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

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.

## closed as off-topic by Klaus-Dieter Warzecha, ron, jerepierre, user467, Martin - マーチン♦Feb 25 '15 at 2:43

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• no, there isn’t… I also think your chance of getting an answer rapidly depends on question clarity and formatting, and this question isn't very attractive. You've dumped your question as a big image with non-English text, provided piecewise translation above it making it hard to read through, and it's not much chemistry as counting atoms… – F'x Oct 29 '12 at 23:15
• Even though I provided an answer, I agree with @F'x. If I was not already familiar with this dendrimer system, this question would have been very challenging. – Ben Norris Oct 30 '12 at 17:12

• 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 $G_0$.