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 in air, given the rms speed of water vapor (H2O) molecules at 676 m/s. The formula used is V_{rms} = √(3RT/M), where R is the universal gas constant and T is the temperature. The relationship between the speeds of the two gases is established through their molar masses, leading to the equation 676 = √(mCO2/mH2O). The mass values of CO2 and H2O are essential for determining the rms speed of CO2.

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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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