The number of moles of $CuO$ that will be utilized in the Dumas method for the estimation of nitrogen in a sample of $57.5 \ g$ of $N,N$-dimethylaminopentane is $..... \times 10^{-2}$. (Nearest integer)

In Dumas' method for estimation of nitrogen,$0.3 \ g$ of an organic compound gave $50 \ mL$ of nitrogen collected at $300 \ K$ temperature and $715 \ mm$ pressure. Calculate the percentage composition of nitrogen in the compound. (Aqueous tension at $300 \ K = 15 \ mm$)

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.

$0.3 \ g$ of an organic compound gave $50 \ mL$ of nitrogen collected at $300 \ K$ and $715 \ mm$ pressure in Dumas method. Calculate the percentage of nitrogen in the compound (aqueous tension of water at $300 \ K$ is $15 \ mm$).

State True or False for the following statements:
$(i)$ The volume of $N_2$ is measured by nitrometer.
$(ii)$ The weight of $N_2$ is measured by nitrometer.
$(iii)$ The weight of $NH_3$ is measured by nitrometer.
$(iv)$ The volume of $NH_3$ is measured by nitrometer.

Explain the principle and estimation method for carbon and hydrogen in an organic compound.