The first time Grace is used in the Scripture is when speaking of Noah:
Grace:
חֵן chen (khane) n-m.
1. graciousness, i.e. subjective (kindness, favor) or objective (beauty)
(160 verses)
Mercy:
חֵסֵד checed (kheh'-sed) n-m.
1. loving kindness, goodness, compassion, faithful, reproach, shame
(262 verses)
Together in one verse, six times.
Grace is unearned favor.
Mercy is really love in action.
This is a wonderful study to make as it's so much more than the definitions. Grace is showing favor for someone who doesn't deserve it, nor is really looking for it. Like what Jesus did for us on the cross. Grace is buying a brand new coat for a homeless person. Grace is to love your neighbor as yourself. In fact in Greek grace can be substituted for agape (unconditional love).
Mercy is both parties know the one did wrong and the one in Authority chooses to extend love over judgement. Mercy is also recognizing someone having authority over another, such as a king over his subjects, a boss over his staff, a father over a child, and that authority not executing judgment. Mercy is also a reproach and shame, such as what Jesus received on the cross.
Hebrews 4:16 (KJV)
Let us therefore come boldly unto the throne of
grace, that we may obtain
mercy, and find
grace to help in time of need.
John 1:16 (KJV)
And of his fulness have all we received, and
grace for grace.
This is a wonderful verse because when we find that our measure of grace is about to run out, we have more grace. In Greek it's:
καὶ χάριν ἀντὶ χάριτος
"and grace anti grace"
Meaning grace upon grace. In fact Paul says this too:
Romans 5:20 (KJV)
Moreover the law entered, that the offence might abound. But where sin abounded, grace did much more abound:
The Greek word for "
much more abound" is
ὑπερπερισσεύω huperperisseuo (hoop-er-per-is-syoo'-o) v. and means to super-abound. Meaning that if the Law was absolute, grace is more absolute with more to spare. If the Law required a $10 fine, grace super-abounds giving $1,000,000!
Mercy is almost an absolution for guilt, whereas grace is receiving something without deserving it.
I hope this helps.