Question

The root-mean-square speed (thermal speed) of a certain sample of carbon dioxide molecules, with a molecular weight of 44 g/mol, is 396 m/s. What is the root-mean-square speed (thermal speed) of water vapor molecules, with a molecular weight of 18 g/mol, at the same temperature?

Answer 1

Answer:

620 m/s

Explanation:

The root-mean-square speed ($v_{rms}$) of a gas can be calculated using the following expression.

$v_{rms}=\sqrt{\frac{3RT}{M} }$

where,

R: ideal gas constant

T: absolute temperature

M: molar mass

We can use the data of carbon dioxide to find the temperature.

$T=\frac{v_{rms}^{2} \times M}{3\times R} \\T=\frac{(396m/s)^{2} \times 0.044kg/mol}{3\times 8.314 J/mol.K}\\T=277K$

Now that we know the temperature, we can calculate the root-mean-square speed of water vapor molecules.

$v_{rms}=\sqrt{\frac{3RT}{M} }=\sqrt{\frac{3\times (8.314J/mol.K)\times 277K}{0.018kg/mol} }=620 m/s$