>1. ~When (to achieve a purpose) >2. ~To express surprise or disappointment or even dissatisfaction. 登＜る＞のに3時間かかりました。 　　　if the verb is a so-called present tense, then it is (1). 頂上まで登っ＜た＞のに何もありませんでした。 　　　if the verb is so-called past tense, then it is (2). おれが真面目に話し＜ている＞のに、おまえのその態度は何だ！ 　　　if the verb is a so-called present progressive tense, then it is (2). You can tell them at 99% using this criterion.

You can perceive them with the main clause. 登るのに3時間かかりました。 The main clause is 3時間かかりました. That doesn't mention disappointment nor dissatisfaction. It's just a fact. On the other hand, in the case of 2, let's think about this example. 約束をしたのに、彼女は来ませんでした。 That mentions the fact that she didn't come, but we can see how the speaker feels with disappointment due to the fact.