Why is the rate of breathing in aquatic organisms much faster than that in terrestrial organisms?

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Hint: The rate of breathing depends on the oxygen requirements of the body as well as the availability of the oxygen in the surrounding environment.

Complete answer:
Since the quantity of dissolved oxygen in water is fairly low as compared to the quantity of oxygen present in the air, aquatic organisms breathe faster to fulfill the required oxygen to the body cells for their proper functioning.
Similar to terrestrial animals, fishes also need oxygen to survive – but instead of breathing air, fish extract their oxygen from the water around them. This is not very easy for them because air can hold 33 times more oxygen than water, so fishes need to be far more efficient breathers than terrestrial animals that mean they have to repeat the process again and again to reach their requirement.
Fortunately, fishes have evolved an ingenious mechanism to overcome their oxygen-deprived environment through their highly specialized gills. The gill is where fish absorbs oxygen from the encompassing water into their blood. However, oxygen can only diffuse into the blood at the gills only if the oxygen level is higher within the water than within the blood.

Note: -Oxygen would quickly pass from the water into the blood until the oxygen levels of the blood and water rapidly became an equivalent, and oxygen diffusion into the blood would stop.
-The maximum amount of oxygen that the blood could devour would be only half the entire amount of oxygen within the water.
-It proves that fish are true masters of breathing.