tn The construction uses a genitive: “a bull of the sin offering,” which means, a bull that is designated for a sin (or better, purification) offering.
sn It is difficult to understand how this verse is to be harmonized with the other passages. The ceremony in the earlier passages deals with atonement made for the priests, for people. But here it is the altar that is being sanctified. The “sin [purification] offering” seems to be for purification of the sanctuary and altar to receive people in their worship.
tn The verb is וְחִטֵּאתָ (véhitte’ta), a Piel perfect of the word usually translated “to sin.” Here it may be interpreted as a privative Piel (as in Ps 51:7 ), with the sense of “un-sin” or “remove sin.” It could also be interpreted as related to the word for “sin offering,” and so be a denominative verb. It means “to purify, cleanse.” The Hebrews understood that sin and contamination could corrupt and pollute even things, and so they had to be purged.
tn The construction is a Piel infinitive construct in an adverbial clause. The preposition bet (ב) that begins the clause could be taken as a temporal preposition, but in this context it seems to express the means by which the altar was purged of contamination—“in your making atonement” is “by [your] making atonement.”