Calcium carbonate is a chemical compound with the formula CaCO3. It is a common substance found in rocks as the minerals calcite and aragonite (most notably as limestone, which contains both of those minerals) and is the main component of pearls and the shells of marine organisms, snails, and eggs.
An ordinary breath for a 70-kg adult is about 500ml of air. We call this the tidal volume. Since oxygen is 21% by volume of air, then the volume of oxygen inhaled is about 105ml. The density of pure oxygen at sea level is 1.43kg per cubic metre.
Assuming you take one deep breath, you have to overcome the dead air space only one time. All the additional air inhaled in that breath is available for gas exchange. If you take two quick breaths, you have to fill the dead air space twice.