I have a container that has CO2 in it. The root-mean-square speed of the gas is equal to 329 m/s. I need to calculate: 1) the molar mass of the...

1) The molar mass of CO2  = 12.1 g/mol + 2(16.0 g/mol) = 44.1 g/mol

2) Knowing the molar mass allows you to use the rms velocity equation to calculate temperature:

`rms =sqrt((3RT)/M)`

Where R = 8.3145 (kg-m^2/sec^2)/K-mol,

and M = 44.1 g/mol = 0.0441 kg/mol

`(rms)^2 = (3RT)/M`

`T = (rms)^2(M)/(3(8.3145))`

`T = [(108241 m^2/s^2)(.0441)( kg)/(mol)]/(3((8.3145 kg (m)^2)/((sec)^2 mol K))`

` `

`T = 191K`

The equation `rms =sqrt((3P)/d)`  shows the dependence of...

1) The molar mass of CO2  = 12.1 g/mol + 2(16.0 g/mol) = 44.1 g/mol

2) Knowing the molar mass allows you to use the rms velocity equation to calculate temperature:

`rms =sqrt((3RT)/M)`

Where R = 8.3145 (kg-m^2/sec^2)/K-mol,

and M = 44.1 g/mol = 0.0441 kg/mol

`(rms)^2 = (3RT)/M`

`T = (rms)^2(M)/(3(8.3145))`

`T = [(108241 m^2/s^2)(.0441)( kg)/(mol)]/(3((8.3145 kg (m)^2)/((sec)^2 mol K))`

` `

`T = 191K`

The equation `rms =sqrt((3P)/d)`  shows the dependence of of rms velocity on pressure: The rms velocity is proportional to the square root of pressure or pressure is proportional to the square of the rms velocity when other factors in the equation remain constant. 

This equation is derived from `rms=sqrt((3RT)/M)`  by:

1. susbstituting (mass/molar mass) for n in the ideal gas equation, and

2. substituting density for mass/volume:

PV=nRT

P=nRT/V

P=mRT/MV

P=dRT/M

P/d=RT/M