You need to supply these verses, so that we can explore their context. "purgatory" is an extra-biblical doctrine based on a lie. See below on works and righteousness.
As to obey: Greek "obey" is sometimes translated as "believe". See John 3:36:
He that believeth (πιστεύων) on the Son hath everlasting life: and he that believeth (ἀπειθῶν) not the Son shall not see life; but the wrath of God abideth on him.
ὁ πιστεύων εἰς τὸν υἱὸν ἔχει ζωὴν αἰώνιον· ὁ δὲ ἀπειθῶν τῷ υἱῷ οὐκ ὄψεται ζωήν ἀλλ' ἡ ὀργὴ τοῦ θεοῦ μένει ἐπ' αὐτόνIt's not dificult to understand the relationship -- to obey the Lord by following him in faith.
Many today believe in this false works doctrine. It's not new. Israel also sought righteousness through works. Not possible.
30 What shall we say then? That the Gentiles, which followed not after righteousness, have attained to righteousness, even the righteousness which is of faith. 31 But Israel, which followed after the law of righteousness, hath not attained to the law of righteousness. 32 Wherefore? Because they sought it not by faith, but as it were by the works of the law. For they stumbled at that stumblingstone; 33 As it is written, Behold, I lay in Sion a stumblingstone and rock of offence: and whosoever believeth on him shall not be ashamed. (Romans 9:30-33)
Trying to achieve righteousness by following after the law is NOT possible.
I do not frustrate the grace of God: for if righteousness come by the law, then Christ is dead in vain. (Galatians 2:21)