[owlpower]

Question: How to arrange the molecules in increasing order of Bronsted acidity?

I know that mineral acid will have the greatest acidity, thus VI is most acidic.

This is followed by carboxylic acids, I and II. II has an electron donating group, which makes it less stable than I.

So I know the ranking will be
X,X,X,II,I,VI.

However, between III, IV and V, I have trouble determining the acidity between them.
IV will be anti-aromatic when it loses H+, which makes it really unstable (hence weak acid).
Not very sure about esters, but the only way it can be an acid is to donate H+ from the Me group.
For alkynes, I know it's rather acidic too (compared to alkanes and alkenes at least).

My guess would be that the ranking is IV,III,V,II,I,VI.
Any thoughts?

[Babcock_Hall]

Your thinking about IV is incorrect.  I would also think about resonance delocalization and which acids might see an effect from this.

[owlpower]

IV is resonance stabilised. Ester has electron donating Me group which decreases stability. So I guess III,V,IV,II,I,Vi

[Babcock_Hall]

IV is also aromatic, not antiaromatic.  The reason why ethyne has a lower pK_a than an alkane is very different from the reason why cyclopentadiene has a lower pK_a, and I think it is difficult to compare the two without looking up the pK_a values for that reason.  I don't see obvious problems with your order.