Question

Oxygen at 1 atmosphere and $0^{\circ }\text{C}$ has a density of $7.5{\text{g L}}^{-1}$. Find the rms speed of oxygen molecule in $m{s}^{-1}$

Answer 1

$P=1\text{atm}=1.01\times {10}^5\text{Pa}$
taking 1.01 approximately equal to 1 for calculation
$d=7.5{\text{g L}}^{-1}=7.5{\text{kg m}}^{-3}$
We know that,
$c=\sqrt{\frac{3P}{d}}=\sqrt{\frac{3\times 1.01\times {10}^5}{7.5}}=\sqrt{\frac{{10}^6}{25}}=0.2\times {10}^3=200{\text{ms}}^{-1}$