Blog: 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...

Tuesday, November 9, 2010

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:

$\displaystyle{r}{m}{s}=\sqrt{{\frac{{{3}{R}{T}}}{{M}}}}$

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

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

$\displaystyle{{\left({r}{m}{s}\right)}}^{{2}}=\frac{{{3}{R}{T}}}{{M}}$

$\displaystyle{T}={{\left({r}{m}{s}\right)}}^{{2}}\frac{{{M}}}{{{3}{\left({8.3145}\right)}}}$

$\displaystyle{T}=\frac{{{\left({108241}\frac{{{m}}^{{2}}}{{{s}}^{{2}}}\right)}{\left({.0441}\right)}\frac{{{k}{g}}}{{{m}{o}{l}}}}}{{{3}{\left(\frac{{{8.3145}{k}{{g{{\left({m}\right)}}}}^{{2}}}}{{{{\left({\sec}\right)}}^{{2}}{m}{o}{l}{K}}}\right)}}}$

$\displaystyle{T}={191}{K}$

The equation $\displaystyle{r}{m}{s}=\sqrt{{\frac{{{3}{P}}}{{d}}}}$ 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.