The penitential Psalm 51, while a comfort to sinners (such as David, who wrote the Psalm after killing Uriah, and committing adultery with Bathsheba) is also a commentary on the power of the word of God.
David prays for both forgiveness, and for the ability to teach sinners.
The 2 go together. When we rejoice in God's forgiveness of our sins, that joy shows forth to others, who are also brought into that forgiveness.
It's important for us to remember that God's word accomplishes what it sets out to do. Vs. 13 speaks of that:
"Then will I teach transgressors thy ways; and sinners shall be converted unto thee."
When God's ways are taught, sinners are converted. Not everyone: there are those who resist and turn away from God's word, but sinners are converted. We can count on that.
We can't see God's word accomplishing these things, and we can't know for sure when that preached word will do the job. But it will do it.
This is the comfort for those who preach. God's word will work. It is not your job to manipulate the hearers. Just preach the word. Let God do His job.