A closed terrarium is a closed ecosystem just on a much smaller scale. The
supply of carbon dioxide in the terrarium air is very small because of the
limited volume of air. Therefore, unless the terrarium contains animals
to provide carbon dioxide or microbes break down large amounts of organic
matter in the soil and release carbon dioxide, the plants in a sealed
terrarium cannot gain significant dry weight. They would basically refix
the same carbon dioxide over and over. The carbon dioxide the plants
release during cellular respiration would be refixed via photosynthesis,
then respired, refixed, respired, refixed, etc.
Most terrariums are not completely sealed so carbon dioxide can enter and
plants can gain dry matter via photosynthesis. The inventor of the
terrarium, Nathaniel Bagshaw Ward (1791-1868), supposedly had a "sealed
terrarium" that survived four years but it is questionable if it was
completely sealed because of the substantial plant growth he observed.
Another attempt at a closed terrarium on a larger scale was the big
Arizona greenhouse called Biosphere Two . It was
originally supposed to be a sealed terrarium for two years containing
several people, many animals and all sorts of plants. However, it got out
of balance, and they had to add more oxygen because the amount of
photosynthesis was less than required to supply adequate oxygen to all the
animals.
References:
Hershey, D.R. 1996. Doctor Ward's accidental terrarium. American Biology
Teacher. 58:276-281.