Problem 12 - Chemistry in 30 days

Question

About \(0.5 \mathrm{~g}\) of an organic compound containing nitrogen on \(\mathrm{Kjeldahlising}\) requires \(29 \mathrm{~mL}\) of N/5 \(\mathrm{H}_{2} \mathrm{SO}_{4}\) for complete neutralization of ammonia. The percentage of nitrogen in the compound is (a) \(34.3 \%\) (b) \(16.2 \%\) (c) \(21.6 \%\) (d) \(14.8 \%\)

Step-by-Step Solution

Answer

The percentage of nitrogen in the compound is \(16.2\%\), choice (b).

Step 1: Calculate moles of H₂SO₄

Calculate the moles of \ \ \( \text{H}_2\text{SO}_4 \) using its given normality (N/5) and volume (29 mL). Since normality is equivalent to molarity for sulfuric acid in this context, we use the formula: \ \( \text{moles} = \frac{\text{N (normality)} \times \text{V (in liters)}}{1} \). \ Convert 29 mL to 0.029 L. \ \( \text{Moles of H}_2\text{SO}_4 = \frac{1/5}{1} \times 0.029 \). \ This equals \( 0.0058 \) moles.

Step 2: Determine moles of NH₃

When ammonia (NH₃) is neutralized, it reacts in a 1:1 molar ratio with \ \( \text{H}_2\text{SO}_4 \), so the moles of NH₃ are the same as the moles of \ \( \text{H}_2\text{SO}_4 \). \ Therefore, moles of NH₃ \( = 0.0058 \).

Step 3: Convert moles of NH₃ to grams of Nitrogen

The formula weight of nitrogen in ammonia (NH₃) is 14 g/mol. \ Calculate the weight of nitrogen by multiplying the moles of NH₃ by the nitrogen molar mass: \ \( \text{Grams of nitrogen} = 0.0058 \times 14 \ = 0.0812 \) grams.

Step 4: Compute the percentage of nitrogen

Finally, to find the percentage of nitrogen in the compound, use the formula: \ \( \text{Percentage of nitrogen} = \left( \frac{\text{grams of nitrogen}}{\text{weight of compound}} \right) \times 100 \). \ With grams of nitrogen \( = 0.0812 \) and weight of the compound \( = 0.5 \) grams, \ \( \text{Percentage of nitrogen} = \left( \frac{0.0812}{0.5} \right) \times 100 \ = 16.24\% \).

Key Concepts

Nitrogen Percentage Calculation

Understanding how to calculate the nitrogen percentage in a compound is crucial when working with the Kjeldahl method. This analytical technique estimates the nitrogen content in organic compounds, which is noteworthy for fields such as agriculture and food science. In our exercise, we're given a compound weighing 0.5 grams, where nitrogen has been isolated using the Kjeldahl method. After a series of reactions, the resulting ammonia (\( \text{NH}_3 \)) is neutralized by sulfuric acid (\( \text{H}_2\text{SO}_4 \)) during titration.
To calculate the nitrogen percentage, you need to:

• Determine the moles of \( \text{NH}_3 \). In our case, this matches the moles of \( \text{H}_2\text{SO}_4 \) used since they react 1:1.
• Convert the moles of \( \text{NH}_3 \) to grams of nitrogen by using the atomic weight of nitrogen.
• Take the grams of nitrogen obtained and divide it by the weight of the original compound.
• Multiply by 100 to convert this value into a percentage, which in this exercise is approximately 16.24%.

These steps help determine how much of the compound's weight is due to nitrogen, delivering insights into its composition.

Stoichiometry

Stoichiometry is the backbone of chemistry and essential to understanding the reactions in this exercise. It allows us to use balanced chemical equations to determine the ratios of reactants and products. In the context of the Kjeldahl method, stoichiometry enables you to predict the results of the chemical reactions involving \( \text{NH}_3 \) and \( \text{H}_2\text{SO}_4 \). This is especially helpful in calculating the moles of the respective chemicals based on their relationships.
In the neutralization step detailed in our solution:

• The reaction between \( \text{NH}_3 \) and \( \text{H}_2\text{SO}_4 \) follows a 1:1 molar ratio.
• As a result, the moles of \( \text{NH}_3 \) are equivalent to the moles of \( \text{H}_2\text{SO}_4 \) used.

This stoichiometric relationship simplifies the conversion from moles of acid to moles of ammonia. Understanding these reactions leads to conclusions about the compound's nitrogen content.

Chemical Reactions

Chemical reactions are transformations that matter undergoes, showcasing changes in chemical properties. In our exercise using the Kjeldahl method, several reactions occur to isolate nitrogen. The focus of this method is on the digestion process, where nitrogen is transformed into ammonia (\( \text{NH}_3 \)).
The key reaction in the exercise is the neutralization of ammonia:

• Ammonia reacts with sulfuric acid (\( \text{H}_2\text{SO}_4 \)) in a linear, straightforward 1:1 ratio.
• This reaction changes the ammonia into an ammonium sulfate compound, ultimately indicating the nitrogen content in a measurable form.

Grasping these reactions is vital as it leads to quantifying the nitrogen involved, from which the compound percentage is derived.

Acid-Base Titration

Acid-base titration is a core technique in chemistry used to determine unknown concentrations. In our Kjeldahl method exercise, titration is employed to precisely measure the amount of \( \text{NH}_3 \) through its reaction with \( \text{H}_2\text{SO}_4 \). The process involves gradually adding the acid to a solution until neutralization is complete, marked by a noticeable change.
Here’s how it works in our exercise:

• The sulfuric acid has a known normality, and its volume is recorded as it neutralizes the ammonia.
• Completion of the reaction indicates that a specific amount of \( \text{NH}_3 \) was present, allowing us to back-calculate to the moles of nitrogen.

This precise method ensures the accurate determination of nitrogen content. The titration endpoint reveals the stoichiometric completion of the neutralization reaction, affirming the balance between acid and ammonia in the analysis.