# Under 3atm , 12.5 litre of a certain gas weigh 15g. Calculate the average speed of gaseous molecules.

$\begin {array}{1,1}(a)\;7\times10^4cm\;sec^{-1}\\(b)\;8.028\times10^4cm\;sec^{-1}\\(c)\;6\times10^5cm\;sec^{-1}\\(d)\;8.028\times10^6cm\;sec^{-1} \end{array}$

Given
Pressure = 3atm
Volume = 12.5 litre
Weight = 15 g
For gas We have PV = $\large\frac{w}{m}RT$
$3\times12.5 = \large\frac{15}{m}\times 0.0821\times T$
$\large\frac{T}{m} = 30.45$
Now $U_{AV} = \sqrt{(\large\frac{8RT}{\pi m})}$
$= \sqrt{\large\frac{8\times 8.314\times 10^7\times 30.4\times 7}{22}}$
$= 8.028\times10^4 cm\;Sec^{-1}$
Hence answer is (b)
answered Feb 15, 2014