Will dissolved oxygen increase in a water sample inside a jar?

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When a glass containing 100mL of water is capped and the temperature is decreased by 20 degrees, the dissolved oxygen (DO) levels are affected. While the absolute amount of oxygen dissolved in the water remains constant, the percentage of oxygen saturation increases. This is because the maximum capacity for oxygen in solution decreases at lower temperatures, leading to a higher saturation percentage. However, if the water is near 100% saturation, some excess gas may escape into the atmosphere of the sealed glass, potentially reducing the absolute amount of dissolved oxygen while increasing the atmospheric pressure inside the glass. This phenomenon is similar to the behavior of CO2 in a sealed soda bottle.
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I know dissolved oxygen increases in water as temperature decreases.

But if I pour some water in a jar and close it, and then decrease temperature, will the DO increase if the sample is just laying in the jar? (No agitation)
If I have 100mL inside a glass with a closed cap. I take the cap off, measure DO, put the cap back on and decrease the temperature 20 degrees. No agitation of any sort.

Does the DO increase?
 
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The amount of oxygen dissolved in the water remains the same.
However, the percentage oxygen saturation in the water will increase.
10% oxygen saturation is the max amount of oxygen the water can maintain in solution under the conditions.

100% oxygen saturation will be less at higher temperatures, but the absolute amount of oxygen will will not. Therefore the percentage oxygen saturation will go up in the sample.

However, it possible that some excess gas will leave solution and go into the atmosphere in the enclose atmosphere of the glass, if any (especially if its about 100% saturation). This will reduce the absolute amount of dissolved oxygen in the water and increase the pressure of the atmosphere in the glass (if its sealed). This is like CO2 in a sealed a bottle of soda.
 
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