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Kemmerich is the first soldier whose death is detailed. In fact, we hardly get to see him alive: we first encounter him when he's in the hospital. Watching Kemmerich's last hours makes a huge impression on Paul—he realizes that he's becoming an expert in the process of dying:
Under the skin the life no longer pulses, it has already pressed out to the boundaries of the body. Death is working through from within. It already has command in the eyes. Here lies our comrade, Kemmerich, who a little while ago was roasting horse-flesh with us and squatting in the shell-holes. He it is still and yet it is not he any longer. (1.72)
Kemmerich's dialogue mostly consists of lamenting the fact that someone has stolen his watch and complaining of pain in his foot, not realizing that his leg has been amputated. He's also preoccupied with his fancy boots, and wants to make sure that they come home safe with him. The men show compassion in not telling him that, at most, he'll only need one...and that probably his boots will be given to a soldier in need after he dies.
Kemmerich's death also makes Paul realize how callously death is treated during wartime. While in the hospital, he notices that the orderlies check on Kemmerich pretty much only to see if he's still alive—they need his bed for other patients.
Ultimately, Kemmerich dies in great pain, crying. And then his bed, along with his boots, get quickly, efficiently recycled.