At 715 mm pressure, 300 K, volume of N\(_2\) (g) evolved was 80 mL by a 0.4 g sample of organic compound. Find the percentage of N in the organic compound. Given aqueous tension at 300 K = 15 mm.
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In gas-related problems, remember to subtract the aqueous tension from the total pressure before applying the Ideal Gas Law.
Provided Data:
- Pressure: \(P = 715 \, \text{mm Hg}\)
- Volume of evolved gas: \(V = 80 \, \text{mL}\)
- Temperature: \(T = 300 \, \text{K}\)
- Mass of organic compound: \(m = 0.4 \, \text{g}\)
- Aqueous tension at 300 K: 15 mm Hg
Objective: Calculate the percentage of nitrogen in the organic compound.
1. Determine the number of moles of N\(_2\) using the Ideal Gas Law (\(PV = nRT\)).
Corrected Pressure: \(P = 715 - 15 = 700 \, \text{mm Hg}\).
Gas Constant: \(R = 0.0821 \, \text{L atm} / \text{mol K}\).
Volume: \(V = 80 \, \text{mL} = 0.08 \, \text{L}\).
Solve for moles (\(n\)):
\[
n = \frac{PV}{RT}
\]
Substitute values:
\[
n = \frac{700 \times 0.08}{0.0821 \times 300}
\]
Result:
\[
n = 0.0284 \, \text{mol}
\]
2. Calculate the mass of nitrogen in the sample.
Molar mass of N\(_2\): \(28 \, \text{g/mol}\).
Mass of Nitrogen: Mass of N = \(n \times \text{Molar mass of N}_2\)
\[
\text{Mass of N} = 0.0284 \times 28 = 0.7952 \, \text{g}
\]
3. Calculate the percentage of nitrogen in the organic compound.
\[
\% \, \text{of N} = \frac{\text{Mass of N}}{\text{Mass of sample}} \times 100
\]
\[
\% \, \text{of N} = \frac{0.7952}{0.4} \times 100 = 15.83\%
\]
The percentage of nitrogen in the organic compound is \(15.83\%\).
