The nitrogen content of organic compounds can be determined by the Dumas method. The compound in question is first reacted by passage over hot \(\mathrm{CuO}(s)\) : $$ \text { Compound } \underset{\text { Cvoss }}{\stackrel{\text { Hot }}{\longrightarrow}} \mathrm{N}_{2}(g)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g) $$ The product gas is then passed through a concentrated solution of \(\mathrm{KOH}\) to remove the \(\mathrm{CO}_{2}\). After passage through the \(\mathrm{KOH}\) solution, the gas contains \(\mathrm{N}_{2}\) and is saturated with water vapor. In a given experiment a \(0.253-g\) sample of a compound produced \(31.8 \mathrm{~mL} \mathrm{~N}_{2}\) saturated with water vapor at \(25^{\circ} \mathrm{C}\) and 726 torr. What is the mass percent of nitrogen in the compound? (The vapor pressure of water at \(25^{\circ} \mathrm{C}\) is \(23.8\) torr.)

Step by step solution

01

Calculate the partial pressure of nitrogen gas

To find the partial pressure of nitrogen gas, subtract the vapor pressure of water from the total pressure: Partial pressure of nitrogen gas (P_N2) = total pressure - vapor pressure of water = 726 torr - 23.8 torr = 702.2 torr

02

Convert pressure to atm and volume to L

For using the ideal gas law, we need the pressure in atm and the volume in L: P_N2 (atm) = P_N2 (torr) / 760 = 702.2 torr / 760 = 0.924 atm Volume of nitrogen gas (V_N2) = 31.8 mL / 1000 = 0.0318 L

03

Use the ideal gas law to find moles of nitrogen gas

Using the ideal gas law \(PV = nRT\), we can determine the moles of nitrogen gas (n_N2). Note that the gas constant R = 0.0821 L atm K⁻¹ mol⁻¹, and the temperature T = 25°C = 298 K. n_N2 = (P_N2 * V_N2) / (R * T) = (0.924 atm * 0.0318 L) / (0.0821 L atm K⁻¹ mol⁻¹ * 298 K) = 0.00134 mol

04

Calculate the mass of nitrogen

To find the mass of nitrogen in the compound, multiply the moles by the molar mass of nitrogen (N₂ = 28.02 g/mol): Mass of nitrogen = n_N2 * M_N2 = 0.00134 mol * 28.02 g/mol = 0.0375 g

05

Calculate the mass percent of nitrogen

Finally, find the mass percent of nitrogen in the compound by dividing the mass of nitrogen by the mass of the compound and multiplying by 100: Mass percent of nitrogen = (Mass of nitrogen / mass of the compound) * 100 = (0.0375 g / 0.253 g) * 100 = 14.8% The mass percent of nitrogen in the compound is 14.8%.

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