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## Homework Statement

The ideal gas law can be recast in terms of the density of a gas.

a) Use dimensional analysis to find an expression for the density [tex]\rho[/tex] of a gas in terms of the number of moles

*n*, the volume

*V*, and the molecular weight

*M*in kilograms per mole.

b) With the expression found in part (a), show that:

P = [tex]\frac{\rho}{M}[/tex]*RT

for an ideal gas.

c) Find the density of the carbon dioxide atmosphere at the surface of Venus, where the pressure is 90.0 atm and the temperature is 7.00 * 10

^{2}K.

d) Would an evacuated steel shell of radius 1.00 m and mass 2.00 * 10

^{2}kg rise or fall in such an atmosphere? Why?

## Homework Equations

Ideal Gas Law: PV = nRT

## The Attempt at a Solution

I have never really worked with dimensional analysis, but here's what I have so far:

PV = nRT

[Pa][m

^{3}] = [mol][J/mol*K][K]

But I'm not sure how to manipulate this.

Unfortunately, I can't complete the rest of the problem because it's all interdependent, and I'm unsure of how to proceed. Any help would be appreciated.