How Does Molar Mass Affect Gas Molecule Speeds at Equal Temperatures?

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The discussion focuses on calculating the translational root mean square (rms) speed of carbon dioxide (CO2) molecules given the rms speed of water vapor (H2O) at the same temperature. The equation used is Vrms = sqrt(3RT/M), where M is the molar mass of the gas. The user has established a relationship between the speeds of the two gases, leading to the equation 676 = sqrt(mCO2/mH2O). The key point is that since both gases are at equal temperatures, their speeds are inversely proportional to the square root of their molar masses. The discussion emphasizes the importance of understanding gas behavior in relation to molar mass and temperature.
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If the translational rms speed of the water vapor molecules (H2O) in air is 676 m/s, what is the translational rms speed of the carbon dioxide molecules (CO2) in the same air? Both gases are at the same temperature.

So what I have so far...

VrmsH20 = squareroot of 3RT/mCO2
VrmsCO2 = squareroot of 3RT/mCO2

676 = squareroot of mCO2/mH2O

And I already found the mass of the CO2 and H2O, but then I'm stuck... Can anyone help please?
 
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V_{rms} = \sqrt{\frac{3RT}{M}}

since the temperature is the same, think proportion.
 

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