How do I solve for dP/dz in the ideal gas law using mass and density?

[pentazoid]

Homework Statement

Calculate the mass of a mole of dry air, which is mixture of N₂(78 percent by volume, O₂ (21 percent) and argon (1 percent).

Use the ideal gas law to write the density of air in terms of pressure, temperature , and the average mass of the air molecules. Show , then, that the pressure obeys the differential equation

dP/dz=-mgP/kT

Homework Equations

PV=nkT

The Attempt at a Solution

m(total)=.78(28 grams)+.21(16 grams)+.01(40 grams)= 29 grams

rho=m/V , from Ideal gas law, V=nKT/P ==> rho=m*P/nkT


I am having difficulties with show that dP/dz=-mgP/kT. I know other thread on the ideal gas law problem concerning the same problem I said that dP/dz=-rho*g. and I know that rho=mP/nkT, therefore I guess dP/dz=rho*g=mgP/nkT. The only problem is how would I get rid of n? Should I assume that they are talking about one mole of air and therefore n=1?

 

[turin]

you just need to be careful about your definition of m and n.

 

[pentazoid]

you just need to be careful about your definition of m and n.

what do you mean?

 

[turin]

There is a number of moles and there is a number of molecules. There is a molar mass and a molecular mass. In your equations, which ones are you using? You don't have to choose a particular number of moles in order to get the answer. You need to write the ideal gas law entirely in terms intensive variables and constants.