פּירוש אויף שמות 24:8

ויזרק means sprinkling — he sprinkled it on the people (not he threw it against the people, as this word might imply; cf. e. g., Exodus 9:8: וזרקו משה השמימה). The Targum, however, renders it by: and he poured it (the blood) upon the altar as atonement for (על) the people, adding the words “upon the altar”, and taking על העם to denote “on behalf of the people”, i. e. he poured it out to atone for the people.

הנה דם הברית, “here is the blood, the symbol of the covenant;”The blood of the covenant is divided into two halves, as always when a covenant is made between two parties. We know this already from the first covenant made between G-d and Avraham in Genesis chapter 15, when Avraham divided all the slaughtered animals except for the bird.[Nowadays when two parties conclude an agreement each receives a copy of the text, and each signs both copies. Ed.] The prophet Jeremiah, in Jeremiah 34,18, refers to העגל אשר כרתו לשנים ויעברו בין בתריו, “the calf which they cut in two so as to pass between the halves.” The reason why in Genesis15,17, G-d is not described as passing between the pieces Avraham had cut, was His way of indicating to Avraham that there would be a price to pay in blood for violating this covenant. This idea has also been referred to again in Leviticus 26,25 in the tochachah, the chapter of dire warnings, where G-d describes His reaction to when the Jewish people become guilty of violating this covenant.

ויזרוק על העם, “he sprinkled on the people.” Some commentators understand the word על here to mean בעד, “on behalf of.” We have a parallel to this in Numbers 17,12 ויכפר על העם “Aaron atoned on behalf of the people.”