Question

The rms speed of a certain sample of carbon dioxide molecules, with a molecular weight of
44 g/mole, is 396 m/s. What is the rms speed of water molecules, with a molecular weight of
18 g/mol, at the same temperature?

Answer 1

The root mean square speed of a object is given as

$V_{rms} = \sqrt{\frac{3RT}{M_0}}$

Where,

$M_0$ = Molar mass

T = Temperature

R = Universal gas constant

Tenemos que ambos estados tienen la misma temperatura tenemos que para el estado 1 y 2 la ecuación en función de ésta es

$T = (\frac{V_{rms}(\sqrt{M_0})}{\sqrt{3R}})^2$

$T_1 = T_2$

$(\frac{V_{1rms}(\sqrt{M_A0})}{\sqrt{3R}})^2 =(\frac{V_{2rms}(\sqrt{M_B0})}{\sqrt{3R}})^2$

$V_{1rms}(\sqrt{M_A0}) = V_{2rms}(\sqrt{M_B0})$

$396*\sqrt{44}=V_{2rms}\sqrt{18}$

$V_{2rms} = 619.134 m/s$

Therefore the rms speed of water molecules is 619.134m/s