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SPECTRA PROBLEM #8 SOLUTION Summary.... Altogether....
We have :  -CO2-, -CH2-CH2-CH3, and HC=CH2
IR and 13C suggest an ester so we have : RCO2R' 
The key is to sort out which group is connected to the carbonyl C=O and which is connected to the -O- of the ester.... 
The -CH2- at 2.4 ppm is not deshielded enough to be -OCH2- (nearer to 4 ppm), so we must have CH3-CH2-CH2-C=O and O-HC=CH2 these connect to give the answer.
vinyl butanoate
vinyl butanoate
or
ethenyl butanoate