Question

The root means square speed of hydrogen molecules of an ideal hydrogen gas kept in a gas chamber at 0${}^o$C is 3180 m/s. The pressure of hydrogen gas will be (Density of hydrogen gas $=8.99\times {10}^{-2}$ kg/rn land 1 atmosphere $=1.01\times {10}^{5}N/m^2)$ :

• A. 3.0 atm
• B. 2.0 atm
• C. 1.0 atm
• D. 2.5 atm

Answer 1

The correct option is A 3.0 atm

R.M.S speed of $H_2$ = 3180 m/s
$P{h}_2$ = 8.99 $\times {10}^{-2}kg/m^3$,
1 atm = 1.01 $\times {10}^{5}N/m^2$
Pressure, P = $\frac{1}{3}p{c}^2$
=$\frac{1}{3}\times \frac{8.99\times {10}^{-2}\times 3180\times 3180}{1.01\times {10}^5}$ atm
= 3 atm