Question

$3.2g$ of $S$ is heated if it occupies a volume of $780ml$ at ${450}^{\circ }C$ and $723mm$ pressure. Formula of sulphur is:

• A. $S_2$
• B. $S$
• C. $S_4$
• D. $S_8$

Answer 1

The correct option is D $S_8$

Given,

Pressure $P=723$ $mmHg$

Volume $V=0.780L$

$R=0.08314$ $L$ $atm$ $K^{-1}mo{l}^{-1}$ [Gas constant]

Temperature $T={450}^{\circ }C$

$=450+273$

$=723K$

$P=\frac{723}{760}=0.9513$ $atm$ $[\because 1atm=760mmHg]$

Now, The gas law states

$PV=nRT$

$\Rightarrow n=\frac{PV}{RT}$

$=\frac{0.9513\times 0.780}{0.08314\times 723}$

$=0.01234$

We know $n=$moles=$\frac{Weightgivenofthesample}{GrammolecularWeightofthesample}$

$0.01234=\frac{3.2g}{G.wt}$ $[\because 3.2g$ is given mass of $S$ sample$]$

$\therefore$ G.wt of the given sample=$260.1g$

Now, we know $1S$ atom has molar mass of $32g$

$\therefore$ No. of atoms in $260.1g$ of sample=$\frac{260}{32}=8$

$\Rightarrow$ Formula of Sulphur=$S_8$