For the first box, the correct answer is "respire."
For the second box, the correct answer is "permeate."
So the complete sentence would read: "One by one, the students in the classroom next to the science lab began to look up and deeply at first and then quickly cover their noses. Something was going terribly wrong in the science lab, and the smell was beginning to respire to the other classrooms on the hall."
The second part would likely make more sense as: "Something was going terribly wrong in the science lab, and the smell was beginning to permeate to the other classrooms on the hall."
The final corrected sentence is: "One by one, the students in the classroom next to the science lab began to look up and deeply at first and then quickly cover their noses. Something was going terribly wrong in the science lab, and the smell was beginning to permeate into the other classrooms on the hall."