Answer:
[tex]\boxed{\text{No}}[/tex]
Explanation:
Na reacts with all OH groups to produce hydrogen.
The reaction with cyclobutanol is shown below.
The reaction with butanoic acid is
[tex]\rm CH_{3}CH_{2}CH_{2}COOH\xrightarrow{\text{Na}} CH_{3}CH_{2}CH_{2}COO^{-} + H_{2}[/tex]
Both compounds release bubbles of hydrogen, so you can't use sodium to distinguish between them.
