A vessel contains $1$ mole of ${O_2}$ gas (molar mass $32)$ at a temperature $T.$ The pressure of the gas is $P. $ An identical vessel containing one mole of $He$ gas (molar mass $4)$ at temperature $2T$ has a pressure of
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If the root mean square velocity of hydrogen molecule at a given temperature and pressure is $2 \mathrm{~km} / \mathrm{s}$, the root mean square velocity of oxygen at the same condition in $\mathrm{km} / \mathrm{s}$ is :
A gas is filled in a cylinder, its temperature is increased by $20\%$ on kelvin scale and volume is reduced by $10\%$ . How much percentage of the gas will leak out at constant pressure ...... $\%$
A mixture of hydrogen and oxygen has volume $2000 \; cm ^{3}$, temperature $300 \; K$, pressure $100 \; kPa$ and mass $0.76 \; g$ The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be
The root mean square speed of molecules of nitrogen gas at $27^{\circ} C$ is approximately$.......m/s$(Given mass of a nitrogen molecule $=4.6 \times 10^{-26}\,kg$ and take Boltzmann constant $k _{ B }=1.4 \times 10^{-23}\,JK ^{-1}$ )
$28\,\, gm$ of $N_2$ gas is contained in a flask at a pressure of $10$ atm and at a temperature of $57^o$. It is found that due to leakage in the flask, the pressure is reduced to half and the temperature reduced to $27\,^oC$. The quantity of $N_2$ gas that leaked out is
The pressure $P,$ volume $V$ and temperature $T$ of a gas in the jar $A$ and the other gas in the jar $B$ at pressure $2P,$ volume $V/4$ and temperature $2T,$ then the ratio of the number of molecules in the jar $A$ and $B$ will be
A cylinder contains $10\, kg$ of gas at pressure of ${10^7}\,\,N/{m^2}.$ The quantity of gas taken out of the cylinder, if final pressure is $2.5 \times {10^6}\,N/{m^2},$ will be ..... $kg$ (Temperature of gas is constant)