This second apartment is bought by Walter after he signed the divorce papers.
After finally agreeing to sign the divorce papers ("Más"), Walter visits a demonstration apartment that he likes immediately. He decides to negotiate with the seller to buy it as it is, the furnishing and the decoration being to his taste ("Sunset").
This is the second apartment Walter occupies, the first being the one he hires after Skyler kicked him out when she uncovers his lies.
Later ("Hazard Pay"), Walter finally relocates into the family home, to the surprise of Skyler, but remains the owner of the apartment to avoid a big loss to resale.