total of 18 (5+2×6+1) valence electrons available. Nitrogen forms a single bond with one oxygen and a double bond with the other oxygen, and all atoms have complete octets. 3. NO₃⁻: Nitrogen (N) has 5 valence electrons, and each of the three oxygen atoms (O) has 6 valence electrons. In NO₃⁻, the molecule has a -1 charge overall, meaning it gains one electron. Thus, there are a total of 24 (5+3×6+1) valence electrons available. Nitrogen forms a double bond with one oxygen and a single bond with the other two oxygen atoms, and all atoms have complete octets.
02

Determine the bond orders for N-O bonds in each molecule/ion

Now, let's determine the bond order for each N-O bond in these molecules/ions: 1. NO₊: N forms a double bond with O; bond order is 2. 2. NO₂⁻: N forms one single bond with O and one double bond with O; average bond order is (1+2)/2 = 1.5. 3. NO₃⁻: N forms one double bond with O and two single bonds with O; average bond order is (2+1+1)/3 = 4/3 ≈ 1.33.
03

Order the N-O bond lengths based on bond order

As a general rule, a higher bond order implies a shorter bond length. With the bond orders calculated in Step 2, we can now order the N-O bond lengths from shortest to longest: 1. NO₊ (bond order = 2) - shortest bond length 2. NO₂⁻ (bond order = 1.5) 3. NO₃⁻ (bond order ≈ 1.33) - longest bond length Therefore, the N-O bond lengths are ordered as NO₊ < NO₂⁻ < NO₃⁻ (from shortest to longest).

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