The denouement of Kate Chopin's "The Story of an Hour" is ironic in that the death of Mrs. Mallard has been inevitable, not because she has a bad heart, but because she has had "a heart trouble," a repressed heart that in its elation cannot return itself to its former state of subjugation without damage--"a heart trouble." Her joy, finally released, is what causes her death as she cannot go back to her life as the wife of Bently Mallard.
A victim of the institution of Victorian life, Mrs. Mallard has been under the "powerful will bending hers in that persistence" of her culture. While she has felt love for her husband, she is like the prisoner who is released, but once outside, is told that he must return and serve more time. This would seem like a death sentence.
Kate Chopin's employment of irony is absolutely superb. The opening line is ironic--"a heart trouble" that Mrs. Mallard has is a spiritual, not a physical problem; the "joy that kills" is also ironic, for the release of her imprisoned grief cannot be repressed again without fatal results because the anguish is too much for her heart.
I think the ending is ironic because it is so far removed from what we would expect to have happen. In addition, the last sentence is full of irony because it is the opposite of what has really happened.
Up until the point that we see Brently Mallard, we assume he is dead and that Louise is going to be able to embark on this new life that she has been envisioning. We assume that her life is at a beginning. But instead, we find out that her new life is coming to an end both literally and figuratively.
The last sentence is ironic because of how badly the people have misunderstood what is going on. They believe that Louise has died of happiness, but we know she has died of sorrow and disappointment.