JEE Main · 2023 · 12 Apr 2023 · Shift 1 · States of Matter

At 600 K, the root mean square (rms) speed of gas X (molar mass

= 40

) is equal to the most probable speed of gas

Y

at 90 K. The molar mass of the gas Y is ______

g mol^{- 1}

. (Nearest integer)

Answer: 4

Solution

Equating the root mean square speed of X at

600 K

to the most probable speed of Y at

90 K

\frac{3 R T _{X}}{M _{X}} = \frac{2 R T _{Y}}{M _{Y}}

Squaring and inserting the data,

\frac{3 \times 600}{40} = \frac{2 \times 90}{M _{Y}}

45 = \frac{180}{M _{Y}}

The molar mass of gas Y is

4 g mol^{- 1}

JEE Main · 2023 · 12 Apr 2023 · Shift 1 · Integer answer

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