Imagine you are a farmer, using \(\mathrm{NH}_{3}\) and \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) as sources of nitrogen. \(\mathrm{NH}_{3}\) costs \(\$ 0.50\) per \(\mathrm{kg},\) and \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) costs \(\$ 0.25\) per kg. Use percentage composition to decide which is the best buy for your money.

Understanding the molar mass of chemical compounds is essential in various areas of chemistry, including agriculture. Molar mass represents the mass of one mole of a substance and is expressed in grams per mole (g/mol). It is calculated by summing the atomic masses of all the atoms present in a molecule, which are found on the periodic table.
For instance, the formula NH₃ consists of one nitrogen (N) atom and three hydrogen (H) atoms. Given that the atomic mass of nitrogen is approximately 14 g/mol and hydrogen is about 1 g/mol, the molar mass of NH₃ can be found using the formula:
Molar mass of NH₃ = (1 x 14 g/mol) + (3 x 1 g/mol) = 17 g/mol.
For NH₄NO₃, you would similarly total the atomic masses of its constituent atoms: two nitrogen atoms and four hydrogen atoms, plus three oxygen atoms, with oxygen having an approximate atomic mass of 16 g/mol.

When evaluating fertilizers, it's crucial to consider their nitrogen content because nitrogen is a key nutrient for plant growth. The nitrogen percentage composition of a fertilizer indicates the fraction of nitrogen it contains by mass.
The calculation is straightforward. Let's take ammonia, NH₃, as an example. With its molar mass being 17 g/mol and 14 g/mol of that being nitrogen, its nitrogen content is high at around 82.35%. Conversely, ammonium nitrate, NH₄NO₃, with a molar mass of 80 g/mol and 28 g/mol from nitrogen, has a lower percentage of 35%.
Hence, percentage of Nitrogen in a compound can be found using the formula:
Percentage of Nitrogen = (Total mass of nitrogen in the formula / Molar mass of the compound) x 100%

Cost-effectiveness analysis is a method used to determine which of several alternatives provides the best outcome for the cost incurred. It is frequently used in agriculture to select the most economical fertilizer option.
In our example, NH₃ has a higher percentage of nitrogen and costs \(0.50/kg, while NH₄NO₃ has a lower nitrogen content and costs \)0.25/kg. To find out which is more cost-effective, one can calculate the cost per kg of nitrogen by dividing the cost per kg of fertilizer by the percentage of nitrogen in the fertilizer:
Cost per kg of Nitrogen in NH₃ = \(0.50 / 0.8235 = \)0.607/kg
Cost per kg of Nitrogen in NH₄NO₃ = \(0.25 / 0.35 = \)0.714/kg
Comparing these costs reveals that NH₃ offers more nitrogen for your dollar, making it the best buy for a farmer seeking to maximize cost-effectiveness.