According to a group of Engineering grads from the Massachusetts Institute of Technology (MIT) the colonists that make the Mars One trip would suffocate within 68 days. This is according to a 35 page report that the group wrote analyzing the current plans for Mars One and they figure that the first fatalities will occur 68 days into the trip.
Mars One plans to send rovers, communication stations, and living quarters to the red planet before sending the colonists. The plan is to have colonists growing their own food to produce oxygen to prevent them from suffocating. However, this is the exact problem that the students have proven to be a flop.
The current plans for Mars One requires the colonists to live within the quarters of their food supplies. If this is the case as the diagram above shows they will have an oxygen spike during the point of maturity which would cause a fire within their living quarters. If they were to try and vent the oxygen at that point than they have the other issue of a lack of nitrogen in the room. This would lead to death by suffocation this would be the best case scenario.
The other outcome is that the sudden pressure decrease from venting it would cause the living quarters to explode. However, the paper does mention a possible solution and that would require the food to be in a separate facility and having the oxygen vented into the living quarters.
This would be very costly and it would be cheaper to send the food to the colonists which would cost them approximately 4.5 billion dollars and considering the entire budget is 6 billion dollars this doesn’t seem like the smartest move. However this hope the technology to properly filter out the oxygen from the rest of the components in the air is expected to be ready before launch time in 2022 but as it stands there is much to be worked out if there is hopes for this to go as planned.