Question

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

• A. $1.0atmosphere$
• B. $1.5atmosphere$
• C. $2.0atmosphere$
• D. $3.0atmosphere$

Answer 1

The correct option is D $3.0atmosphere$

The root mean square speed (u) of hydrogen molecule is related to its pressure (P) and density (d) by the following expression.
$u=\sqrt{\frac{3P}{d}}$
$3180m/s=\sqrt{\frac{3P}{8.99\times {10}^{-2}kg/m^3}}$
$P=303034.9N/m^2$
$P=\frac{303034.9N/m^2}{1.01\times {10}^{5}N/m^2}$
$P=3.0atm$
Hence, the pressure on the hydrogen gas is 3.0 atm.