JEE Main · 2023 · 12 Apr 2023 · Shift 1 · Heat & Thermodynamics

If the r.m.s. speed of chlorine molecule is

490 m/s

2 7^{\circ} C

, the r.m.s. speed of argon molecules at the same temperature will be (Atomic mass of argon

= 39.9 u

, molecular mass of chlorine

= 70.9 u

)

(A) $751.7 m/s$
(B) $451.7 m/s$
(C) $651.7 m/s$ ✓ Correct
(D) $551.7 m/s$

Answer: (C)

Solution

The r.m.s. speed is given by

v_{r m s} = \frac{3 R T}{M}

. At the same temperature, the ratio of r.m.s. speeds is

\frac{v _{A r}}{v _{C l}} = \frac{M _{C l}}{M _{A r}} = \frac{70.9}{39.9} \approx 1.33

. Therefore,

v_{A r} = 1.33 \times 490 \approx 651.7 m/s

JEE Main · 2023 · 12 Apr 2023 · Shift 1 · Single correct option

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