What makes Atticus’s closing argument in Chapter 21 of To Kill a Mockingbird effective? (Please include a description of how the argument...

The closing argument of Atticus Finch in the Tom Robinson trial speaks to the consciences of each man as an American citizen because Atticus invokes the principles of the American Constitution, which also appeals to their sense of Christian duty.

Earlier in Chapter 11, as Atticus counsels Scout following the insults to Atticus by Mrs. Dubose, he tells his daughter that she will probably be subjected to more invectives. But, he explains that there is one thing that does not "abide by majority rule" and that is an individual's conscience. Further, he explains,

"This case, Tom Robinson's case, is something that goes to the essence of a man's conscience."

That is, if someone believes that the words of the United States Constitution that "all men are created equal" apply in the court of law, then Tom Robinson is entitled to a fair trial, and the fact that the Ewells are white and he is black should not enter into any judgments by the jury.
While Atticus does not express his argument quite this way, the implications are there.

When he first addresses the jury, Atticus quotes Thomas Jefferson's statement made in the Declaration of Independence that all men are created equal, adding that he knows that, in reality, people are not really equal. For, some people are more intelligent, some are more talented, some have more opportunities, some are more clever and successful. However, Atticus adds, there is one single place where all people are treated equally: a court of law. "In this country, the courts are the great levelers," Atticus declares. This is no ideal, Atticus adds. "It is a living, working reality."
Then, Atticus talks directly to the jury, reminding them that a court is no better than each man who sits in the jury:

"A court is only as sound as its jury, and a jury is only as sound as the men who make it up."

Finally, Atticus tells the jurors that he is confident that they will review dispassionately the evidence that they have heard, and that they will reach a decision and restore the defendant to his family. Atticus also appeals to their consciences as he urges the jurors,

"In the name of God, do your duty."

Having appealed to the twelve men of the jury to remember that all men are equal under the law, and having appealed further to their consciences in respecting this Constitutional right of all men, Atticus ends by exhorting them to perform their duty as American citizens and be fair as they review the evidence without prejudice, as is their duty.