Volume of a mole of air 15km above sea level

[wannabero]

Homework Statement

one mole of an ideal gas takes up 0.0225m3 at 0 degrees celsius and 1.01x10(5) pascals. (calculated)
hence, calculate the volume of 1 mole of air (ideal) at an altitude of 15km above sea level.
average molecular mass of air = 29 amu.
T @ altitude of 15km = 0 degrees C.

Homework Equations

I used pv=nrt for the first part.
another equation i can find is

M = m N A
where M is the mass of the mole in kg, m is the atomic mass unit in kg, N is the atomic mass, and A is avogadros constant.

The Attempt at a Solution

volume of a mole of air can be calculated using pv=nrt, rearranged for v which is v=nrt/p.
however, i have no idea how to bring the altitude into it!

thanks for help!

Edit: Perhaps equation P = P0 exp (-mgy/k(b) t)?
where m = average molecular mass in kg, g = acceleration due to gravity, y = altitude in m, kb is boltzmanns constant and t is temperature?
but I'm not sure where to find volume.

 

[gneill]

Homework Statement

one mole of an ideal gas takes up 0.0225m3 at 0 degrees celsius and 1.01x10(5) pascals. (calculated)
hence, calculate the volume of 1 mole of air (ideal) at an altitude of 15km above sea level.
average molecular mass of air = 29 amu.
T @ altitude of 15km = 0 degrees C.

Homework Equations

I used pv=nrt for the first part.
another equation i can find is

M = m N A
where M is the mass of the mole in kg, m is the atomic mass unit in kg, N is the atomic mass, and A is avogadros constant.

The Attempt at a Solution

volume of a mole of air can be calculated using pv=nrt, rearranged for v which is v=nrt/p.
however, i have no idea how to bring the altitude into it!

thanks for help!




Edit: Perhaps equation P = P0 exp (-mgy/k(b) t)?
where m = average molecular mass in kg, g = acceleration due to gravity, y = altitude in m, kb is boltzmanns constant and t is temperature?
but I'm not sure where to find volume.

Your "EDIT" formula looks promising; Use it in conjunction with the pv = nRt that you mentioned earlier.