The root mean square speed of oxygen molecules at a certain absolute temperature is v . If the temperature is doubled and the oxygen gas dissociates into atomic oxygen, the root mean square speed would be -

Question

The root mean square speed of oxygen molecules at a certain absolute temperature is v . If the temperature is doubled and the oxygen gas dissociates into atomic oxygen, the root mean square speed would be - (A) v (B) √2v (C) 2v (D) 2√2v

Tardigrade Admin · Accepted Answer

RMS speed is given by vr m s=v=√[](3 R T/M) New temperature Tâ²=2T New molar mass Mâ²= (M/2) ∴ (vrms)new =√(3 R (. 2 T .)/((M)2)) (vrms)new =2v

Q. The root mean square speed of oxygen molecules at a certain absolute temperature is $v$ . If the temperature is doubled and the oxygen gas dissociates into atomic oxygen, the root mean square speed would be -

$v$

$2 v$

$2 v$

$22 v$

RMS speed is given by
$v_{r m s} = v = \frac{3 RT}{M}$
New temperature $T^{'} = 2 T$
New molar mass $M^{'} = \frac{M}{2}$
$∴ (v_{r m s})_{n e w} = \frac{3 R ( 2 T )}{( \frac{M}{2} )}$
$(v_{r m s})_{n e w} = 2 v$

Q. The root mean square speed of oxygen molecules at a certain absolute temperature is v . If the temperature is doubled and the oxygen gas dissociates into atomic oxygen, the root mean square speed would be -

v

2​v

2v

22​v

RMS speed is given by vrms​=v=M3RT​​ New temperature T′=2T New molar mass M′=2M​ ∴(vrms​)new​=(2M​)3R(2T)​​ (vrms​)new​=2v

Q. The root mean square speed of oxygen molecules at a certain absolute temperature is $v$ . If the temperature is doubled and the oxygen gas dissociates into atomic oxygen, the root mean square speed would be -

$v$

$2 v$

$2 v$

$22 v$

RMS speed is given by
$v_{r m s} = v = \frac{3 RT}{M}$
New temperature $T^{'} = 2 T$
New molar mass $M^{'} = \frac{M}{2}$
$∴ (v_{r m s})_{n e w} = \frac{3 R ( 2 T )}{( \frac{M}{2} )}$
$(v_{r m s})_{n e w} = 2 v$