Alma 42:15-21

15  And now, the plan of mercy could not be brought about except an atonement should be made; therefore God himself atoneth for the sins of the world, to bring about the plan of mercy, to appease the demands of justice, that God might be a perfect, just God, and a merciful God also.

Alma 42:15 (Emphasis mine)

Alma(2) emphasized how the demands of justice must be met.  Now Alma(2) formally introduces the concept of mercy.  How is the plan of mercy to be brought about?  There must be an atonement. 

I'd like to look at the etymology of the word.  

According to the Online Etymology Dictionary,  atone comes from the "1550s, from adv. phrase atonen (c.1300) 'in accord,' lit. 'at one,' a contraction of at and one. It retains the older pronunciation of one. The phrase perhaps is modeled on L. adunare 'unite,' from ad- 'to, at' + unum "'ne.'"   So, atone comes from words meaning "at one" or "unite."  

Now, we move to atonement.  According to the Online Etymology Dictionary, atonement is from the "1510s, 'condition of being at one (with others)', from atone + -ment. Meaning 'reconciliation' (especially of sinners with God) is from 1520s."  

Further, according to the Oxford DIctionary, "1533 Q. Cath. Parr Erasm. Comm. Crede 162 To reconcile hymselfe and make an onement with god [sic].1599 Bp. Hall Sat. iii. vii. 69 Which never can be set at onement more.1555 Fardle Facions ii. xii. 298 The redempcion, reconciliacion, and at onement of mankinde with God the father.]"  (Quote accessed at The etymology of “Atonement”  (accessed 2/8/2011).

Through the atonement, we not only "unite" with God, but we reconcile our sins with God and are redeemed by God.  

Alma(2) tells us the "God himself anotneth" for our sins.  Because "God himself atoneth," the plan of mercy will "appease" the demands of justice.  The makes God a just and merciful God.

16  Now, repentance could not come unto men except there were a punishment, which also was eternal as the life of the soul should be, affixed opposite to the plan of happiness, which was as eternal also as the life of the soul.

17  Now, how could a man repent except he should sin?  How could he sin if there was no law?  How could there be a law save there was a punishment?
18  Now, there was a punishment affixed, and a just law given, which brought remorse of conscience unto man.
19  Now, if there was no law given—if a man murdered he should die—would he be afraid he would die if he should murder?
20  And also, if there was no law given against sin men would not be afraid to sin.
21  And if there was no law given, if men sinned what could justice do, or mercy either, for they would have no claim upon the creature?

Alma 42:16 - 21 (Emphasis mine)

There had to be law.  Without law, there is no sin.   Without law, there is no punishment.  Without law, neither mercy nor justice could have claim upon us.  There had to be law for there to be an atonement. Neither justice nor mercy could make a claim upon us.  It was essential there be a law for the works of God to go forward.

The words of Paul.

7  What shall we say then?  Is the law sin?  God forbid.  Nay, I had not known sin, but by the law: for I had not known lust, except the law had said, Thou shalt not covet.
8  But sin, taking occasion by the commandment, wrought in me all manner of concupiscence.  For without the law sin was dead.

Romans 7:7 - 8  (Emphasis mine)

For there to be sin, justice, and mercy, there must be a law.