Question 10.14: Estimating Bond Lengths Provide the best estimate you can of...
Estimating Bond Lengths
Provide the best estimate you can of these bond lengths for the (a) the nitrogen-to-hydrogen bonds in NH_3: (b) the bromine-to-chlorine bond in BrCl.
Analyze
If no bond length is listed for a particular bond, \begin{matrix} A-B \end{matrix}, then look up the bond lengths for \begin{matrix} A-A \end{matrix} and \begin{matrix} B-B \end{matrix}. The \begin{matrix} A-B \end{matrix} bond length can then be estimated as one-half the \begin{matrix} A-A \end{matrix} bond length plus one-half the \begin{matrix} B-B \end{matrix} bond length.
(a) The Lewis structure of ammonia (page 400) shows the nitrogen-to-hydrogen bonds as single bonds. The value listed in Table 10.2 for the \begin{array}{r c} \begin{matrix} N-H \end{matrix} \end{array} bond is 100 pm, so this is the value we would predict. (The measured \begin{matrix} N-H \end{matrix} bond length in NH_3 is 101.7 pm.)
| TABLE 10.2 Some Average Bond Lengths^a | |||||
| Bond | Bond Length, pm | Bond | Bond Length, pm | Bond | Bond Length, pm |
| \begin{array}{r c} \begin{matrix} H-H \end{matrix} \end{array} | 74.14 | \begin{array}{r c} \begin{matrix} C-C \end{matrix} \end{array} | 154 | \begin{array}{r c} \begin{matrix} N-N \end{matrix} \end{array} | 145 |
| \begin{array}{r c} \begin{matrix} H-C \end{matrix} \end{array} | 110 | \begin{array}{r c} \begin{matrix} C=C \end{matrix} \end{array} | 134 | \begin{array}{r c} \begin{matrix} N=N \end{matrix} \end{array} | 123 |
| \begin{array}{r c} \begin{matrix} H-N \end{matrix} \end{array} | 100 | \begin{array}{r c} \begin{matrix} C \equiv C \end{matrix} \end{array} | 120 | \begin{array}{r c} \begin{matrix} N \equiv N \end{matrix} \end{array} | 109.8 |
| \begin{array}{r c} \begin{matrix} H-O \end{matrix} \end{array} | 97 | \begin{array}{r c} \begin{matrix} C-N \end{matrix} \end{array} | 147 | \begin{array}{r c} \begin{matrix} N-O \end{matrix} \end{array} | 136 |
| \begin{array}{r c} \begin{matrix} H-S \end{matrix} \end{array} | 132 | \begin{array}{r c} \begin{matrix} C=N \end{matrix} \end{array} | 128 | \begin{array}{r c} \begin{matrix} N=O \end{matrix} \end{array} | 120 |
| \begin{array}{r c} \begin{matrix} H-F \end{matrix} \end{array} | 91.7 | \begin{array}{r c} \begin{matrix} C \equiv N \end{matrix} \end{array} | 116 | \begin{array}{r c} \begin{matrix} O-O \end{matrix} \end{array} | 145 |
| \begin{array}{r c} \begin{matrix} H-Cl \end{matrix} \end{array} | 127.4 | \begin{array}{r c} \begin{matrix} C-O \end{matrix} \end{array} | 143 | \begin{array}{r c} \begin{matrix} O=O \end{matrix} \end{array} | 121 |
| \begin{array}{r c} \begin{matrix} H-Br \end{matrix} \end{array} | 141.4 | \begin{array}{r c} \begin{matrix} C=O \end{matrix} \end{array} | 120 | \begin{array}{r c} \begin{matrix} F-F \end{matrix} \end{array} | 143 |
| \begin{array}{r c} \begin{matrix} H-I \end{matrix} \end{array} | 160.9 | \begin{array}{r c} \begin{matrix} C-Cl \end{matrix} \end{array} | 178 | \begin{array}{r c} \begin{matrix} Cl-Cl \end{matrix} \end{array} | 199 |
| \begin{array}{r c} \begin{matrix} Br-Br \end{matrix} \end{array} | 228 | ||||
| \begin{array}{r c} \begin{matrix} I-I \end{matrix} \end{array} | 266 | ||||
_{}^{a}\textrm{Most} values (\begin{matrix} C-H \end{matrix}, \begin{matrix} N-H \end{matrix}, \begin{matrix} C-H \end{matrix} and so on) are averaged over a number of species containing the indicated bond and may vary by a few picometers. Where a diatomic molecule exists, the value given is the actual bond length in that molecule (H_2 , N_2 , HF, and so on) and is known more precisely.
(b) There is no bromine-to-chlorine bond length in Table 10.2, so we need to calculate an approximate bond length using the relationship between bond length and covalent radii. BrCl contains a \begin{matrix} Br-Cl \end{matrix} single bond [imagine substituting one Br atom for one Cl atom in structure (10.4)]. The length of the \begin{matrix} Br-Cl \end{matrix} bond is one-half the \begin{matrix} Cl-Cl \end{matrix} bond length plus one-half the \begin{matrix} Br-Br \end{matrix} bond length: \left(\frac{1}{2} \times 199 pm \right) + \left(\frac{1}{2} \times 228 pm \right) = 214 pm. (The measured bond length is 213.8 pm.)
Assess
The data in Table 10.2 can be used to make estimates of bond lengths in a variety of molecules.