Regional Jet 700 ER/LR (CRJ700)
Flight Crew Air Transport Pilot (ATP)
Aircraft Equipment Problem Critical; Flight Deck / Cabin / Aircraft Event Illness / Injury; Flight Deck / Cabin / Aircraft Event Smoke / Fire / Fumes / Odor
Flight Crew Diverted; Flight Crew Landed As Precaution; Flight Crew Landed in Emergency Condition; General Evacuated
Aircraft
The airplane already had the R PACK [deferred inoperative under an] MEL. After reaching FL310; we were there for no more than 10 minutes deviating around for some weather when the warning L BLEED DUCT message started going off.  At this point I transferred the controls to the first officer and I reached for the QRH and asked ATC to descend to lower altitude.  As soon as I opened the QRH; the fwd FA called me to notify me that there was a medical emergency in the back and there was an unresponsive passenger.  I told the FA that we had a situation upfront and that I was going to call her back shortly.  As soon as we got off the intercom; the CABIN ALT warning message came on followed by PASS OXY ON message and soon after that the brake overheat warning message came on as well.  The indications were going from 12 to 16 in the red box.  At this point we notified ATC and we needed to divert to [a nearby alternate].I called the FA to ask her if she can see any smoke and she said yes; there is smoke in the cabin and [it] is burning her eyes.  At the same time strong fumes got into the cockpit and the FO and I decided that [the nearby alternate] was not going to be a good alternate airport and we needed to put it down quick in the nearest suitable airport; which was only less than 10 NM away and [our first selected alternate] was about 44 NM out.  [The newly selected alternate was] perfect for the weather we were in.  I informed the FA of what we were doing and gave her special instructions for the evacuation.  On short final I gave the order for brace and after landing we evacuated the airplane.  Everything went smooth past this point with EMS and the incident response team.
[Report narrative contained no additional information.]
CRJ-700 flight crew reported diverting to the nearest suitable airport after departing with one pressurization pack deferred inoperative and losing the other bleed system at FL310.