Learn Finnish: Ostan tynnyrin seosta. - I buy a barrel of mixture.

This is the classic measure and container structure. The head noun (tynnyri) changes case to fit its role in the sentence. Here it takes the accusative -n because it is a total object. The substance being measured (seos) stays locked in the partitive singular (seosta) to mean 'of mixture', regardless of what the container is doing.

Why does tynnyri take the -n ending here instead of being in the partitive?

Because it is the total object of the verb ostaa. You are buying one whole barrel, so the object takes the genitive-looking accusative -n. If the action was ongoing or incomplete, you would use the partitive: Ostan tynnyriä seosta.

The basic word for mixture is seos. Why is its partitive form seosta and not seoksea?

Many nouns ending in -s (like seos, kerros, kiitos) attach the partitive -ta ending directly to their basic nominative form, giving you seosta. The stem with -kse- is used for most other cases, such as the genitive seoksen.

How would this sentence change if I bought 'two barrels of mixture'?