Question

The pressure needed to confine 1.5 mole of $N_2$ molecules to 28 L flask is 1.0 bar. Thus, root mean square velocity of the gas (assuming ideal behaviour) is

• A. $370{\text{m s}}^{-1}$
• B. $200{\text{m s}}^{-1}$
• C. $51.5{\text{m s}}^{-1}$
• D. $37.0{\text{m s}}^{-1}$

Answer 1

The correct option is B $200{\text{m s}}^{-1}$

The given quantities in the question are $P$ $=$ 1 bar $={10}^{5}Pa$, $1L=1\times {10}^{-3}{m}^3$, $1g=1\times {10}^{-3}\text{kg}$

As $u_{rms}=\sqrt{\frac{3RT}{M}}$
(using $PV=nRT$)

$u_{rms}=\sqrt{\frac{3PV}{nM}}=\sqrt{\frac{3\times {10}^{5}Pa\times 28\times {10}^{-3}{m}^3}{1.5\times 28\times {10}^{-3}\text{kg}}}=\sqrt{0.2\times {10}^6}=0.2\times {10}^3$
$=200{\text{m s}}^{-1}$ (all data in SI units).