How do we know the blood of Christ can clear our conscience?

The effectiveness of Christ's blood in clearing our conscience is rooted in its power to atone for our sins completely. Hebrews 9:12-14 explains that it is not the blood of animals, but the perfect sacrifice of Christ that purifies our consciences from dead works. This means that feeling guilty about sin is met with the truth that Christ's blood has already satisfied the justice of God on our behalf. In acknowledging our sinfulness and trusting in Christ's sacrifice, our guilt is replaced with the peace of knowing we have been accepted by God (Romans 3:24).