Calcium carbide reacts with $\mathrm{N}_{2}$ at high temperatures to yield compound $\mathbf{A}$. Hydrolysis of $\mathbf{A}$ produces an important pesticide intermediate $\mathbf{B}$. Under alkaline conditions, $\mathbf{B}$ polymerizes to form dimer $\mathbf{C}$. Heating $\mathbf{C}$ with dimethylamine hydrochloride and recrystallization yields $\mathbf{D}$. Reaction of $\mathbf{B}$ with sodium cyanide and chlorine under alkaline conditions gives the sodium salt $\mathbf{E}$. Researchers reacted $0.15\space\mathrm{g}\space\mathrm{Cu(NO_{3})_{2}{\cdot}6H_{2}O}$, $1.07\space\mathrm{g}\space \mathbf{E}$, and $0.52\space\mathrm{g}$ N,N-dimethylethylenediamine in an aqueous solution to obtain a dinuclear copper complex $\mathbf{F}$, with an experimentally determined copper mass fraction of $22.55\%$. X-ray diffraction data reveal that ligand $\mathbf{E}$ in $\mathbf{F}$ exhibits two distinct configurations—monodentate coordination and bridging coordination—in a 1:1 ratio, with both configurations utilizing the same coordinating atom.  

In the molecular structure of $\mathbf{F}$, how many bonds separate the two farthest N atoms along the shortest path?
电石高温下与 $\mathrm{N}_{2}$ 反应得到化合物$\mathbf{A}$，由$\mathbf{A}$水解得到一种重要的农药中间体$\mathbf{B}$，$\mathbf{B}$在碱性条件下发生聚合得到二聚体 $\mathbf{C}$。 $\mathbf{C}$ 与盐酸二甲胺加热反应，重结晶后得到$\mathbf{D}$。$\mathbf{B}$与氰化钠、氯气在碱性条件下反应可得到钠盐$\mathbf{E}$。研究者将 $0.15\space\mathrm{g}\space\mathrm{Cu(NO_{3})_{2}{\cdot}6H_{2 }O}$，$1.07\space\mathrm{g}\space \mathbf{E}$和$0.52\space\mathrm{g}$ N,N-二甲基乙二胺在水溶液中反应，得到一种双核铜配合物 $\mathbf{F}$ ，实验测得其中$\mathrm{Cu}$的质量分数为 $22.55\%$。晶体衍射数据表明，$\mathbf{F}$中配体$\mathbf{E}$存在两种不同的构型，分别对应于单齿配位和桥连配位，其数目比为$1:1$，两种构型的配体使用相同的配位原子。

在$\mathbf{F}$的分子中，最短路径上距离最远的两个N原子相距多少根键？
2
4
6
7
8
9
10
11
12
13
14
15
16
17
18
19
2
4
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Based on the properties and reactions, it is inferred that:

$\mathbf{A}:\mathrm{Ca\left(NCN\right)}$,

$\mathbf{B}:\mathrm{H_{2}NCN}$,

$\mathbf{E}:\mathrm{Na\left[N\left(CN\right)_{2}\right]}$.

<Checkpoint>[$\mathbf{E}:\mathrm{Na[N(CN)_{2}]}$](1)</Checkpoint>

and $\mathbf{C}:$
<MultiModal>![C(\N)NC(=N)N](/media/uploads/43c44587-34ee-4bc3-95b3-980722c61baa.png)</MultiModal>

$\mathbf{D}:$
<MultiModal>![CN(C)C(=N)NC(=N)N.Cl](/media/uploads/7dc7b253-5baf-48ea-ab61-0ff2705be752.png)</MultiModal>

The anion of $\mathbf{E}$ is abbreviated as dca, and N,N-dimethylethylenediamine is abbreviated as dmen.

The molar ratio is calculated as $\mathrm{Cu:dca:dmen=1:2:1}$

<Checkpoint>[$\mathrm{1:2:1}$](1)</Checkpoint>

Based on the mass fraction of copper, it is determined that $\mathbf{F}$ contains no water of crystallization,

<Checkpoint>[no water of crystallization](1)</Checkpoint>

hence the chemical formula of $\mathbf{F}$ can be inferred as $\mathrm{Cu\left[N\left(CN\right)_{2}\right]_{2}\left(C_{4}H_{12}N_{2}\right)}$

<Checkpoint>[$\mathrm{Cu\left[N\left(CN\right)_{2}\right]_{2}\left(C_{4}H_{12}N_{2}\right)}$](2)</Checkpoint>

$\mathbf{F}$ is a dimer, containing monodentate terminal and bridging $\mathrm{[N(CN)_2]^-}$ ligands. The two farthest N atoms originate from the two most distant N atoms on the monodentate ligands of the two Cu atoms.

The shortest path between the two farthest N atoms is: $\mathit{N}\mathrm{-C-N-C-N-Cu-N-C-N-C-N-Cu-N-C-N-C-}\mathit{N}$

<Checkpoint>[The farthest path is $\mathit{N}\mathrm{-C-N-C-N-Cu-N-C-N-C-N-Cu-N-C-N-C-}\mathit{N}$](2)</Checkpoint>

There are 17 atoms along this path, hence 16 bonds.

<Checkpoint>[The farthest distance is 16 bonds](1)</Checkpoint>
由性质和反应推断出

$\mathbf{A}:\mathrm{Ca\left(NCN\right)}$，

$\mathbf{B}:\mathrm{H_{2}NCN}$，

$\mathbf{E}:\mathrm{Na\left[N\left(CN\right)_{2}\right]}$。

<Checkpoint>[$\mathbf{E}:\mathrm{Na[N(CN)_{2}]}$](1)</Checkpoint>

以及$\mathbf{C}:$
<MultiModal>![C(\N)NC(=N)N](/media/uploads/43c44587-34ee-4bc3-95b3-980722c61baa.png)</MultiModal>

$\mathbf{D}:$
<MultiModal>![CN(C)C(=N)NC(=N)N.Cl](/media/uploads/7dc7b253-5baf-48ea-ab61-0ff2705be752.png)</MultiModal>

将$\mathbf{E}$的阴离子简写作dca，N,N-二甲基乙二胺简写作dmen，

计算摩尔比为$\mathrm{Cu:dca:dmen=1:2:1}$

<Checkpoint>[$\mathrm{1:2:1}$](1)</Checkpoint>

根据铜的质量分数确定$\mathbf{F}$中不含结晶水，

<Checkpoint>[不含结晶水](1)</Checkpoint>

因此可推断出$\mathbf{F}$的化学式为$\mathrm{Cu\left[N\left(CN\right)_{2}\right]_{2}\left(C_{4}H_{12}N_{2}\right)}$

<Checkpoint>[$\mathrm{Cu\left[N\left(CN\right)_{2}\right]_{2}\left(C_{4}H_{12}N_{2}\right)}$](2)</Checkpoint>

$\mathbf{F}$为二聚体，含有单齿端基和桥连的$\mathrm{[N(CN)_2]^-}$，距离最远的两个N原子来自两个Cu原子的单齿配体上的两个最远端N。

距离最远的两个N原子之间的最短路径为：$\mathit{N}\mathrm{-C-N-C-N-Cu-N-C-N-C-N-Cu-N-C-N-C-}\mathit{N}$

<Checkpoint>[距离最远的路径为$\mathit{N}\mathrm{-C-N-C-N-Cu-N-C-N-C-N-Cu-N-C-N-C-}\mathit{N}$](2)</Checkpoint>

该路径上有17个原子，因此有16根键

<Checkpoint>[最远距离为16根键](1)</Checkpoint>