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In this world, there are certain genetically engineered creatures, that are able to tolerate the side effects of mouth breathing (like sore throat) without increasing the normal air resistance in the mouth and throat.

Considering that they can breathe through their mouth with no negative effects, would they be able to gain more oxygen (e.g: the same amount of oxygen gets into their lungs under shorter time or vice-versa when compared to nasal breathing)? Would that bonus be significant, considering that their lungs are large (not a limiting factor)?

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    $\begingroup$ What do you mean by gain more oxygen? $\endgroup$
    – dot_Sp0T
    May 28 '17 at 9:26
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    $\begingroup$ More oxygen than what? $\endgroup$
    – Willk
    May 28 '17 at 12:54
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    $\begingroup$ Ever since I can remember, I've primarily breathed through my mouth. I don't have problems with dry mouth, sore throat, etc. Do I have an increased lung capacity? idk. I can hold my breath longer than most, but that probably has nothing to do with mouth breathing and a lot to do with other stuff (like working on cardio, being a classically trained vocalist, and doing breath holding challenges). $\endgroup$ May 28 '17 at 13:05
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Yes.

We breathe by moving our diaphragm down, which creates a partial vacuum in our lungs (air pressure inside is lower than pressure outside the body). Instead of the outside air crushing the chest (which it will, a bit, if you try to inhale with your airway closed), the open airway allows air to rush in (it's pushed in by the surrounding air expanding into the airway).

Given that, it's hopefully easy to see why a larger opening to the airway allows for more air to enter, more quickly. The strength of the muscles moving the diaphragm is obviously a factor, too, which you might want to "tweak" in your story if you are trying to maximize air intake. But for the purposes of this answer, we can assume it's constant.

Inhaling through the nose means that difference in pressure has to be resolved by piping air through two very narrow little nostrils. The trachea isn't exactly roomy at 15-20cm inside diameter, so you don't exactly have to have your mouth wide open to maximize breathing, but it's going to be a lot better than nose breathing.

Solving the dryness problem

The humidity and temperature of the air coming in makes a big difference. (A colder ambient temperature really reduces the relative humidity when the air is heated in the airway.) Higher airflow means you're going to need more temperature and humidity, either within the airway, or perhaps even outside the body in a heated humidifier. Anyone who has ever slept with a CPAP machine, especially in a colder climate, knows this very well.

Other ways to get more oxygen

You may have already considered this as well, but humans breathe in 20% oxygen and exhale 15% oxygen, so we're not especially good at it. If your geneticists can improve that number by 5%, you double the available oxygen in each breath, over and above anything I've already discussed. Adding supplemental oxygen helps in a similar fashion.

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Yes for average, but no for max

You have increased the rate at which the lungs can replenish the air in them. However, humans already can do this for limited amounts of time. Even if your creature can maintain this state permanently you have not increased the max oxygen exchange that their lungs can achieve beyond that which a human is capable of.

Most of the time the body does not need to breathe at the max rate, if we intentionally do it anyways it will result in hyperventilation. It will likely be the same thing with your creature. If you are not doing intense physical activity then your body will not need all that oxygen anyways. When doing intense physical activity that would require this, odds are other limiting factors are going to kick in before the sore throat does. Under normal conditions it would not matter how long you can maintain quick breathing.

Low oxygen environments

This is one case where it will make a huge difference. Being in such an environment causes one to need to breathe rapidly, and as such it will give your creature a major advantage since they can do that for as long as they want.

Larger lungs

Having larger lungs will allow more oxygen to get into the body, but again does their body need that extra oxygen? Also can the heart handle pumping more blood into the larger lungs? It would be best to upgrade everything with the respiratory system if you decide to upgrade the lungs to avoid putting an extra strain on any one part.

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No

Under normal circumstances, humans breathe through their noses, acquiring their base-line required amount of oxygen.

Under strain (physical exertion, stress, etc.), humans breathe through their mouths to acquire more oxygen faster than they normally get through the nose.

In other words, humans have already solved the "mouth breathing problems": we have a nose for most breathing, but can still breathe through the mouth when necessary.

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