Given, gas has Pressure (P) = 105 Pa , Volume (V) = 0.3 m3 and Temperature (T) = 300 K.
The ideal gas equation is
PV = nRT
Where, n is no of moles of gas and
R = 8.314 J/mol.K is universal gas constant
So, for the given gas
So, 12 moles of gas is present in the system.
We know that , 1 mol = 6.022 x 1023 particle
So, total no of molecules present in the system = 12.027 x 6.022 x 1023 = 72.43 x 1023
Now, the area under the Maxwell-Boltzmann (MB) distribution of a certain system from zero up to a certain molecular speed (v), represents the probability of finding a molecule with a molecular speed smaller or equal than v in that system.
According to the question, The area under the MB distribution between v = 0 to 1730 m/s is 0.81.
i.e. the probability of finding a molecule with a molecular speed 0 to 1730 m/s is 0.81.
So, probability of finding a molecule with a molecular speed greater than 1730 m/s is = 1 -0.81 = 0.19
i.e. 19 % molecules have molecular speed greater than 1730 m/s.
or, the no of molecules with a molecular speed greater than 1730 m/s
For any doubt please comment and please give an up vote. Thank you.
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