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If we keep on increasing \[C{O_2}\] concentration in the air what will be the rate of photosynthesis?

Answer
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Hint: Photosynthesis is a process of converting light energy into chemical energy through green plants and many other organisms (Algae, Euglena, Bacteria, etc). Light energy is absorbed and used to convert \[C{O_2}\], water, and minerals into oxygen and energy-rich organic compounds during photosynthesis in green plants.

Complete answer:
An increase in \[C{O_2}\] concentration increases the rate of photosynthesis in green plants but only if it is not limited by other factors such as the amount of sunlight present and the rate of light absorption by the plant.

Even if we ignore these limiting factors, the photosynthetic rate can only increase up to a certain point (generally up to $1\% $ of \[C{O_2}\] concentration). How high that point depends on temperature and plant size and plant species, so it’s hard to say exactly how much photosynthetic rate will increase based on \[C{O_2}\] concentration and it’s also hard to say when it’ll plateau.

So, the amount of release of \[C{O_2}\] decides the rate of photosynthesis. From a pragmatic standpoint, the photosynthetic rate should not be pumped up too much. If the plants are put in an environment with \[C{O_2}\] concentration and light incidence above what they’re native to, plants will show some toxic effects and will inhibit photosynthesis. It’s better to keep the environment you’re growing plants in as close to what they’re native to (or what they’ve been bred to be comfortable with) as possible if you want them to grow up healthy.

Note: During the process of photosynthesis, cells of plants use \[C{O_2}\] and energy obtained from the Sun to make glucose molecules and oxygen. Then through respiration processes, cells use oxygen and glucose to synthesize energy-rich carrier molecules, such as ATP, and \[C{O_2}\] is emitted as a waste product.