Why are there less air molecules up there on the mountain?

[justx007]

I know that on top of a mountain, water boils at a lower temperature because the pressure there is lower. Pressure is lower since there are less air molecules there.

Can someone tell me why are there less air molecules up there?

[YT2095]

gravity is keeping the air close to earth, and the higher you go there`s less air above pushing down on it.

[dirtyamerica]

and to add to YT's post, the air is made up of compressable gases. The atmosphere at the bottom gets squished more.

 

Think of a big pile up in a football game. The guy at the bottom of the pile is getting smashed down by all the other players on top. Some one near the top isn't squished so badly.

 

And generally, the air mixes enough where there is a constant ratio of N, O, CO2 and others. Some people might argue that there is less oxygen in the mountains. True but there is also less of the other gases per volume.

 

The oxygen (etc.) is spaced out further so when it goes into your lungs, less oxygen can be absorbed so you're out of breath.

[Sessumaru]

...because the gravity is less on the high grounds than the lower grounds, which means that the air molecules are compactly held near the lower grounds that the higher grounds...did that help?

[insane_alien]

the gravity difference is negligible, it is due to the fact that air is compressible and has mass.

[D H]

the gravity difference is negligible, it is due to the fact that air is compressible and has mass.

That is exactly correct. The difference in gravitational acceleration is very small, decreasing by about 3.1×10^-6 m/s² for every meter above the surface. This is the free-air correction to gravity. For the air pressure at the top of a mountain, the correction for altitude is even smaller because there is mountain rather than air between the top of the mountain and the mean surface of the Earth. In short, gravity is not the cause of the decrease in pressure.

 

Imagine building a cylindrical column 11 kilometers tall. The air at any point in the column must buoy the weight of all of the air above that point. This buoyant force comes from compression, or pressure. The pressure must increase from the top of the column to sea level to buoy the increasing mass of all of the air above some point in the column.

[Bignose]

Let's look at results the equations of fluid mechanics give us:

 

If the fluid is at rest, and gravity is in the negative z direction, the Navier-Stokes equations (actually the full conservation of momentum equations, N-S is specifically for Newtonian fluids only) becomes

 

[math]\frac{\partial p}{\partial z}= - \rho g [/math]

 

where [math]p[/math] is pressure in Pa

[math]\rho[/math] is density in kg/m^3 and

[math]g[/math] is the acceleration due to gravity

 

Now, for an incompressible fluid, like water, the density is constant, so the integration of the equations above is easy:

 

[math]p = \rho g h + p_0[/math] where p is the pressure at a height, h, from the height the reference pressure, p_0 was taken from.

 

Now, with a compressible fluid, like air, density is not constant. If we use the simplest relationship between a gas's temperature, pressure, and density, the ideal gas law, this is:

 

[math]\rho = \frac{p}{RT}[/math] where R is the gas constant and T is the temperature

 

Putting that equation in for density and integrating the above equation yields:

 

[math]p_2 = p_1 \exp[-\frac{g(z_2-z_1)}{RT_0}][/math]

 

So, you can easily see how the pressure goes down exponentially, even assuming the acceleration due to gravity is constant. Pressure and number of molecules are basically the same thing as pressure is caused by the impact of the the molecules running into things.