Medium
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: $1 \ atm = 101.3 \ kPa$)
(A) Step $1$: Convert pressure to $atm$: $P = \frac{96 \ kPa}{101.3 \ kPa/atm} \approx 0.9477 \ atm$.
Step $2$: Use the Ideal Gas Law $PV = nRT$ to find moles of $N_2$: $n = \frac{PV}{RT} = \frac{0.9477 \ atm \times 0.038 \ L}{0.0821 \ L \cdot atm \cdot K^{-1} \cdot mol^{-1} \times 300 \ K} \approx 0.00146 \ mol$.
Step $3$: Calculate mass of $N_2$: $Mass = 0.00146 \ mol \times 28 \ g/mol \approx 0.04088 \ g$.
Step $4$: Calculate percentage of $N$: $\frac{0.04088 \ g}{0.25 \ g} \times 100 \approx 16.35 \%$.
The calculated value is approximately $16.38 \%$.
Step $2$: Use the Ideal Gas Law $PV = nRT$ to find moles of $N_2$: $n = \frac{PV}{RT} = \frac{0.9477 \ atm \times 0.038 \ L}{0.0821 \ L \cdot atm \cdot K^{-1} \cdot mol^{-1} \times 300 \ K} \approx 0.00146 \ mol$.
Step $3$: Calculate mass of $N_2$: $Mass = 0.00146 \ mol \times 28 \ g/mol \approx 0.04088 \ g$.
Step $4$: Calculate percentage of $N$: $\frac{0.04088 \ g}{0.25 \ g} \times 100 \approx 16.35 \%$.
The calculated value is approximately $16.38 \%$.
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Match Column-$I$ and Column-$II$ with the correct relation:
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| Column-$I$ | Column-$II$ |
|---|---|
| $(i)$. Estimation of carbon and hydrogen | $(p)$. $AgX$ |
| $(ii)$. Estimation of nitrogen | $(q)$. $CO_2$ and $H_2O$ |
| $(iii)$. Estimation of halogen | $(r)$. $N_2$ |
| $(iv)$. Estimation of sulphur | $(s)$. $Mg_2P_2O_7$ |
| $(v)$. Estimation of phosphorus | $(t)$. $BaSO_4$ |
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View SolutionGiven below are two statements $I$ and $II.$
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Statement $II :$ Dumas method involves the formation of ammonium sulphate by heating the organic compound with conc $H_2SO_4$. In the light of the above statements,choose the correct answer from the options given below.
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