Root Mean Square Speed Units Question

[spockjones20]

Homework Statement

"At 273 K and 1.00x10^-2 atm, the density of a gas is 1.24x10^-5 g/cm^3.

A.) Find the Vrms for the gas molecules
B.) Find the molar mass and identify the gas (Choose from H2, He, H20, N2, O2, or CO2)"

Homework Equations

Vrms = √(3RT/Mm)
pV = nRT

The Attempt at a Solution

n = mass/Mm
pV = mass/Mm *RT
Mm = mass*RT/(pV)
Mm = ρRT/p

Vrms = √(3RT/(ρRT/p)) = √(3p/ρ)

So I have the solution up until this point, the main thing I am worried about is the units of my answer. I have pressure in atm, which is some form of Force/Area. I have density in g/cm^3. So pressure/density will be some form of (distance/time)^2, which of course is taken care of with the radical. The only thing I can not come up with is what exact units it will be in. Any help here would be greatly appreciated. Thanks in advance.

 

[Gamma]

A rule of thumb is that if you use SI units for every term in an expression, you can expect the answer to be in SI units. You can do a dimensional analysis to verify this as well. Converting atm to Pascals and g/cm^3 to Kg/m^3, should give you m/s for Vrms.

 

[spockjones20]

Ok, that makes sense. Thanks a lot!

 

[SteamKing]

Since ideal gas calculations can sometimes involve a mixture of different units, the following article gives values of R in several different unit combinations:

http://en.wikipedia.org/wiki/Gas_constant

 

[paranormal]

The units for Vrms will be in units of velocity, specifically cm/s. This is because the units of pressure are in force per area (N/m^2 or kg/(m*s^2)), and the units of density are in mass per volume (g/cm^3 or kg/m^3). When we take the square root, the units will simplify to m/s or cm/s. Therefore, for the given conditions, the Vrms of the gas molecules would be in units of cm/s.

To find the molar mass and identify the gas, we can use the ideal gas law, pV = nRT, where p is pressure, V is volume, n is moles, R is the gas constant, and T is temperature. Rearranging this equation, we get n = (pV)/(RT). We already have the values for p, V, and T, so we can plug those in and solve for n. Then, using the given density, we can calculate the mass of the gas using the formula m = ρV. Finally, we can divide the mass by the number of moles to get the molar mass, which will allow us to identify the gas.