Question

All-purpose fertilizers contain the essential elements nitrogen, phosphorus, and potassium. A typical fertilizer carries numbers on its label, such as "5-10-5". These numbers represent the \% \(\mathrm{N}, \% \mathrm{P}_{2} \mathrm{O}_{5},\) and \(\% \mathrm{K}_{2} \mathrm{O},\) respectively. The \(\mathrm{N}\) is contained in the form of a nitrogen compound, such as \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}, \mathrm{NH}_{4} \mathrm{NO}_{3}\) or \(\mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2}\) (urea). The \(\mathrm{P}\) is generally present as a phosphate, and the \(K\) as \(K C\). The expressions \(\% \mathrm{P}_{2} \mathrm{O}_{5}\) and \(\% \mathrm{K}_{2} \mathrm{O}\) were devised in the nineteenth century, before the nature of chemical compounds was fully understood. To convert from \% \(\mathrm{P}_{2} \mathrm{O}_{5}\) to \% \(\mathrm{P}\) and from \% \(\mathrm{K}_{2} \mathrm{O}\) to \% \(\mathrm{K}\), the factors \(2 \mathrm{mol} \mathrm{P} / \mathrm{mol}\) \(\mathrm{P}_{2} \mathrm{O}_{5}\) and \(2 \mathrm{mol} \mathrm{K} / \mathrm{mol} \mathrm{K}_{2} \mathrm{O}\) must be used, together with molar masses. (a) Assuming three-significant-figure precision, what is the percent composition of the "5-10-5" fertilizer in \% \(\mathrm{N}, \% \mathrm{P},\) and \(\% \mathrm{K} ?\) (b) What is the \(\% \mathrm{P}_{2} \mathrm{O}_{5}\) in the following compounds (both common fertilizers)? (i) \(\mathrm{Ca}\left(\mathrm{H}_{2} \mathrm{PO}_{4}\right)_{2}\) (ii) \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{HPO}_{4}\) (c) In a similar manner to the "5-10-5" fertilizer described in this exercise, how would you describe a fertilizer in which the mass ratio of \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{HPO}_{4}\) to KCl is 5.00:1.00? (d) Can a "5-10-5" fertilizer be prepared in which \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{HPO}_{4}\) and \(\mathrm{KCl}\) are the sole fertilizer components, with or without inert nonfertilizer additives? If so, what should be the proportions of the constituents of the fertilizer mixture? If this "5-10-5" fertilizer cannot be prepared, why not?

Short answer

The percentage composition of 5-10-5 will vary depending on the molar mass and the molar mass of the particular formula used. The percentage compositions of \(P_{2}O_{5}\) in common fertilizers will be calculated accordingly, using their respective formulas and molar masses. The ratios of the content in a new fertilizer can be calculated using the provided mass ratios. And finally, whether or not a '5-10-5' fertilizer can be prepared from given components will depend on the possible combinations of the compounds based on their chemical composition.

Step-by-step solution

Calculation of Percentage Composition of 5-10-5 Fertilizer

The given numbers denote the percentages of \(N\), \(P_{2}O_{5}\), and \(K_{2}O\). We'll need to convert those for \(P_{2}O_{5}\) and \(K_{2}O\) into percentages for \(P\) and \(K\). Since 1 mol \(P_{2}O_{5}\) contains 2 mol \(P\) and 1 mol \(K_{2}O\) contains 2 mol \(K\), you can find equivalence in percentages using the molar masses of \(P_{2}O_{5}\), \(P\), \(K_{2}O\), and \(K\). Find those molar masses(using periodic table), then calculate the percentage composition for \(P\) and \(K\) using the given percentage composition for \(P_{2}O_{5}\) and \(K_{2}O\).

Calculation of Percentage Composition of \(P_{2}O_{5}\) in the Given Fertilizers

To find the percentage composition of \(P_{2}O_{5}\) in the given compounds, first calculate the molar mass of each given compound and the molar mass of \(P_{2}O_{5}\) present in each of them. Then, use this to calculate the percentage composition of \(P_{2}O_{5}\) in each fertilizer.

