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How could IR spectroscopy distinguish between
$C{H_3}C{H_2}CH = CHC{H_3}$ and $C{H_3}C{H_2}CH \equiv CC{H_3}$

Answer
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Hint: When we look at both the compounds we can infer that one contains double bond and other has triple bond in an alkyl carbon chain, which makes us easier to identify compounds as an alkene and alkynes.

Complete answer:
We need to know that alkene $\left( {C = C} \right)$ stretches appear around \[1660c{m^{ - 1}}\], and are of either weak or medium intensity. If you’re unsure whether a small blip in that region of the spectrum represents an alkene, you can look for the unsaturated hydrogen stretches $\left( {C = C - H} \right)$ above \[{\text{ 3}}000c{m^{ - 1}}\]. Typically, these are of medium intensity. Drawing a line down the spectrum at \[{\text{ 3}}000c{m^{ - 1}}\] is often a good idea. Any stretches slightly higher than that frequency are a good indication of having an alkene (or an aromatic ring).Alkynes (carbon-carbon triple bonds) have absorptions between $2,100$ and $2,250c{m^{ - 1}}$, and are of medium intensity. A terminal alkyne (one at the end of a chain) is easy to spot because of the high-intensity alkynyl $C - H$ stretch that comes at around $3,300c{m^ - }$.
The ranges in the IR spectrum are different for alkenes and alkynes. Alkynes have characteristic IR absorbance peaks in the range of $2,100$ and $2,250c{m^{ - 1}}$ due to stretching of the carbon-carbon triple bond, and terminal alkenes can be identified by their absorbance at about\[{\text{3}}000c{m^{ - 1}}\], due to stretching of the bond between the sp-hybridized carbon and the terminal hydrogen.

Note:
We have to know that there are many chemical methods in labs to distinguish between alkene and alkynes. Out of which one of bromine reacts with alkene and alkynes and not alkanes. Since both alkene and alkyne are unsaturated compounds, an unsaturation test can also be performed which shows positive results for alkene and alkyne and negative for alkane.