Question

\(0.5 \mathrm{~g}\) of an organic compound in \(\mathrm{Kjeldahl}\) experiment needs \(29 \mathrm{ml}\) of \(\frac{\mathrm{N}}{5} \mathrm{H}_{2} \mathrm{SO}_{4}\) for complete neutralization of \(\mathrm{NH}_{3} .\) The \(\mathrm{N} \%\) is: (a) \(16.2\) (b) \(8.1\) (c) \(24.3\) (d) \(32.4\)

Short answer

The nitrogen percentage is 32.4%, which corresponds to option (d).

Step-by-step solution

Calculate the moles of H2SO4 used

First, we need to determine the number of moles of sulfuric acid (H_{2}SO_{4}) used in the neutralization reaction. The solution is \frac{N}{5} normal, implying it has a molarity of \frac{1}{5} M. The volume used is 29  ml, which is 0.029  L.\[ \text{Moles of } H_{2}SO_{4} = 0.029 imes \frac{1}{5} = 0.0058 \text{ moles} \]

Determine moles of NH3 neutralized

Using the fact that 1 mole of H_{2}SO_{4} neutralizes 2 moles of NH_{3}, we can find the moles of ammonia neutralized as follows.\[ \text{Moles of } NH_{3} = 2 \times 0.0058 = 0.0116 \text{ moles} \]

Calculate mass of nitrogen in the compound

Now we calculate the mass of nitrogen originating from the moles of NH_{3}, knowing that the molar mass of nitrogen (N) is 14 g/mol.\[ \text{Mass of } N = 0.0116 \times 14 = 0.1624 \text{ grams} \]

Determine percentage of nitrogen in the organic compound

Calculate the nitrogen percentage (N ext{%}) by dividing the mass of nitrogen by the total mass of the organic compound and multiplying by 100 to express it as a percentage.\[ N ext{%} = \left(\frac{0.1624}{0.5}\right) \times 100 = 32.48\% \]

Select the closest answer from options

With the calculated percentage 32.48 ext{}, we compare it to the given options. Option (d) 32.4 ext{ is the closest to our calculation.

Key concepts

Neutralization Reaction

In the Kjeldahl method for determining nitrogen content, a neutralization reaction plays a crucial role. This chemical reaction occurs when an acid and a base interact to form water and a salt. In the context of analyzing an organic compound, the key players are sulfuric acid ( H_2SO_4 ), and ammonia ( NH_3 ).
Ammonia is typically released when the organic compound is decomposed. It is then absorbed in a known concentration of acid—in this example, rac{N}{5} sulfuric acid. The basic ammonia reacts with this sulfuric acid, leading to the neutralization reaction where the complete process consumes 2 moles of ammonia for every mole of sulfuric acid used.
Neutralization is completed when the base (ammonia) is completely reacted with the acid, forming a salt and water without leftover reagents. Understanding this reaction is fundamental to analyzing the nitrogen content in the compound.

Moles Calculation

Calculating moles is essential to convert the measurable amounts of a substance (like grams or liters) into its basic chemical quantities. In the Kjeldahl method, the process begins with finding out how many moles of sulfuric acid participate in the reaction. Given 29 ml of rac{N}{5} sulfuric acid, its molarity is rac{1}{5} M, converting this to liters gives 0.029 L.
We apply the formula to find moles: Moles = Molarity \times Volume. Substituting the known values, we have: \[ \text{Moles of } H_{2}SO_{4} = 0.029 \times \frac{1}{5} = 0.0058 \text{ moles} \]This calculation forms the baseline for further steps as moles of NH_3 are determined by their stoichiometric relationship in the neutralization reaction. Thus, understanding moles aids us in relating different substances within a chemical equation.

Nitrogen Percentage

The nitrogen percentage in an organic compound is a critical measure when analyzing its composition. Once the mass of nitrogen is derived from the moles of NH_3, it's utilized to find out how much of the original sample's weight is made up of nitrogen.
From our calculations: \[ \text{Mass of } N = 0.0116 \times 14 = 0.1624 \text{ grams} \]Knowing that our starting sample was 0.5 grams, we calculate the nitrogen percentage with the formula: \[ N\% = \left(\frac{\text{mass of } N}{\text{mass of compound}}\right) \times 100 \]Substituting in our values gives: \[ N\% = \left(\frac{0.1624}{0.5}\right) \times 100 = 32.48\% \]This value reflects the proportion of nitrogen in the compound, a critical piece for those studying its chemistry and potential applications.

Organic Compound Analysis

Organic compound analysis through the Kjeldahl method is one of the traditional and most effective means to determine nitrogen content. The process begins by decomposing the organic matter to release ammonia, which signifies nitrogen presence.
The analysis involves several chemical operations, such as a digestion phase where the compound is treated chemically to convert nitrogen into ammonia. It's followed by the neutralization reaction, where quantitative moles of products are calculated. Each step is aimed at precision, ensuring nitrogen released accurately correlates with the compound's makeup.
This analytical method is pivotal in various domains such as agriculture, food science, and pharmaceuticals. Each field requires a precise understanding of nitrogen percentages for purposes like soil quality assessment, nutritional evaluations, or chemical manufacturing. The Kjeldahl method provides robust data crucial for these scientific and industrial fields.