If the r.m.s speed of chlorine molecule is 490 m s - 1 at 27 o C , the r.m.s speed of argon molecules at the same temperature will be (Atomic mass of argon = 39 . 9 u , molecular mass of chlorine = 70

Question

If the r.m.s speed of chlorine molecule is 490 m s - 1 at 27 o C , the r.m.s speed of argon molecules at the same temperature will be (Atomic mass of argon = 39 . 9 u , molecular mass of chlorine = 70 . 9 u )

TestHub · Accepted Answer

The formula to calculate the rms speed of the argon molecules is given by
$v_{A r} = \sqrt{\frac{3 R T}{M_{A r}}} . . . (1)$
The formula to calculate the rms speed of chlorine molecule is given by
$v_{C l} = \sqrt{\frac{3 R T}{M_{C l}}} . . . (2)$
Divide equation (1) by equation (2) and simplify to obtain the required ratio.
$\frac{v_{Ar}}{v_{Cl}} = \sqrt{\frac{M_{Cl}}{M_{Ar}}} . . . (3)$
Substitute the values of the known parameters into equation (3) and solve to calculate the required value.
$\begin{array}{rcl} \frac{v_{Ar}}{490 m s^{- 1}} & = & \sqrt{\frac{71}{40}} \\ \Rightarrow & v_{A r} = \sqrt{\frac{71}{40}} \times 490 m s^{- 1} \\ \approx & 651.7 m s^{- 1} \end{array}$

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