Mrs Mallard is a sincere character and her reactions to her husband's death are those of a woman who has devoted her life to someone else and has finally been given a chance to be herself. While she appears to celebrate her husband's death, she is really celebrating her own life, a focus she has not been able to have until his death.
Mrs Mallard's initial reaction on hearing of her husband's death is one of release rather than grief, "She did not hear the story as many women have heard the same, with a paralyzed inability to accept its significance. She wept at once, with sudden, wild abandonment, in her sister's arms." Her immediate weeping is a natural reaction of Mrs Mallard. It is not how she decides to act, it is her direct emotional response to the news. In this weeping Mrs Mallard is acting on her own basic feelings and this shows that her reaction is genuine.
It is when she retires to her room that her actions become less emotional and more rational. She is no longer acting on instinct,
It is in the next passage that Mrs Mallard finally becomes aware of her own feelings. She has acted on her emotional response and now she is developing the clarity to understand her own reaction, "There was something coming to her and she was waiting for it, fearfully. What was it? She did not know; it was too subtle and elusive to name." This 'something' coming to her is actually the knowledge of her own feelings, which she voice repeating the words "free,free, free!" In speaking these words her first reaction was a "look of terror" showing that Mrs Mallard's recognition that her feelings are of joy, rather than of grief, is a shocking one for her. This shows the genuineness of her reaction.
We then see Mrs Mallard's rational reaction. She is sad for her husband's death but she is also glad of her own life. She is looking forward to a life that is just her own, "There would be no one to live for during those coming years; she would live for herself. There would be no powerful will bending hers i