Final answer:
To estimate at what height the molecular density of air is reduced by a factor of 2, we consider the ideal gas law and the exponential decrease of pressure with altitude. While exact calculation would require additional specific data, a rough estimate suggests the density halves every 5.6 km in altitude in the lower atmosphere under isothermal conditions.
Step-by-step explanation:
To determine at what height above sea level the molecular density of air (at 22C) is reduced by a factor of 2, assuming the molar mass of air is 29 g/mol, we need to consider the behavior of the atmosphere and the ideal gas law. The equation that relates the pressure, volume, and temperature of an ideal gas is PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the universal gas constant, and T is the temperature.
As the altitude increases, the pressure of the atmosphere decreases. This change in pressure is what impacts the density of air. Assuming the temperature remains constant and that pressure decreases with altitude exponentially, the altitude at which the density of air is halved can be estimated using the barometric formula. However, for this specific calculation, additional information such as the rate of change of atmospheric pressure with altitude (the scale height) would be required, which is not provided in the question.
As an approximation, at mid-latitudes, the air pressure (and thus the density) halves approximately every 5.6 km in the lower atmosphere under isothermal conditions. This approximation can give us a rough estimate in lieu of the exact calculation.