What is the purpose of this Sunday's collection at First Purchase African Methodist Episcopal Church in To Kill a Mockingbird?
The purpose of the collection is to aid Tom Robinson's wife while he's in jail.
When Mayella Ewell accuses Tom Robinson of rape and he's put in jail, it makes things difficult for Helen and their children. Without Tom, the household doesn't have as many resources.
Calpurnia takes Jem and Scout to First Purchase African M.E. Church with her one Sunday morning where they attend church services. When Reverend Sykes is making announcements, he says:
"You all know of Brother Tom Robinson’s trouble. He has been a faithful member of First Purchase since he was a boy. The collection taken up today and for the next three Sundays will go to Helen—his wife, to help her out at home."
When the collection is gathered in the black enameled coffee can, Reverend Sykes says it isn't enough. He reminds everyone that Helen can't leave her children to work and says they have to make at least ten dollars. He instructs someone to shut the doors and says that no one can leave until they've reached that amount.
When Scout is leaving, she asks Reverend Sykes why Helen can't take her children to work with her when so many other women do. He says that Helen is having trouble finding work. Calpurnia tells Scout that because of the crimes of which Tom's accused, people are not associating with the Robinson family.
In Chapter Twelve of To Kill a Mockingbird, Jem and Scout accompany Calpurnia to a Sunday service at the First Purchase African M.E. Church in the Quarters.
After the first round of collections is brought to Reverend Sykes, he empties the black enameled coffee can that has been used as the collection vessel out onto the table and examines the pile of coins. Much to Scout's amazement, the Reverend demands that the churchgoers contribute more and that, "we must have ten dollars."
The entirety of this charitable collection will go to supporting the family of Tom Robinson: his wife, Helen, and their children, who Helen is now singularly responsible for taking care of since Tom has been jailed on charges of rape.
Reverend Sykes demands that no one leaves the church until the proper sum has been donated, and, thus, "[s]lowly, painfully, the ten dollars was collected."
Calpurnia decides to take Jem and Scout to the First Purchase AME Church because Atticus was out of town, and he had not given Cal any specific instructions about going to church. Cal was worried that if she allowed the children to go alone, they would get in trouble again, just as they had when they tied Eunice Ann Simpson to a chair in the furnace room. So, Cal made sure the kids were spruced up, and she took them to her church. On this Sunday, Reverend Sykes announced to the congregation that
"The collection taken up today and for the next three Sundays will go to Helen--(Tom Robinson's) wife, to help her out at home."