In two vessels of the same volume,atomic hydr | vedclass

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Question

(C) The average speed of a gas molecule is given by the formula: $\langle C \rangle = \sqrt{\frac{8RT}{\pi M}}$.Since the temperature $T$ is the same

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$\langle C_H \rangle = 2 \langle C_{He} \rangle$

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(C) The average speed of a gas molecule is given by the formula: $\langle C \rangle = \sqrt{\frac{8RT}{\pi M}}$.Since the temperature $T$ is the same for both gases,the average speed is inversely proportional to the square root of the molar mass $M$,i.e.,$\langle C \rangle \propto \frac{1}{\sqrt{M}}$.The molar mass of atomic hydrogen $(H)$ is $M_H = 1 \, g/mol$ and the molar mass of helium $(He)$ is $M_{He} = 4 \, g/mol$.Taking the ratio of the average speeds:$\frac{\langle C_H \rangle}{\langle C_{He} \rangle} = \sqrt{\frac{M_{He}}{M_H}} = \sqrt{\frac{4}{1}} = 2$.Therefore,$\langle C_H \rangle = 2 \langle C_{He} \rangle$.

In two vessels of the same volume,atomic hydrogen and helium at pressures of $1\, atm$ and $2\, atm$ are filled,respectively. If the temperature of both samples is the same,then the average speed of hydrogen atoms $\langle C_H \rangle$ will be related to that of helium $\langle C_{He} \rangle$ as:

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