A flask contains Argon and Chlorine in the ratio of 2 : 1 by mass. The temperature of the mixture is \( 27^\circ\mathrm{C} \). The ratio of root mean square speed of molecules of two gases will be: (atomic mass of Argon = 40 u and molecular mass of Chlorine = 71 u)
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1.33
The root mean square speed of a gas molecule is \( v_{\mathrm{rms}} = \sqrt{3k_BT/m} \). In a mixture both gases are at the same temperature, so \( v_{\mathrm{rms}} \propto 1/\sqrt{m} \); the amounts of the two gases do not enter.
\( \displaystyle \frac{v_{\mathrm{Ar}}}{v_{\mathrm{Cl}}} = \sqrt{\frac{m_{\mathrm{Cl}}}{m_{\mathrm{Ar}}}} = \sqrt{\frac{71}{40}} = \sqrt{1.775} \approx 1.33 \)