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Hydrogenation of poly(butadiene) converts both cis and trans isomers to the same linear structure, and vinyl groups to ethyl branches. A poly(butadiene) sample of molecular weight 168,000 g/mol was found by infrared spectroscopy to contain double bonds consisting of 47.2% cis, 44.9% trans, and 7.9% vinyl.
After hydrogenation, what is the average number of backbone carbon atoms between ethyl side chains?

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Answer:

The average number is given as 48.6

Explanation:

From the question we see that the

                    Percentage of cis = 47.2%

                    Percentage of trans = 44.9%

                    Percentage of  vinyl = 7.9%

The chemical  reaction equation for the hydrogenation of polybutadiene is shown on the first uploaded image

    To obtain the average number of  backbone carbon between the ethyl side chains ,we divide the total number of carbon on the backbone by the total number of ethyl group

              That is

                             = (44.9% × 4 + 47.2% ×4 + 7.9% × 2) ÷(7.9% × 1)

                             = (384.2%/7.7%)

                              = 48.6

Note :  The percentage will cancel out

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