At 400 K, the root mean square (rms) speed of a gas X (molecular weight = 40) is equal to the most probable speed of gas Y at 60 K. The molecular weight of the gas Y is

Question

At 400 K, the root mean square (rms) speed of a gas X (molecular weight = 40) is equal to the most probable speed of gas Y at 60 K. The molecular weight of the gas Y is (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Velocity of gaseous molecules is increased by increasing temeprature.
Velocity of gaseous molecules is decreased by increasing molecular mass of gas.

v_{r m s}

of

X = \frac{3 R T _{x}}{M _{x}}; v_{m p}

of

Y = \frac{2 R T _{y}}{M _{y}}

Given

v_{r m s} = v_{m p}

\frac{3 R T _{x}}{M _{x}} = \frac{2 R T _{y}}{M _{y}}

M_{y} = \frac{2 R T _{y} M _{x}}{3 R T _{x}} = \frac{2 \times 60 \times 40}{3 \times 400} = 4

Q. At 400K, the root mean square (rms) speed of a gas X (molecular weight =40) is equal to the most probable speed of gas Y at 60K. The molecular weight of the gas Y is

Q. At $400 K,$ the root mean square (rms) speed of a gas $X$ (molecular weight $= 40$ ) is equal to the most probable speed of gas $Y$ at $60 K$ . The molecular weight of the gas $Y$ is