Final answer:
The mass of a 2.00 L deep breath of air can be estimated using the ideal gas law, considering environmental conditions and the average molecular mass of air. Taking a deep breath increases the body's volume and slightly decreases its density, following the principle that density is mass divided by volume.
Step-by-step explanation:
To calculate the mass of a deep breath of air having a volume of 2.00 L at body temperature, we can use the ideal gas law under the assumption that air behaves like an ideal gas. The molecular mass of air is approximately 29 g/mol, considering it's a mixture primarily of nitrogen (about 79%) and oxygen (about 20%). To find the mass, we first need the number of moles, which we can calculate using the ideal gas law PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.
Assuming standard body temperature of 37.0°C, which is 310 K, and atmospheric pressure as 1 atm, we can estimate the number of moles and then multiply by the molecular mass of air to find the mass. However, this calculation would also require the gas constant R in appropriate units (0.0821 L atm mol⁻¹ K⁻¹).
Upon taking a deep breath, the volume of the body increases slightly due to the increase in lung volume, and since mass has not significantly changed, the density of the body decreases marginally. This is because density is defined as mass per unit volume, and as volume increases with no significant change in mass, density decreases.