0.1877g of an organic compound when analysed by the Duma's method yields 32ml of moist nitrogen measured at 287k and 758mm mercury pressure. what is percentage of nitrogen in the organic compound. (aqueous tension at 287k=12mm)

To determine the percentage of nitrogen in the organic compound using the data provided, we can follow a systematic approach. The Dumas method allows us to analyze the nitrogen content by measuring the volume of nitrogen gas produced during the combustion of the organic sample. Let's break down the steps involved in solving this problem.

Step 1: Adjust for Aqueous Tension

First, we need to account for the aqueous tension of the gas. The total pressure measured is 758 mmHg, but this includes the pressure exerted by water vapor. To find the pressure of the dry nitrogen gas, we subtract the aqueous tension from the total pressure:

• Total pressure = 758 mmHg
• Aqueous tension at 287 K = 12 mmHg
• Dry nitrogen pressure = Total pressure - Aqueous tension = 758 mmHg - 12 mmHg = 746 mmHg

Step 2: Convert Volume to Standard Conditions

Next, we need to convert the volume of nitrogen gas to standard conditions (0°C and 1 atm). The ideal gas law can help us with this conversion. The formula we use is:

PV = nRT

Where:

• P = pressure in atm
• V = volume in liters
• n = number of moles
• R = ideal gas constant (0.0821 L·atm/(K·mol))
• T = temperature in Kelvin

First, convert the pressure from mmHg to atm:

P = 746 mmHg × (1 atm / 760 mmHg) = 0.9803 atm

Next, convert the volume from milliliters to liters:

V = 32 mL × (1 L / 1000 mL) = 0.032 L

Step 3: Calculate Moles of Nitrogen

Now we can rearrange the ideal gas law to solve for n (the number of moles of nitrogen):

n = PV / RT

Substituting in the values:

n = (0.9803 atm) × (0.032 L) / (0.0821 L·atm/(K·mol) × 287 K)

Calculating this gives:

n ≈ 0.0013 moles of nitrogen

Step 4: Calculate the Mass of Nitrogen

To find the mass of nitrogen, we use the molar mass of nitrogen (N₂), which is approximately 28 g/mol:

Mass of nitrogen = n × molar mass = 0.0013 moles × 28 g/mol ≈ 0.0364 g

Step 5: Determine the Percentage of Nitrogen in the Organic Compound

Finally, we can calculate the percentage of nitrogen in the organic compound using the formula:

Percentage of nitrogen = (mass of nitrogen / mass of organic compound) × 100

Substituting the values:

Percentage of nitrogen = (0.0364 g / 0.1877 g) × 100 ≈ 19.4%

Final Result

Thus, the percentage of nitrogen in the organic compound is approximately 19.4%.