Describing a New Fertilizer

Given a mass ratio of \( (NH_{4})_{2}HPO_{4}\) to KCl as 5.00:1.00, use this to describe the new fertilizer in terms of the percenatge compositions of \(N\), \(P\), and \(K\).

Preparation of 5-10-5 Fertilizer

To find whether a '5-10-5' fertilizer can be prepared using \( (NH_{4})_{2}HPO_{4}\) and KCl, perform analysis similar to steps above. If it cannot be prepared, explain why not using results of calculations and material balances.

Key concepts

Nitrogen Content in Fertilizers

Nitrogen is a crucial nutrient for plants as it is a major component of chlorophyll, which plants use for photosynthesis. Nitrogen is also a vital part of amino acids, the building blocks of proteins. In fertilizers, nitrogen is often represented as the first number in formulations like "5-10-5." For example, if a fertilizer is labeled as "5-10-5," that means it contains 5% nitrogen by weight.

Nitrogen in fertilizers is usually provided in different chemical forms, such as ammonium nitrate \((NH_{4}NO_{3})\), ammonium sulfate \(((NH_{4})_{2}SO_{4})\), and urea \(CO(NH_{2})_{2} \). These compounds release nitrogen gradually into the soil, which is then absorbed by plants. Choosing the right nitrogen source depends on factors like soil type, weather conditions, and the specific plant needs.

• Ammonium Nitrate: Known for its high nitrogen content, favoured for quick absorption by plants.
• Ammonium Sulfate: Supplies both nitrogen and sulfur, beneficial for plants that require sulfur.
• Urea: Concentrated nitrogen source, widely used due to its relatively low cost.

Understanding the percentage of nitrogen helps farmers and gardeners determine the right amount of fertilizer needed to meet their crops' nitrogen requirements.

Phosphorus Content in Fertilizers

Phosphorus is another essential nutrient, vital for root development, flowering, and fruiting in plants. It is generally represented by the second number in a fertilizer's formula, such as "5-10-5," which indicates 10% phosphorus pentoxide \(P_{2}O_{5}\) content. However, to find the actual percentage of phosphorus \(P\) from \(P_{2}O_{5}\), conversion using molar masses is needed.

The conversion factor from \(P_{2}O_{5}\) to \(P\) considers that 1 mole of \(P_{2}O_{5}\) contains 2 moles of phosphorus. By calculating the molar masses, you can determine the actual phosphorus content, which helps in accurate application rates. This is important, as too little phosphorus can stunt plant growth while too much can lead to environmental issues.

• Phosphate Availability: Phosphorus in soil is usually fixed and not readily available to plants without aiding agents.
• Plant Uptake: Phosphorus is absorbed mostly during the early stages of growth, thus initial fertilization is crucial.
• Environmental Impact: Excess phosphorus can lead to water pollution due to runoff, causing algal blooms.

Proper phosphorus management ensures that plants receive this nutrient efficiently without causing environmental harm.

Potassium Content in Fertilizers

Potassium is indispensable for plant health, playing a key role in water regulation, enzyme activation, and photosynthesis. In a typical "5-10-5" fertilizer, the last number indicates the percentage of potash \(K_{2}O\) content, such as 5%. To convert this to the actual potassium content, you need to calculate based on molar masses, just like phosphorus.

Potassium in fertilizers often comes in the form of potassium chloride \(KCl\) or potassium sulfate. These provide potassium that plants can use effectively. However, calculating the exact percentage of potassium can be crucial, especially when mixing custom fertilizer blends to meet specific crop needs.

• Importance of Potassium: It enhances drought resistance, improves fruit quality, and increases disease resistance.
• Adjusting Potassium Levels: Consider the crop type and growth stage to adjust potassium levels accordingly.
• Sources of Potassium: While \(KCl\) is common, other sources might be used depending on soil type and crop requirements.

Ensuring the right potassium levels can boost overall crop yield and improve the quality of produce, making it an essential element in fertilizer composition.