A flask contains argon and chlorine in the ratio of 2:1 by mass. The temperature of the mixture is 27^ . The ratio of root mean square speed of the molecules of the two gases ( v_ rms ^ Ar v_ rms ^ Cl ) is : (Atomic mass of argon = 40.0 u and molecular mass of chlorine = 70.0 u)
A. 7 2
The root mean square speed of a gas molecule is given by v_ rms = 3RT 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: v_ rms ^ Ar v_ rms ^ Cl = M_ Cl M_ Ar Given the molecular mass of chlorine M_ Cl = 70.0 u and atomic mass of argon M_ Ar = 40.0 u: v_ rms ^ Ar v_ rms ^ Cl = 70.0 40.0 = 7 4 = 7 2 The mass ratio of the gases in the mixture is extra information and not required for this calculation. Answer: 7 2
Related: Physics — Kinetic Theory of Gases · All PYQ Banks