The Lord Jesus, in His human nature thus united to the divine, in the person of the Son, was sanctified and anointed with the Holy Spirit above measure, having in Him all the treasures of wisdom and knowledge; in whom it pleased the Father that all fullness should dwell, to the end that being holy, harmless, undefiled, and full of grace and truth, He might be thoroughly furnished to execute the office of mediator and surety; which office He took not upon himself, but was thereunto called by His Father; who also put all power and judgement in His hand, and gave Him commandment to execute the same.
The Lord Jesus, by His perfect obedience and sacrifice of Himself, which He through the eternal Spirit once offered up to God, has fully satisfied the justice of God, procured reconciliation, and purchased an everlasting inheritance in the kingdom of heaven, for all those whom the Father has given unto Him. (8:5)
It pleased God, in His eternal purpose, to choose and ordain the Lord Jesus, His only begotten Son, according to the covenant made between them both, to be the mediator between God and man (8:1)
This office of mediator between God and man is proper only to Christ, who is the prophet, priest, and king of the church of God; and may not be either in whole, or any part thereof, transferred from Him to any other. (8:9)
This sinlessness of our Lord, however, does not amount to absolute impeccability. It was not a non potest peccare [not possible to sin]. If He was a true man He must have been capable of sinning. Systematic Theology: The Complete Three Volumes, Kindle Edition, location 20205.
Of course, Hodge makes it clear that Jesus did not in fact sin, but he goes on to say,
Temptation implies the possibility of sin. If from the constitution of his person it was impossible for Christ to sin, then his temptation was unreal and without effect, and He cannot sympathize with his people. (Systematic Theology, location 20205-20212).
But later the Princeton divine states,
All Christ’s acts and sufferings in the execution of his mediatorial work were, therefore, the acts and sufferings of a divine person. (Systematic Theology, location 20232).
All Christ’s acts, sufferings [and any possible sins committed] in the execution of his mediatorial work were, therefore, the acts, sufferings [and sins] of a divine person.
You see the problem?