# Find the Root-Mean-Square of the gas

## Homework Statement

At 329 K and 1.37 x 10-2 atm, the density of a gas is 1.39 x 10-5 g/cm3. (a) Find vrms for the gas molecules. (b) Find the molar mass of the gas.

## Homework Equations

PV = nRT
Vrms = sqrt(3RT/M)

## The Attempt at a Solution

I could do this problem right now if there was a molar mass given in the question. How does the density help with finding the answer to the problem? I don't see any examples utilizing it so I'm not sure what to do.

Hint:
Try to find a relation between density and molar mass from the equation PV=nRT
n=m/M , where m is the mass of the gas and M the molar mass

All I can see is that density = mass/volume. So you are saying to replace n with m/m? And then set the equation equal to M? So it would be M = mRT/PV and substitite it in for M in the Vrms equation? So then it would be M = D(RT/P) and substitute that in for M in the Vrms equation? Or I guess I could find M right then and there and that gives me answer to part b then just plug M into the Vrms equation and that finds Vrms. Is that basically the solution to this problem?

Pressure in Pascals, density in kg/m^3 right?

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Or I guess I could find M right then and there and that gives me answer to part b then just plug M into the Vrms equation and that finds Vrms. Is that basically the solution to this problem?

Its better this way. Use R=0.0821 Lit atm K-1mol-1 because pressure is given in atm. Substitute the 'D' as it is and you will get 'M' in g units

Pressure in Pascals, density in kg/m^3 right?

Once you find out M in g units, convert it in kg units and plug it in your equation for Vrms. Use R in SI units here.

I was always told to conver to Pascals for pressure and use 8.31 J/mol*K for R. But I'm sure either works. I believe what I got is correct. I got M = .027 Kg/mol and Vrms = 497 m/s roughly.

D H
Staff Emeritus