How do you show that glucose contains a linear chain of six carbon atoms?

Hint: To answer this question we must have the knowledge of structure elucidation for determining the structure of glucose. It means performing chemical reactions on the molecule to find out its structure. Glucose has 6 carbons in its structure.

Complete step by step answer:
Structure elucidation is the process by which one can obtain the structure of any chemical compound by performing a number of chemical reactions to find the presence of a functional group, number of carbon, saturation or unsaturation in compounds.
To show the presence of number of carbon in glucose and has a linear chain, we can perform the following reaction:
When glucose reacts with \[{\text{HI}}\] and red phosphorus it forms 2-iodo Hexane. If we do reduction of 2-iodo Hexane we get n-Hexane. \[{\text{HI}}\] And red phosphorus acts as reducing agents. The formation of hexane indicates that a linear chain must be present in glucose. Also hexane has 6 carbon in it so glucose must also have 6 carbons because we haven’t added any carbon based reagent.
We can do another reaction for confirmation. When we oxidize the glucose with bromine water it forms gluconic acid which upon reduction with \[{\text{HI}}\] and red phosphorus gives n-hexanoic acid.
Glucose reacts with \[{\text{HCN}}\] to form cyanohydrin. When we do hydrolysis and react with \[{\text{HI}}\] it forms heptanoic acid. So according to the above facts the structure of glucose is:
\[{\text{OHC}} - {\text{C}}({\text{OH}}){\text{H}} - {\text{C}}({\text{OH}}){\text{H}} - {\text{C}}({\text{OH}}){\text{H}} - {\text{C}}({\text{OH}}){\text{H}} - {\text{C}}{{\text{H}}_2}{\text{OH}}\]

Note:
Nowadays we don’t use the traditional method for determining the structure. Due the introduction of spectroscopy it has become very easy to study the properties of the given compounds. Mainly NMR spectroscopy is used for the determination of structure of organic compounds. All we need to do is to put the sample in an NMR machine and we will get the peaks for the various functional groups present in the graph of that molecule.