Number of hydrogen molecules necessary in acetonitrile/butanediamine polymerisation [closed]








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The beginning of the picture, from the word 'Acrylonitril' to the word 'structuurformule:', means the following: *Acrylotitrile reacts with 1,4-butanediamine. When you use a lot of acrylonitrile, under certain circumstances you almost exclusively get the following:* Then you can see the first of the 2 structural formulas. The text between the 2 structural formulas, says *This 'bond' can react with hydrogen. You'll get addition. When this addition finished, you get a bond with the following structural formula:* And then you see the picture. The final blob of text: *We can make polymer molecules which keep branching on and on because of reactions with hydrogen and acrylonitrile.*


The final question is: *We start with 1 molecule of 1,4-butanediamine. Explain how many molecules of hydrogen are needed to make a polymer molecule with 16 $\ce{NH2}$ groups, assume that all reactions are complete.*


The answer should be 56, but I have no clue why, can someone explain? I have half of 56, I just did 14x2, because you get 2 $\ce{H2}$ molecules per added acrylonitrile, and you have to get 14 acrylonitrile molecules to get to 16 $\ce{NH2}$ groups, so that would equal 2x14=28.


![enter image description here](https://i.stack.imgur.com/CJR0v.gif)




This question appears to be about the preparation of polyacrylonitrile dendrimers. Each addition of acrylonitrile completely reacts away the NH2 groups previously present:



> 
> assume that all reactions are complete. 
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Your answer of 28 assumes that the reactions could be controllable to allow partial consumption of NH2 groups, which requires less addition of acrylonitrile and fewer equivalents of H2. 
You need 16 NH2 groups, which is 8 on each side. This is the third generation dendrimer: 


* Generation 0 is butanediamine (2 NH2 groups). Let $G\_n$ represent the interior region of the $n^{th}$ generation. 
$$\ce{NH2CH2CH2CH2NH2} \equiv \ce{NH2}G\_0\ce{NH2}$$
* Generation 1 involves reaction of 4 acrylonitriles followed by 8 molecules of hydrogen to make 4 NH2 groups.
$$\ce{NH2}G\_0\ce{NH2 +4CH2=CHCN->(NCCH2CH2)2N}G\_0\ce{N(CH2CH2CN)2} $$
$$\ce{(NCCH2CH2)2N}G\_0\ce{N(CH2CH2CN)2 +8H2-> (NH2CH2CH2CH2)2N}G\_0\ce{N(CH2CH2CH2NH2)2} \equiv \ce{(NH2)2}G\_1\ce{(NH2)2} $$
* Generation 2 involves reaction of 8 acrylonitriles followed by 16 molecules of hydrogen to make 8 NH2 groups.
$$ \ce{(NH2)2}G\_1\ce{(NH2)2 +8CH2=CHCN-> [(NCCH2CH2)2N]2}G\_1\ce{[N(CH2CH2CN)2]2} $$
$$\ce{[(NCCH2CH2)2N]2}G\_1\ce{[N(CH2CH2CN)2]2 +16H2 -> [(NH2CH2CH2CH2)2N]2}G\_1\ce{[N(CH2CH2CH2NH2)2]2} \equiv \ce{(NH2)4}G\_2\ce{(NH2)4}$$
* Generation 3 involves reaction of 16 acrylonitriles followed by 32 molecules of hydrogen to make 8 NH2 groups.
$$ \ce{(NH2)4}G\_2\ce{(NH2)4 +16CH2=CHCN-> [(NCCH2CH2)2N]4}G\_2\ce{[N(CH2CH2CN)2]4} $$
$$\ce{[(NCCH2CH2)2N]4}G\_2\ce{[N(CH2CH2CN)2]4 +32H2 -> [(NH2CH2CH2CH2)2N]4}G\_2\ce{[N(CH2CH2CH2NH2)2]4} \equiv \ce{(NH2)8}G\_3\ce{(NH2)8}$$



> 
> Total number of H2 molecules = 8 + 16 + 32 = 56 starting at $G\_0$. 
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