Answer:
620 m/s
Explanation:
The root-mean-square speed ([tex]v_{rms}[/tex]) of a gas can be calculated using the following expression.
[tex]v_{rms}=\sqrt{\frac{3RT}{M} }[/tex]
where,
R: ideal gas constant
T: absolute temperature
M: molar mass
We can use the data of carbon dioxide to find the temperature.
[tex]T=\frac{v_{rms}^{2} \times M}{3\times R} \\T=\frac{(396m/s)^{2} \times 0.044kg/mol}{3\times 8.314 J/mol.K}\\T=277K[/tex]
Now that we know the temperature, we can calculate the root-mean-square speed of water vapor molecules.
[tex]v_{rms}=\sqrt{\frac{3RT}{M} }=\sqrt{\frac{3\times (8.314J/mol.K)\times 277K}{0.018kg/mol} }=620 m/s[/tex]
