Chapter 3, Problem 112FP

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 %N, % ${\text{P}}_{\text{2}}{\text{O}}_{\text{5}}$ , and % ${\text{K}}_{\text{2}}\text{O}$ ,respectively. The N is contained in the form ofa nitrogen compound, such as ${({\text{NH}}_4)}_2{\text{SO}}_4,{\text{ NH}}_4{\text{NO}}_3$ ,or $\text{CO}{({\text{NH}}_2)}_2$ (urea). The P is generally present as a phosphate and the K as KCI. The expressions % ${\text{P}}_{\text{2}}{\text{O}}_{\text{5}}$ and% ${\text{K}}_{\text{2}}\text{O}$ were devised in the nineteenth century, before the nature of chemical compounds was fully understood. To convert from % ${\text{P}}_{\text{2}}{\text{O}}_{\text{5}}$ to %P and from % ${\text{K}}_{\text{2}}\text{O}$ to %K, the factors 2 mol P/mol ${\text{P}}_{\text{2}}{\text{O}}_{\text{5}}$ and 2 molK/mol ${\text{K}}_{\text{2}}\text{O}$ must be used, together with molar masses.

a. Assuming three-significant-figure precision, what is the percent composition of the fertilizer in%N, %P, and%K?

b. What is the % ${\text{P}}_{\text{2}}{\text{O}}_{\text{5}}$ in the following compounds (both common fertilizers}? (i) $\text{Ca}{\left({\text{H}}_{\text{2}}{\text{PO}}_{\text{4}}\right)}_{\text{2}}$ ; (ii) ${\left({\text{NH}}_{\text{4}}\right)}_{\text{2}}{\text{HPO}}_{\text{4}}$ .

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 ${{\text{(NH}}_{\text{4}}\text{)}}_{\text{2}}{\text{HPO}}_{\text{4}}$ to KCI is 5.00:1.00?

d. Can a $“5-10-5"$ fertilizer be prepared in which ${{\text{(NH}}_{\text{4}}\text{)}}_{\text{2}}{\text{HPO}}_{\text{4}}$ and KCI are the sole fertilizer components,with or without inert non-fertilizer additives? It so, what should be the proportions of the constituents of the fertilizer mixture? If this $“5-10-5"$ fertilizer cannot be prepared, why not?