With the removal from the earth's surface air density decreases. This is because the pressure in the upper layers of the atmosphere is lower than that of the earth.
What is the relationship between air pressure and its density?
The density of a gas is directly proportional to its pressure. The dependence of the density of the air from the pressure equation describes Clapeyron: for an ideal gas
,
where ? - air density, p is the absolute pressure, R is the specific gas constant for dry air (287,058 j?(kg·K)) , T is the absolute temperature in Kelvin.
To calculate the density of the air ? at a certain height above sea level h using the following formula:
where 
Here
p0 is the standard atmospheric pressure at sea level (101325 PA);
T0is the standard temperature at sea level (288,15 K);
g - free fall acceleration on the surface of the Earth (9.8 m?sec2);
L - rate of fall of temperature with height in the troposphere (0,0065 K?m);
R is the universal gas constant (8,31447 j?(Mol·K) );
M - molar mass of dry air (0,0289644 kg?Mol).
It is clear and intuitive: the lower layers of air are under the most intense pressure than the top.
What does low blood pressure and reduced air density? This means that such thin air contains fewer molecules, including molecules of oxygen. That is why at high altitude hard to breathe.
By the way...
At 0°C the mass of one cubic meter (1 m3) of air is:
- at the earth's surface - 1, 293 kilograms;
- at the altitude of 12 km - 319 grams;
- at a height of 40 km - 4 grams.
