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 Exodus 5:17).
Related Commentaries of Exodus 19:1
Exodus 19:1-2
1 In the third month, when the children of Israel were gone forth out of the land of Egypt, the same day came they into the wilderness of Sinai.
2 For they were departed from Rephidim, and were come to the desert of Sinai, and had pitched in the wilderness; and there Israel camped before the mount.