The root mean square (R.M.S.) Speed V of the molecules of an ideal gas is given by the expressions,
v = √ (3RT/M) and
v = √ (3KT/m) where R is universal gas constant, T is the absolute (Kelvin) temperature M is the molar mass, K is Boltzman's constant and M is the molecular mass. The R.M.S. speed of oxygen molecules (O2) at temperature T1 is V1. When the temperature is doubled, if the oxygen molecules are dissociated into atomic oxygen, what will be R.M.S. speed of oxygen atoms? (Treat the gas as ideal).
The root mean square (R.M.S.) Speed V of the molecules of an ideal gas is given by the expressions,
v = √ (3RT/M) and
v = √ (3KT/m) where R is universal gas constant, T is the absolute (Kelvin) temperature M is the molar mass, K is Boltzman's constant and M is the molecular mass. The R.M.S. speed of oxygen molecules (O2) at temperature T1 is V1. When the temperature is doubled, if the oxygen molecules are dissociated into atomic oxygen, what will be R.M.S. speed of oxygen atoms? (Treat the gas as ideal).
The correct option is D 2v1
We have V1 = √ (3RT1/M) or
V1 = √ (3kT1/m)
on dissociation the molar mass as well as the molecular mass gets halved. Using the second equation, the R.M.S. speed V after dissociation is given by
V = √[3k x 2T1/(m/2)] = 2 √ (3kT1/m) = 2V1
2v1
We have V1 = √ (3RT1/M) or
V1 = √ (3kT1/m)
on dissociation the molar mass as well as the molecular mass gets halved. Using the second equation, the R.M.S. speed V after dissociation is given by
V = √[3k x 2T1/(m/2)] = 2 √ (3kT1/m) = 2V1
