Question

Determine the root-mean-square speed of CO2 molecules that have an average kinetic energy of
4.21 × 10–21 J per molecule.

Answer 1

The root mean square speed formula is

$E=\dfrac{1}{2}mv^2$

1 mole of CO2 =44.0 g or 0.044 kg

If energy is in form of Joules then, mass should be in kilograms.

$average mass of CO2 =\dfrac{mass ofCO2}{Avagadros constant}$

$=\dfrac{4.40*10^{-2}kg}{6.02*10^{23}kg}$ = 7.31* 10^-26 kg

since$E=\dfrac {1}{2}mv^2 then,$

v^2=2 E/m

=$2\dfrac{4.2*10^{-21}J}{7.31*10^{-26}kg}=115184.68$

V =$\sqrt{115184.68}$

= 339

therefore,root-mean-square speed is 339 m/s