Notes on the Bible, by Albert Barnes, , at sacred-texts.com
The wilderness ... the desert of Sinai - If the mount from which the law was delivered be the rock of Ras Safsafeh, then the spacious plain of Er Rahah would be the "desert" of Sinai (see Exo 5:17).
Moses went up unto God - This seems to imply that the voice was heard by Moses as he was ascending the mount.
House of Jacob - This expression does not occur elsewhere in the Pentateuch. It has a special fitness here, referring doubtless to the special promises made to the Patriarch.
On eagles' wings - Both in the law Deu 32:11 and in the Gospel Mat 23:37, the Church is compared to fledgelings which the mother cherishes and protects under her wings: but in the law that mother is an eagle, in the Gospels "a hen"; thus shadowing forth the diversity of administration under each covenant: the one of power, which God manifested when He brought His people out of Egypt with a mighty hand and an outstretched arm, and led them into the promised land; the other of grace, when Christ came in humility and took the form of a servant and became obedient unto death, even the death of the Cross. Compare also Rev 12:14.
A peculiar treasure - A costly possession acquired with exertion, and carefully guarded. The special relation in which Israel stands, taken out of the pagan world and consecrated to God, as His slaves, subjects, and children, determines their privileges, and is the foundation of their duties. The same principle applies even in a stronger sense to the Church. See Act 20:28; Co1 6:20; Pe1 2:9.
All the earth is mine - It was a point of great practical importance, to impress upon the Jews that their God was no mere national Deity. Compare Deu 10:14; Psa 24:1.
A kingdom of priests - Israel collectively is a royal and priestly race: a dynasty of priests, each true member uniting in himself the attributes of a king and priest. Compare Pe1 2:5; Rev 1:6.
An holy nation - The holiness of Israel consisted in its special consecration to God: it was a sacred nation, sacred by adoption, by covenant, and by participation in all means of grace. Compare Deu 7:6; Deu 26:19; Deu 28:9; Co1 3:17; Th1 5:27.
All that the Lord ... - By this answer the people accepted the covenant. It was the preliminary condition of their complete admission into the state of a royal priesthood.
Sanctify them - The injunction involves bodily purification and undoubtedly also spiritual preparation. Compare Heb 10:22. The washing of the clothes was an outward symbol well understood in all nations.
Set bounds unto the people - The low line of alluvial mounds at the foot of the cliff of Ras Safsafeh exactly answers to the bounds which were to keep the people off from touching the mount: but the bounds here spoken of were to be set up by Moses.
Touch it - Rather "touch him." The person who had touched the mount was not to be touched, since the contact would be pollution.
Out of the camp - The encampment must have extended far and wide over the plain in front of the mountain. From one entrance of the plain to the other there is space for the whole host of the Israelites.
A furnace - The word in the original is Egyptian, and occurs only in the Pentateuch.
The priests also - Sacrifices had hitherto been offered by firstborn, or the heads of families. See Gen 14:18 note.