Question

Ammonium nitrate \(\left(\mathrm{NH}_{4} \mathrm{NO}_{3}\right)\) is one of the most important nitrogen-containing fertilizers. Its purity can be analyzed by titrating a solution of \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) with a standard \(\mathrm{NaOH}\) solution. In one experiment a \(0.2041-\mathrm{g}\) sample of industrially prepared \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) required \(24.42 \mathrm{~mL}\) of \(0.1023 \mathrm{M} \mathrm{NaOH}\) for neutralization. (a) Write a net ionic equation for the reaction. (b) What is the percent purity of the sample?

Short answer

Net ionic equation: \(\mathrm{NH}_{4}^{+} + \mathrm{OH}^{-} \rightarrow \mathrm{NH}_{3} + \mathrm{H}_{2}\mathrm{O}\). Percent purity: 98.04%.

Step-by-step solution

Write the Balanced Molecular Equation

The neutralization reaction between ammonium nitrate (NH₄NO₃) and sodium hydroxide (NaOH) involves the conversion of the ammonium ion to ammonia and water. The balanced molecular equation is: \(\mathrm{NH}_{4}^{+} + \mathrm{OH}^{-} \rightarrow \mathrm{NH}_{3} + \mathrm{H}_{2}\mathrm{O}\).

Convert to Net Ionic Equation

The net ionic equation represents only the species that actually change during the reaction. Both NH₄⁺ and OH⁻ are involved in the chemical reaction, forming NH₃ and H₂O. Hence, the net ionic equation is already balanced as: \(\mathrm{NH}_{4}^{+} + \mathrm{OH}^{-} \rightarrow \mathrm{NH}_{3} + \mathrm{H}_{2}\mathrm{O}\).

Calculate Moles of NaOH Used

Use the titration data to find the moles of NaOH. Multiply the volume in liters by the molarity: \(24.42 \, \text{mL} \times \frac{1 \, \text{L}}{1000 \, \text{mL}} \times 0.1023 \, \text{mol L}^{-1} = 0.00250 \, \text{mol NaOH}\).

Calculate Moles of NH₄NO₃ in Sample

From the 1:1 ratio in the balanced equation, the moles of NH₄⁺ are equal to the moles of OH⁻, which means moles of NH₄NO₃ are also 0.00250 mol.

Calculate Mass of Pure NH₄NO₃

Determine the molar mass of NH₄NO₃: \(\mathrm{N} = 14.01, \mathrm{H} = 1.01 \times 4, \mathrm{O} = 16.00 \times 3\). Therefore, molar mass is \(80.04 \, \text{g mol}^{-1}\). The mass of pure NH₄NO₃ in the sample is \(0.00250 \, \text{mol} \times 80.04 \, \text{g mol}^{-1} = 0.2001 \, \text{g}\).

Calculate Percent Purity

Percent purity is calculated by dividing the mass of pure NH₄NO₃ by the total mass of the sample and multiplying by 100: \(\frac{0.2001 \, \text{g}}{0.2041 \, \text{g}} \times 100 \approx 98.04\%\).

Key concepts

Ammonium Nitrate

Ammonium nitrate (\(\mathrm{NH}_4\mathrm{NO}_3\)) is a widely used nitrogen-based fertilizer. It is valued for its high nitrogen content, which is essential for plant growth. This compound consists of ammonium ions (\(\mathrm{NH}_4^+\)) and nitrate ions (\(\mathrm{NO}_3^-\)). When used in agriculture, it delivers nitrogen more effectively, promoting healthy plant development.
Ammonium nitrate is not only important for its fertilizer properties but is also utilized in specific industrial applications. Understanding its purity is crucial for ensuring its effectiveness and safety. Titration, a common laboratory method, helps in assessing the purity of ammonium nitrate by reacting it with a base, like sodium hydroxide (NaOH), in a controlled way.

Net Ionic Equation

The net ionic equation focuses on the essential parts of a chemical reaction, highlighting only the ions that undergo a change. In this case, we are analyzing the reaction between ammonium nitrate and sodium hydroxide in a titration. The relevant ions are the ammonium ions (\(\mathrm{NH}_4^+\)) and hydroxide ions (\(\mathrm{OH}^-\)).
When these ions react, they form ammonia (\(\mathrm{NH}_3\)) and water (\(\mathrm{H}_2\mathrm{O}\)), simplifying the equation to:

• \(\mathrm{NH}_4^+ + \mathrm{OH}^- \rightarrow \mathrm{NH}_3 + \mathrm{H}_2\mathrm{O}\)

This equation omits the spectator ions that don't participate directly in the reaction, providing a clear view of the process.

Percent Purity

Determining the percent purity of a substance helps us understand how much of the sample is composed of the actual compound of interest compared to impurities. For ammonium nitrate, this involves calculating how much of the sample’s mass is pure ammonium nitrate.
Using titration, you can find the moles of ammonium nitrate, and then calculate the mass of the pure compound. The formula is:

• Percent Purity = \(\frac{\text{Mass of Pure Compound}}{\text{Total Mass of Sample}} \times 100\)

In our example, with a total sample mass of 0.2041 g and a pure compound mass of 0.2001 g, the purity is approximately 98.04%. This high purity indicates a well-prepared sample, important for effective and safe usage.

Neutralization Reaction

Neutralization reactions occur when an acid and a base react to form water and a salt. In the titration of ammonium nitrate with sodium hydroxide, the process neutralizes the ammonium ions (\(\mathrm{NH}_4^+\)) with hydroxide ions (\(\mathrm{OH}^-\)).
This type of reaction is key in analytical chemistry for determining concentrations and purity. A neutralization reaction is described by the general equation:

• Acid + Base → Water + Salt

Here, the reaction results in the formation of water and ammonia. Understanding this concept is essential for studying titrations and other chemical processes involving acids and bases.