Question

All the substances listed here are fertilizers that contribute nitrogen to the soil. Which of these is the richest source of nitrogen on a mass percentage basis? (a) Urea [(NH \(\left._{2}\right)_{2} \mathrm{CO}\) (b) Ammonium nitrate \(\left(\mathrm{NH}_{4} \mathrm{NO}_{3}\right)\) (c) Guanidine [HNC(NH \(\left._{2}\right)_{2}\) ] (d) Ammonia \(\left(\mathrm{NH}_{2}\right)\)

Short answer

Ammonia is the richest source of nitrogen with 82.35% nitrogen by mass.

Step-by-step solution

Determine Molar Mass

First, calculate the molar mass for each compound to determine the mass of nitrogen relative to the compound. Use the atomic masses of nitrogen (N = 14 g/mol), hydrogen (H = 1 g/mol), carbon (C = 12 g/mol), and oxygen (O = 16 g/mol).

Calculate Molar Mass of Urea

For urea \((NH_2)_2CO\), calculate molar mass: \[(2 \times 14 + 4 \times 1 + 12 + 16) = 60 \, \text{g/mol}\]. Urea contains two nitrogen atoms, so the total nitrogen mass is \(28 \, \text{g}\).

Calculate Nitrogen Percentage in Urea

Nitrogen percentage in urea is \((28 \, \text{g nitrogen} / 60 \, \text{g urea}) \times 100\), which results in \[46.67\%\] nitrogen.

Calculate Molar Mass of Ammonium Nitrate

For ammonium nitrate \(NH_4NO_3\), calculate molar mass: \[(14 + 4 \times 1 + 14 + 3 \times 16) = 80 \, \text{g/mol}\]. It contains two nitrogen atoms, totaling \(28 \, \text{g}\).

Calculate Nitrogen Percentage in Ammonium Nitrate

Nitrogen percentage in ammonium nitrate is \((28 \, \text{g nitrogen} / 80 \, \text{g ammonium nitrate}) \times 100\), which equals \[35\%\] nitrogen.

Calculate Molar Mass of Guanidine

For guanidine \([HNC(NH_2)_2]\), calculate molar mass: \[(1 \times 1 + 14 + 12 + 4 \times 14 + 6 \times 1) = 59 \, \text{g/mol}\]. It has three nitrogen atoms, so the total nitrogen mass is \(42 \, \text{g}\).

Calculate Nitrogen Percentage in Guanidine

Nitrogen percentage in guanidine is \((42 \, \text{g nitrogen} / 59 \, \text{g guanidine}) \times 100\), which amounts to \[71.19\%\] nitrogen.

Calculate Molar Mass of Ammonia

For ammonia \(NH_3\), calculate molar mass: \[(14 + 3 \times 1) = 17 \, \text{g/mol}\]. It contains one nitrogen atom, \(14 \, \text{g}\) of nitrogen.

Calculate Nitrogen Percentage in Ammonia

Nitrogen percentage in ammonia is \((14 \, \text{g nitrogen} / 17 \, \text{g ammonia}) \times 100\), equal to \[82.35\%\] nitrogen.

Compare Nitrogen Percentages

Compare the nitrogen percentages calculated for each compound: urea (46.67%), ammonium nitrate (35%), guanidine (71.19%), and ammonia (82.35%). Identify the compound with the highest percentage.

Key concepts

Molar Mass Calculation

Understanding molar mass is key in determining how many grams one mole of a substance weighs. It's like finding the substance's weight in terms of moles, using the atomic weights of each element. Essential for any chemistry student, calculating molar mass involves summing up all the atomic masses in a compound.

Let's consider a compound like urea (\(NH_2CONH_2\)). We combine the atomic weight of each atom involved: Nitrogen is 14 g/mol, Hydrogen is 1 g/mol, Carbon is 12 g/mol, and Oxygen is 16 g/mol. Multiply these values by the number of each atom in the compound, and you'll get the total molar mass.

This way, you can bridge the gap from individual atoms to an entire compound, unlocking a key to quantify and compare substances in chemistry.

Nitrogen Percentage

When dealing with fertilizers, the nitrogen percentage is crucial. It shows how much of the product's weight is actually nitrogen, which is vital for plant growth. Calculating this percentage involves both the molar mass and the number of nitrogen atoms in the compound.

Suppose we have a compound with a molar mass of 100 g/mol and contains 40 g of nitrogen. The nitrogen percentage would be calculated as \((40 \text{ g nitrogen} / 100 \text{ g compound}) \times 100\), resulting in a 40% nitrogen content.

Determining the nitrogen percentage allows you to assess and compare different fertilizers' nitrogen content effectively, helping you choose the best option for enriching the soil.

Urea

Urea, a common nitrogen fertilizer, is represented by the formula \(NH_2CONH_2\). It's an organic compound that provides a significant amount of nitrogen by weight. Calculating the molar mass for urea involves considering each element: Nitrogen, Hydrogen, Carbon, and Oxygen.

After calculating its molar mass as 60 g/mol, it's clear that urea has two nitrogen atoms, amounting to 28 g of nitrogen. The nitrogen percentage in urea is calculated as \((28 \, \text{g nitrogen} / 60 \, \text{g urea}) \times 100\), resulting in approximately 46.67% nitrogen.

This makes urea a valuable source for providing nitrogen, aiding in plant growth effectively.

Ammonium Nitrate

Ammonium nitrate, \(NH_4NO_3\), is another popular nitrogen fertilizer. It combines both ammonium and nitrate ions, delivering nitrogen and contributing positively to soil nutrition.

To calculate its molar mass, you add the masses of all its atoms, reaching a total of 80 g/mol. With two nitrogen atoms present, it has 28 g of nitrogen. Consequently, the nitrogen percentage in ammonium nitrate is \((28 \, \text{g nitrogen} / 80 \, \text{g ammonium nitrate}) \times 100\), equating to 35% nitrogen.

While somewhat less rich in nitrogen compared to others, ammonium nitrate plays a role in a balanced fertilization strategy.

Guanidine

Guanidine, represented as \([HNC(NH_2)_2]\), is another nitrogen-abundant compound. It's slightly more complex than the other fertilizers but still offers a nook for nitrogen supply.

Calculating its molar mass results in 59 g/mol. With three nitrogen atoms, the total nitrogen amount is 42 g. Hence, the nitrogen percentage in guanidine is \((42 \, \text{g nitrogen} / 59 \, \text{g guanidine}) \times 100\), yielding an impressive 71.19% nitrogen.

This makes guanidine an excellent candidate for specific agricultural applications where high nitrogen is beneficial.

Ammonia

Ammonia, \(NH_3\), stands out among nitrogen fertilizers due to its simplicity and potency. As a gas, it's often used in liquid form to directly supply nitrogen to plants.

With a straightforward calculation, ammonia has a molar mass of 17 g/mol, deriving mainly from 1 nitrogen atom weighing 14 g. The nitrogen percentage is \((14 \, \text{g nitrogen} / 17 \, \text{g ammonia}) \times 100\), which rounds up to about 82.35% nitrogen.

Being the top choice in terms of nitrogen content, ammonia ensures efficient nitrogen delivery, making it central to agricultural practices.