Question

Most fertilizers consist of nitrogen-containing compounds such as \(\mathrm{NH}_{3}, \mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2}, \mathrm{NH}_{4} \mathrm{NO}_{3},\) and \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4} .\) Plants use the nitrogen content in these compounds for protein synthesis. Calculate the mass percent composition of nitrogen in each of the fertilizers listed. Which fertilizer has the highest nitrogen content?

Short answer

The mass percent composition of nitrogen in each fertilizer is as follows: \text{NH}_3: 82.21%, \text{CO(NH}_2)_2: 46.66%, \text{NH}_4\text{NO}_3: 35.01%, and \text{(NH}_4)_2\text{SO}_4: 21.20%. Ammonia (NH3) has the highest nitrogen content.

Step-by-step solution

Calculate the molar mass of \text{NH}_3

Calculate the molar mass of ammonia (NH3) by adding up the atomic masses of nitrogen and hydrogen. Nitrogen has a molar mass of 14.01 g/mol, and each hydrogen has a molar mass of 1.01 g/mol. There are 3 hydrogen atoms in ammonia, so the total molar mass is: Molar mass of NH3 = 14.01 g/mol + 3*(1.01 g/mol) = 17.04 g/mol.

Calculate the mass percent of nitrogen in \text{NH}_3

To find the mass percent of nitrogen in ammonia, divide the molar mass of nitrogen by the molar mass of ammonia and multiply by 100%. Mass percent of N in NH3 = (14.01 g/mol / 17.04 g/mol) * 100% = 82.21%.

Calculate the molar mass of \text{CO(NH}_2)_2

Calculate the molar mass of urea, CO(NH2)2. Carbon has a molar mass of 12.01 g/mol, oxygen has a molar mass of 16.00 g/mol, nitrogen is 14.01 g/mol, and hydrogen is 1.01 g/mol. Urea has 1 carbon, 1 oxygen, 2 nitrogen, and 4 hydrogen atoms. Molar mass = 12.01 g/mol + 16.00 g/mol + 2*(14.01 g/mol) + 4*(1.01 g/mol) = 60.05 g/mol.

Calculate the mass percent of nitrogen in \text{CO(NH}_2)_2

Mass percent of N in urea = (2 * 14.01 g/mol / 60.05 g/mol) * 100% = 46.66%.

Calculate the molar mass of \text{NH}_4\text{NO}_3

Calculate the molar mass of ammonium nitrate, NH4NO3. It consists of two nitrogen atoms, four hydrogen atoms, and three oxygen atoms. Molar mass = 2*(14.01 g/mol) + 4*(1.01 g/mol) + 3*(16.00 g/mol) = 80.04 g/mol.

Calculate the mass percent of nitrogen in \text{NH}_4\text{NO}_3

Mass percent of N in ammonium nitrate = (2 * 14.01 g/mol / 80.04 g/mol) * 100% = 35.01%.

Calculate the molar mass of \text{(NH}_4)_2\text{SO}_4

Calculate the molar mass of ammonium sulfate, (NH4)2SO4. It has two nitrogen atoms, eight hydrogen atoms, one sulfur atom, and four oxygen atoms. Molar mass = 2*(14.01 g/mol) + 8*(1.01 g/mol) + 32.07 g/mol + 4*(16.00 g/mol) = 132.14 g/mol.

Calculate the mass percent of nitrogen in \text{(NH}_4)_2\text{SO}_4

Mass percent of N in ammonium sulfate = (2 * 14.01 g/mol / 132.14 g/mol) * 100% = 21.20%.

Compare nitrogen content by mass percent

Compare the mass percent of nitrogen in each compound to determine the highest nitrogen content. NH3: 82.21%, CO(NH2)2: 46.66%, NH4NO3: 35.01%, and (NH4)2SO4: 21.20%.

Key concepts

Molar Mass Calculation

Understanding molar mass is crucial when studying chemistry, especially with substances like fertilizers where specific dosages are essential for their effectiveness. The molar mass is the weight of one mole of a chemical compound or element, usually expressed in grams per mole (g/mol). It is calculated by summing the atomic masses of all the atoms in the formula. For example, ammonia (NH₃) has one nitrogen atom and three hydrogen atoms. The molar mass is determined by adding the molar mass of nitrogen (14.01 g/mol) to thrice the molar mass of hydrogen (3 x 1.01 g/mol).

Completing these calculations allows us to understand the proportions of individual elements within compounds, which is particularly useful when evaluating fertilizers for their nitrogen content.

Percent Composition by Mass

Percent composition by mass is a valuable perspective in chemistry that indicates the percentage of a particular element within a compound. For fertilizers, agronomists are often interested in the nitrogen percentage due to its essential role in plant growth. To calculate the mass percent of nitrogen in a fertilizer, divide the total molar mass of nitrogen in the formula by the total molar mass of the compound and multiply the result by 100%. As seen in the textbook exercise, ammonia's mass percent of nitrogen is calculated as (14.01 g/mol / 17.04 g/mol) * 100%, yielding 82.21%. This simple yet informative calculation helps determine the efficacy of different fertilizers based on their nutrient content.

Nitrogen Content in Fertilizers

Nitrogen is a key nutrient for plant growth, and its content in fertilizers is of paramount importance. Plants use nitrogen to synthesize proteins, DNA, and other essential molecules. Nitrogen content in fertilizers varies depending on the chemical composition of the product. The exercise compared the nitrogen content in several fertilizers. By calculating the mass percent composition of nitrogen, one can determine which fertilizer options would provide more nitrogen to plants. For example, ammonia has a considerably higher nitrogen content (82.21%) compared to ammonium sulfate with only 21.20%, making it a more concentrated source of nitrogen.

Chemical Formulae of Fertilizers

The chemical formula of a fertilizer provides valuable insights into its composition and potential benefits for plants. Common nitrogenous fertilizers include ammonia (NH₃), urea (CO(NH₂)₂), ammonium nitrate (NH₄NO₃), and ammonium sulfate ((NH₄)₂SO₄). Each formula shows the elements and proportions used in the fertilizer. For instance, urea is composed of carbon, oxygen, nitrogen, and hydrogen in a specific arrangement that can be recognized by its molecular formula. Understanding these formulae enables deeper knowledge of how fertilizers will behave and how they can be used effectively in agriculture.