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 named above. Which fertilizer has the highest nitrogen content?

Short answer

NH3: 82.21%, CO(NH2)2: 46.63%, NH4NO3: 35.00%, (NH4)2SO4: 21.20%. Ammonia (NH3) has the highest nitrogen content.

Step-by-step solution

Determine the molar mass of NH3

First, calculate the molar mass of ammonia (NH3) by adding the atomic mass of nitrogen (N) and three times the atomic mass of hydrogen (H). The atomic mass of nitrogen is approximately 14.01 g/mol, and the atomic mass of hydrogen is approximately 1.01 g/mol. Thus, the molar mass of NH3 is: 14.01 g/mol + (3 x 1.01 g/mol) = 17.04 g/mol.

Calculate percent nitrogen in NH3

Next, calculate the mass percent composition of nitrogen in NH3. This can be done by dividing the atomic mass of nitrogen by the molar mass of NH3 and multiplying by 100%. This gives: (14.01 g/mol / 17.04 g/mol) x 100% ≈ 82.21%.

Determine the molar mass of CO(NH2)2

Calculate the molar mass of urea, CO(NH2)2, by adding the atomic mass of carbon (C), oxygen (O), nitrogen (N), and hydrogen (H). The atomic mass of carbon is approximately 12.01 g/mol and oxygen is 16.00 g/mol. Thus, the molar mass of CO(NH2)2 is: 12.01 g/mol + 16.00 g/mol + (4 x 14.01 g/mol) + (4 x 1.01 g/mol) = 60.06 g/mol.

Calculate percent nitrogen in CO(NH2)2

Divide the combined atomic mass of nitrogen in urea (4 x 14.01 g/mol) by the molar mass of urea calculated in the previous step and multiply by 100%. This gives: (4 x 14.01 g/mol / 60.06 g/mol) x 100% ≈ 46.63%.

Determine the molar mass of NH4NO3

Calculate the molar mass of ammonium nitrate, NH4NO3, by adding the atomic mass of nitrogen (N), hydrogen (H), and oxygen (O). The molar mass of NH4NO3 is: (2 x 14.01 g/mol) + (4 x 1.01 g/mol) + (3 x 16.00 g/mol) = 80.05 g/mol.

Calculate percent nitrogen in NH4NO3

Divide the combined atomic mass of nitrogen from both ammonium (NH4+) and nitrate (NO3-) by the molar mass of NH4NO3 calculated in the previous step and multiply by 100%. This gives: (2 x 14.01 g/mol / 80.05 g/mol) x 100% ≈ 35.00%.

Determine the molar mass of (NH4)2SO4

Calculate the molar mass of ammonium sulfate, (NH4)2SO4, by adding the atomic mass of nitrogen (N), hydrogen (H), sulfur (S), and oxygen (O). The molar mass of (NH4)2SO4 is: (2 x 14.01 g/mol) + (8 x 1.01 g/mol) + (32.07 g/mol) + (4 x 16.00 g/mol) = 132.14 g/mol.

Calculate percent nitrogen in (NH4)2SO4

Divide the combined atomic mass of nitrogen from the two ammonium groups by the molar mass of (NH4)2SO4 calculated in the previous step and multiply by 100%. This gives: (2 x 14.01 g/mol / 132.14 g/mol) x 100% ≈ 21.20%.

Compare the nitrogen content

Compare the percentage of nitrogen in all four fertilizers: NH3 has 82.21%, CO(NH2)2 has 46.63%, NH4NO3 has 35.00%, and (NH4)2SO4 has 21.20%. NH3 has the highest nitrogen content.

Key concepts

Molar Mass Calculation

The concept of molar mass is fundamental in chemistry and is particularly important for understanding chemical compounds in various applications like fertilizers. Molar mass is described as the mass (in grams) of one mole of a substance. To calculate the molar mass, one must sum the masses of all atoms within a molecule. For example, to find the molar mass of ammonia (NH₃), you add the molar mass of nitrogen (approximately 14.01 g/mol) with three times the molar mass of hydrogen (3 x 1.01 g/mol), arriving at 17.04 g/mol.

This calculation is critical when you want to determine the mass percentage of a particular element in a compound, such as nitrogen in fertilizers. Having an accurate molar mass allows us to compare the ‘amount’ of nitrogen across different compounds, despite their varying structures and additional components.

Nitrogen Content in Fertilizers

Nitrogen is an essential component of fertilizers as it is vital for plant growth, particularly for protein synthesis. To evaluate the effectiveness of a fertilizer in terms of nitrogen delivery, one needs to calculate the nitrogen content. This is expressed as a percentage by mass of nitrogen relative to the total mass of the fertilizer compound.

For instance, when we calculate the molar mass of urea, CO(NH₂)₂, and determine the proportion of nitrogen, we provide insight into the fertilizer's potential nourishment capabilities. Understanding the nitrogen content is important for agricultural purposes, allowing for the selection of the most appropriate fertilizer to meet the specific nutritional needs of crops. Furthermore, this understanding helps in managing the environmental impact of nitrogen-rich fertilizers by enabling more efficient usage and reducing potential runoff into waterways.

Percent Composition by Mass

Percent composition by mass is a quantitative method of expressing the concentration of an element in a compound. It is calculated by dividing the mass of the element in one mole of the compound by the molar mass of the entire compound and then multiplying by 100%. This provides a percentage that indicates what fraction of the total mass of a compound is accounted for by a specific element.

Continuing with our fertilizer example, after finding the molar mass of ammonium nitrate, NH₄NO₃, we can then determine what mass percent of that compound is nitrogen. This percentage is essential not only for gauging the nutrient content of fertilizers but also in various chemical industries and scientific research to formulate or analyze substances. Accurate percent compositions by mass calculations allow chemists to tailor compounds for desired properties and ensure that reactions proceed with the correct stoichiometry.