Describe the principle and reactions involved in the estimation of oxygen in an organic compound.

$0.5 \ g$ of an organic compound containing phosphorus was heated with conc. $HNO_3$ in a Carius tube. The phosphoric acid thus formed was precipitated with magnesia mixture $[MgNH_4PO_4]$,which on ignition gave a residue of $1.0 \ g$ of magnesium pyrophosphate $(Mg_2P_2O_7)$. The percentage of phosphorus in the organic compound is:

In the Carius method,$0.099 \, g$ of an organic compound gave $0.287 \, g$ of $AgCl$. The percentage of chlorine in the compound is:

During $S$ estimation,$160 \ mg$ of an organic compound gives $466 \ mg$ of barium sulphate. The percentage of Sulphur in the given compound is . . . . . . $\%.$ (Given molar mass in $g \ mol^{-1}$ of $Ba: 137, S: 32, O: 16$)

Calculate the percentage of nitrogen in $0.25 \ g$ of an organic compound if $38 \ cm^3$ of $N_2$ gas is evolved at $300 \ K$ and $96 \ kPa$ pressure. (Given: $1 \ atm = 101.3 \ kPa$)

State whether the following statements are True or False:
$(i)$ The estimation of sulphur is detected by the weight of $BaSO_4$.
$(ii)$ $BaCl_2$ is added in the estimation of sulphur.
$(iii)$ The Carius tube is used in the estimation of sulphur.
$(iv)$ The magnesium mixture is added in the estimation of sulphur.