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?

Step by step solution

01

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 \(K_{2}O\).

02

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.

03

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 \(K\).

04

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.

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