Problem 111 - A Complete Resource Book in Chemistry for JEE Main

Question

\(29.5 \mathrm{mg}\) of an organic compound containing nitrogen was digested according to Kjeldahl's method and the evolved amomnia was absorbed in \(20 \mathrm{~mL}\) of \(0.1 \mathrm{M} \mathrm{HCl}\) solution. The excess of the acid required \(15 \mathrm{~mL}\) of \(0.1 \mathrm{M} \mathrm{NaOH}\) solution for complete neutralization. The percentage of nitrogen in the compound is (a) \(59.0\) (b) \(47.4\) (c) \(23.7\) (d) \(29.5\)

Step-by-Step Solution

Answer

The percentage of nitrogen in the compound is 23.7%, so the correct answer is (c) 23.7.

Step 1: Determine the Moles of HCl Initially Added

First, calculate the moles of HCl that were initially added to the solution. We have a volume of 20 mL of 0.1 M HCl.The formula to calculate moles is:\[\text{Moles of HCl} = \text{Molarity of HCl} \times \text{Volume of HCl in Liters}\]\[\text{Moles of HCl} = 0.1 \times \frac{20}{1000} = 0.002 \text{ moles}\]

Step 2: Determine the Moles of NaOH Used for Neutralization

Next, calculate the moles of NaOH used to neutralize the excess HCl. The volume of NaOH used is 15 mL with a concentration of 0.1 M.Using the same moles formula:\[\text{Moles of NaOH} = 0.1 \times \frac{15}{1000} = 0.0015 \text{ moles}\]

Step 3: Calculate the Moles of HCl that Reacted with Ammonia

Subtract the moles of NaOH from the initial moles of HCl to find the moles of HCl that reacted with ammonia:\[\text{Moles of HCl that reacted} = 0.002 - 0.0015 = 0.0005 \text{ moles}\]

Step 4: Relate Moles of HCl to Moles of Ammonia

Since the reaction between HCl and ammonia is a 1:1 ratio, the moles of ammonia absorbed is equal to the moles of HCl that reacted:\[\text{Moles of } NH_3 = 0.0005\]

Step 5: Calculate the Mass of Nitrogen in Ammonia

Calculate the mass of nitrogen in the absorbed ammonia using the atomic weight of nitrogen (14 g/mol):\[\text{Mass of } N = 0.0005 \times 14 = 0.007 \text{ grams} = 7 \text{ mg}\]

Step 6: Calculate the Percentage of Nitrogen in the Compound

Now, calculate the percentage of nitrogen in the compound based on its total mass:\[\text{Percentage of } N = \left(\frac{7}{29.5}\right) \times 100\approx 23.7\%\]

Step 7: Provide the Correct Answer

Based on the calculation above, the percentage of nitrogen in the compound is 23.7%. Therefore, the correct answer is (c) 23.7.

Key Concepts

Percentage of Nitrogen

Determining the percentage of nitrogen in an organic compound is key in understanding its composition. The percentage of nitrogen essentially tells us how much of the compound's weight is due to nitrogen. This is critical in fields like biochemistry, agriculture, and pharmaceuticals.
To find this percentage, especially using Kjeldahl's method as mentioned in the exercise, you start by isolating the nitrogen. This is typically done by converting the nitrogen into a simpler form, such as ammonia, which can then be easily measured.
The math begins when the nitrogen is present as ammonia in the compound, and we neutralize it with a known quantity of hydrochloric acid (HCl).

• The first step involves determining how much HCl reacts with the nitrogen, specifically how many moles.
• Then, we need the atomic mass of nitrogen (14 g/mol) to convert these moles into mass.
• Finally, we compare this mass to the total mass of the original sample to get the nitrogen percentage.

This percentage offers insight into the functional and nutritional values of the compound in various applications.

Organic Compound Analysis

Organic compound analysis, such as determining the amount of nitrogen, can unveil significant details about the molecular structure and properties of a substance. This involves breaking down complex organic molecules to study their individual components.
Kjeldahl's method is an analytical procedure widely employed to analyze nitrogen content separately. The process involves:

• Digestion: Converting organic nitrogen into ammonia by heating the sample with concentrated acid.
• Neutralization: Adding a base, such as sodium hydroxide, to neutralize the free ammonia.
• Distillation and titration: Which helps capture and measure the ammonia.

This systematic breakdown and analysis are critical in fields like food quality assessment and environmental studies. It pieces together the puzzle of what makes up different organic compounds, and thus defines their behaviors and applications.

Chemical Calculations

Chemical calculations offer a roadmap for understanding reactions and conversions in chemistry. When analyzing compounds, these calculations help quantify the exact amounts of chemicals involved. This is a vital part of any laboratory practice.

In the exercise, consider the calculations done: each step in the problem involves using formulas to determine quantities and conversions, such as moles of a substance. Here is how it unfolds:

• Firstly, mole calculations determine the number of moles from the given molarity and volume of solutions. This is an essential skill—expressing weight in moles aligns with how atoms and molecules interact in reactions.
• Next, compare these moles in stoichiometry, which allows us to calculate the amounts needed for a reaction.
• Finally, use ratios to connect these findings back to the mass of nitrogen and its percentage in the compound.

These calculations underpin not just nitrogen analysis, but all fields requiring chemical insight—from the production of fertilizers to pharmaceuticals development. Understanding them is foundational for anyone working with chemical substances.