The root mean square speed of hydrogen molecu | vedclass

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(D) The formula for the root mean square speed $(v_{rms})$ of an ideal gas is given by $v_{rms} = \sqrt{\frac{3P}{\rho}}$,where $P$ is the pressure an

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$3$

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(D) The formula for the root mean square speed $(v_{rms})$ of an ideal gas is given by $v_{rms} = \sqrt{\frac{3P}{ho}}$,where $P$ is the pressure and $ho$ is the density.Rearranging the formula to solve for pressure $P$,we get $P = \frac{v_{rms}^2 ho}{3}$.Given $v_{rms} = 3180 \ m/s$ and $ho = 8.99 	imes 10^{-2} \ kg/m^3$.Substituting the values: $P = \frac{(3180)^2 	imes 8.99 	imes 10^{-2}}{3}$.$P = \frac{10112400 	imes 0.0899}{3} \approx \frac{909104.76}{3} \approx 303034.9 \ N/m^2$.Since $1 \ atm = 1.01 	imes 10^5 \ N/m^2$,then $P \approx \frac{303034.9}{101000} \approx 3 \ atm$.

The root mean square speed of hydrogen molecules of an ideal hydrogen gas kept in a gas chamber at $0^{\circ}C$ is $3180 \ m/s$. The pressure on the hydrogen gas is ..... $atm$ (Density of hydrogen gas is $8.99 \times 10^{-2} \ kg/m^3$,$1 \ atm = 1.01 \times 10^5 \ N/m^2$).

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