Question

A gas cylinder contains $12\times {10}^{24}$ molecules of oxygen gas.
If Avogadro's member is $6\times {10}^{23}$; Calculate :
(i) the mass of oxygen present in the cylinder.
(ii) the volume of oxygen at S.T.P. present in the cylinder. [O =16]

Answer 1

Step 1 Given data

We have given,

A gas cylinder contains $12\times {10}^{24}$ molecules of oxygen gas.

and the Avogadro's member is $6\times {10}^{23}$

Step 2 the mass of oxygen present in the cylinder

If $6\times {10}^{23}$ molecules are present than the mass is $32\mathrm{g}$,
Therefore mass of 1 molecule$=\frac{32}{6\times {10}^{23}}g$

Thus,
if $12\times {10}^{24}$ molecules are present than the mass is $\frac{32}{6\times {10}^{23}}\times 12\times {10}^{24}g$

Hence, the mass of oxygen present in the cylinder is $\frac{32}{6\times {10}^{23}}\times 12\times {10}^{24}=640g$

Step 3 the volume of oxygen at S.T.P. present in the cylinder

$32\mathrm{g}⟶22.4\mathrm{L}\text{at S.T.P.}$
$1\mathrm{g}$ will occupy a volume of $\frac{22.4}{32}$

Hence,

$640\mathrm{g}$ will occupy a volume of $\frac{22.4}{32}\times 640=448L$