The irony of the cause of Mrs. Mallard's death revolves around the definition of the word heart. For, in Western culture, there are both literal and figurative meanings: literally, the heart is the main organ of the body, and figuratively, the heart is the soul, the inner being.
In the opening lines of Chopin's story, Mrs. Mallard is described as "afflicted with a heart trouble," a phrase that suggests she is emotionally repressed. When she learns that her husband has been a victim of a train wreck, she privately breathes "free, free, free!" as she realizes that she is independent. However, as she triumphantly descends the stairs from her room, she sees her husband come through the front door. This shock causes her to die of "heart disease--a joy that kills." That is, her soul, finally freed from its repression, is so overcome with despair upon seeing her repressor return that she dies because her joy is taken from her and this deprivation kills her soul/heart. Thus, it is "a joy that kills."
She arose at length and opened the door...There was a feverish triuimph in her eyes...Someone was opening the front door...It was Bently Mallard who entered....He stood amazed at Josephine's piercing cry....she had died of heart disease--of joy that kills.
Furthermore, the statement "a joy that kills" is of itself ironic since joy does not normally bring about death. Louise Mallard's sense of freedom, having been suddenly received, is just as quickly rescinded.
With these considerations, then, the student can explain in the introduction how the irony of the last line with its phrase "a joy that kills" is connected to that of the first line with its phrase "a heart trouble." That is, in the hour's time, the condition of Mrs. Mallard returns to its starting point of repression.
The thesis, then, can be developed around the irony of this hour being that the joy which is born of the lightening of her repression, "a heart trouble," becomes a tragic joy at the return of the husband, Bently Mallard, because he is alive, but she again is in her repressed state. So overcome is Louise Mallard that her soul gives out and the joy of Bently Mallard's return instead, ironically, kills her.