Primary alkanol has OH at terminal C, while secondary doesn't.
Primary can be oxidised to form aldehyde, secondary to form ketone.
Aldehyde goes on further to be oxidised to form carboxylic acids, ketones do not.
Bit of unnecessary info, but it can't hurt to know
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On the contrary, that is important information. That is one of the chemical tests to distinguish a primary alcohol (e.g. propan-1-ol) from a secondary alcohol (e.g. propan-2-ol).
So what's the test?
Alkanol can either be primary, secondary or tertiary.
When you have a mixture of alkanols [e.g. mixture of propan-1-ol, propan-2-ol and t-butanol], fractional distillation will give you pure [or almost pure] fractions [e.g. pure propan-1-ol, pure propan-2-ol and t-butanol]. However, their identity is not known, since boiling point is often difficult to predict, thus, chemical tests are needed to characterise these fractions.
One of the chemical test is to oxidize the fraction, usually with acidified solution of permanganate or dichromate (you should be familiar with these).
Primary alkanol will be oxidized to an aldehyde, then carboxylic acid. This oxidation process will decolourize the permanganate solution (purple -> clear). Addition of an alkanol (such as ethanol) will give an ester, which tends to have a distinct fragrance [fruity smell usually].
Secondary alkanol will be oxidized to a ketone. This oxidation process will decolourize the permanganate, however, since the oxidized carbon doesn't have any more hydrogen, it cannot become an acid. Addition of an alkanol (such as ethanol) will do nothing.
Tertiary alkanol will not oxidize, and the permanganate does not decolourize.
So by adding the same chemical (permanganate then another alkanol), these three very similar compounds will give three distinctively different results: 1
o = decolourization and fruit scent, 2
o = decolourization, 3
o = no reaction.
You should be familiar with a range of chemical tests, such as the bromine test, the test for acidity using sodium bicarbonate.
*note, t-butanol is the lazy way of saying 2-methylpropan-2-ol, I don't recommend you using it in an exam, but I am lazy.