If the r.m.s speed of chlorine molecule is 490m s ^ - 1 at 27 ^ o C...

The formula to calculate the rms speed of the argon molecules is given by

${v}_{Ar} = \sqrt{\dfrac{3RT}{{M}_{Ar}}} . . . \left(1\right)$

The formula to calculate the rms speed of chlorine molecule is given by

${v}_{Cl} = \sqrt{\dfrac{3RT}{{M}_{Cl}}} . . . \left(2\right)$

Divide equation (1) by equation (2) and simplify to obtain the required ratio.

$\dfrac{{v}_{Ar}}{{v}_{Cl}} = \sqrt{\dfrac{{M}_{Cl}}{{M}_{Ar}}} . . . \left(3\right)$

Substitute the values of the known parameters into equation (3) and solve to calculate the required value.

$\begin{cases}\dfrac{{v}_{Ar}}{490m{s}^{- 1}} & = & \sqrt{\dfrac{71}{40}} \\ & ⇒ & {v}_{Ar} = \sqrt{\dfrac{71}{40}} \times 490m{s}^{- 1} \\ & \approx & 651 . 7m{s}^{- 1}\end{cases}$