About all you can do is ventilate the room and wait for it to evaporate, which shouldn't take long. It's hard to say exactly how long without knowing the type of carpet, ambient temperature, relative humidity, etc, but I would expect a few hours, not days.
Although isopropyl alcohol evaporates quickly, keep in mind that a 50% solution is 50% water, so your carpet may remain damp even after you no longer smell the alcohol.
According to the MSDS for isopropyl alcohol, the primary hazard is fire. The vapors are combustible so avoid smoking and open flames in the room. However, 200 ml is not a large amount, and the 50% water will greatly reduce its flammability. Opening windows and letting the room air out should be sufficient to avoid fire danger.
Although the MSDS says it's a mild inhalation and contact hazard, keep in mind that the MSDS refers to 100% isopropyl alcohol. 200 ml of 50% alcohol spilled in a room should present no particular health hazards, although I would open windows and keep pets and small children out of the room until you can no longer smell it.