A flask contains argon and chlorine in the ratio of 2:1 by mass. The temperature of the mixture is \(27^{\circ} C\). The ratio of root mean square speed of the molecules of the two gases \(\left(\frac{v_{r m s}^{A r}}{v_{r m s}^{C l}}\right)\) is :
(Atomic mass of argon =40.0 u and molecular mass of chlorine =70.0 u)

(A) \(\frac{\sqrt{7}}{2}\)
The root mean square speed of a gas molecule is given by \(v_{r m s}=\sqrt{\frac{3 R T}{M}}\), where \(T\) is the absolute temperature and \(M\) is the molar mass.
For argon and chlorine in the same flask, the temperature \(T\) is the same.
Therefore, the ratio of their rms speeds is inversely proportional to the square root of their molar masses:
\(\frac{v_{r m s}^{A r}}{v_{r m s}^{C l}}=\sqrt{\frac{M_{C l}}{M_{A r}}}\)
Given the molecular mass of chlorine \(M_{C l}=70.0 u\) and atomic mass of argon \(M_{A r}=40.0 u\) :
\(\frac{v_{r m s}^{A r}}{v_{r m s}^{C l}}=\sqrt{\frac{70.0}{40.0}}=\sqrt{\frac{7}{4}}=\frac{\sqrt{7}}{2}\)
The mass ratio of the gases in the mixture is extra information and not required for this calculation.