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Chapter 8: Problem 69

In Dumas method, \(0.2 \mathrm{~g}\) of an organic nitrogenous compound gave \(28 \mathrm{ml}\) of \(\mathrm{N}_{2}\) (volume reduced to \(0^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\) ). What is the percentage of nitrogen, by mass, in the compound? (a) \(17.5\) (b) \(8.75\) (c) \(35.0\) (d) \(14.0\)

Short Answer

Expert verified
Question: Calculate the percentage of nitrogen by mass in an organic nitrogenous compound if 0.2 g of the compound produced 28 ml of N2 gas at 0°C and 1 atm through the Dumas method. Answer: 17.5%

Step by step solution

01

Understand the Dumas Method and Given Information

In the Dumas method, nitrogen in the organic compound is converted to nitrogen gas (N2). We are given that 0.2 g of the organic nitrogenous compound produced 28 ml of N2 gas at 0°C and 1 atm. Keep these given values in mind for further calculations.
02

Convert the volume of N2 gas to moles using the Ideal Gas Law

The ideal gas law states that PV = nRT, where P is the pressure, V is the volume, n is the amount of gas in moles, R is the ideal gas constant, and T is the temperature in Kelvin. In this case, we have P = 1 atm, V = 28 ml (or 0.028 L), R = 0.0821 L atm/mol K, and T = 273 K (0°C). To find the moles of N2 gas (n), we can rearrange the ideal gas law: n = PV / RT n = (1 atm * 0.028 L) / (0.0821 L atm/mol K * 273 K) n ≈ 0.00125 moles
03

Calculate the mass of nitrogen gas (N2) using its molar mass

To find the mass of N2 gas, multiply the moles of N2 by its molar mass: m_N2 = n_N2 * M_N2. The molar mass of nitrogen gas (N2) is 28 g/mol. m_N2 = 0.00125 moles * 28 g/mol m_N2 ≈ 0.035 g
04

Calculate the percentage of nitrogen by mass in the organic compound

Now that we have the mass of N2 gas (which is solely comprised of nitrogen), we can calculate the percentage of nitrogen in the organic compound using the following formula: Percentage of Nitrogen = (Mass of Nitrogen in the compound / Total mass of the compound) * 100 Percentage of Nitrogen = (0.035 g / 0.2 g) * 100 Percentage of Nitrogen = 17.5% The correct answer is (a) 17.5%.

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Most popular questions from this chapter

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