The nitrogen content of organic compounds can be determined by the Dumas method. The compound in question is first reacted by passage over hot \(\mathrm{CuO}(s)\) : $$ \text { Compound } \stackrel{\mathrm{Hot}}{\longrightarrow} \mathrm{N}_{2}(g)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g) $$ The product gas is then passed through a concentrated solution of \(\mathrm{KOH}\) to remove the \(\mathrm{CO}_{2}\). After passage through the KOH solution, the gas contains \(\mathrm{N}_{2}\) and is saturated with water vapor. In a given experiment a \(0.253-\mathrm{g}\) 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 moles of nitrogen gas

To calculate moles of nitrogen gas produced, first, we need to determine the pressure of nitrogen gas in the mixture. The total pressure of the mixture is 726 torr, and we know the vapor pressure of water at 25 degrees Celsius is 23.8 torr. We can calculate the pressure of nitrogen gas (P_N2) by subtracting the vapor pressure of water from the total pressure: \(P_{N2} = P_{total} - P_{H2O} = 726\,\text{torr} - 23.8\,\text{torr} = 702.2\,\text{torr}\) Now, we use the ideal gas equation to determine the moles of nitrogen gas produced: \(n_{N2} = \dfrac{P_{N2}\,V_{N2}}{RT}\) where \(n_{N2}\) is the moles of nitrogen gas, \(P_{N2}\) is the pressure of nitrogen gas, \(V_{N2}\) is the volume of nitrogen gas, R is the ideal gas constant and T is the temperature. Using the values given in the problem, we can calculate the moles of nitrogen gas.

02

Use the ideal gas equation to calculate the moles of nitrogen gas

First, it is important to convert the volume of nitrogen gas from milliliters to liters: \(V_{N2} = 31.8\,\text{mL} \times \dfrac{1\,\text{L}}{1000\,\text{mL}} = 0.0318\,\text{L}\) Additionally, we need to convert the pressure of nitrogen gas from torr to atmospheres: \(P_{N2} = 702.2\,\text{torr} \times \dfrac{1\,\text{atm}}{760\,\text{torr}} = 0.924\,\text{atm}\) Now, we can plug these values into the ideal gas equation using the gas constant R = 0.08206 L*atm/mol*K and the temperature T = 25 degrees Celsius + 273.15 = 298.15 K: \(n_{N2} = \dfrac{0.924\,\text{atm} \times 0.0318\,\text{L}}{0.08206\,\text{L}\cdot\text{atm/mol}\cdot\text{K} \times 298.15\,\text{K}}\) \(n_{N2} = 0.00134\,\text{moles}\)

03

Convert moles of nitrogen to mass

Now, we will convert moles of nitrogen to mass using the molar mass of nitrogen, which is 14.01 g/mol: mass_N2 = moles_N2 x molar_mass_N2 mass_N2 = 0.00134 moles × 14.01 g/mole = 0.0188 g

04

Calculate mass percent of nitrogen

Finally, we will calculate the mass percent of nitrogen in the compound: mass_percent_N = (mass_N2 / mass_sample) × 100% mass_percent_N = (0.0188 g / 0.253 g) × 100% = 7.43% The mass percent of nitrogen in the compound is 7.43%.

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