7:7 As the sin offering is, so is the trespass offering: there is one law for them: the priest that maketh atonement therewith shall have it.
7:11 And this is the law of the sacrifice of peace offerings, which he shall offer unto the LORD.
(See Scofield "Exodus 29:33")
7:13 Besides the cakes, he shall offer for his offering leavened bread with the sacrifice of thanksgiving of his peace offerings.
In the "law of the offerings," the peace-offering is taken out of its place as third of the sweet savour offerings, and placed alone, and after all the non-sweet savour offerings. The explanation is as simple as the fact is beautiful. In revealing the offerings Jehovah works from Himself out to the sinner. (See Scofield "Exodus 25:10") . The whole burnt-offering comes first as meeting what is due to the divine affections, and the trespass-offering last as meeting the simplest aspect of sin-- its injuriousness. But the sinner begins of necessity with that which lies nearest to a newly awakened conscience--a sense, namely, that because of sin he is at enmity with God. His first need, therefore, is peace with God. And that is precisely the Gospel order. Christ's first message is, "Peace" John 20:19 afterward He shows them His hands and His side. It is the order as 2 Corinthians 5:18-21 first "the word of reconciliation," Leviticus 7:19, then the trespass- and sin-offering, Leviticus 7:21 . Experience thus reverses the order of revelation.
The use of leaven here is significant. Peace with God is something which the believer shares with God. Christ is our peace-offering Ephesians 2:13 . Any thanksgiving for peace must, first of all, present Him. In verse 12 we have this, in type, and so leaven is excluded. In verse 13 it is the offerer who gives thanks for his participation in the peace, and so leaven fitly signifies, that though having peace with God through the work of another, there is still evil in him. This is illustrated in Amos 4:5 where the evil in Israel is before God.